Image Analysis, Sediments and Paleoenvironments

Image Analysis, Sediments and Paleoenvironments Developments in Paleoenvironmental Research VOLUME 7 Image Analysis...

Author: Pierre Francus

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Image Analysis, Sediments and Paleoenvironments

Developments in Paleoenvironmental Research VOLUME 7

Image Analysis, Sediments and Paleoenvironments Edited by

Pierre Francus

Springer

eBook ISBN: Print ISBN:

1-4020-2122-4 1-4020-2061-9

©2005 Springer Science + Business Media, Inc. Print ©2004 Springer Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Springer's eBookstore at: and the Springer Global Website Online at:

http://ebooks.springerlink.com http://www.springeronline.com

DEDICATION I dedicate this book to my wife, Sophie Magos

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Table of Contents

The Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii Aims & Scope of Developments in Paleoenvironmental Research Book Series . . . . xiii Editors and Board of Advisors of Developments in Paleoenvironmental Research Book Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv List of Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

1. An introduction to image analysis, sediments and paleoenvironments Pierre Francus, Raymond S. Bradley and Jürgen W. Thurow . . . . . . . . . . . . . . . . . . . . . . 1

Part I: Getting started with Imaging Techniques (or methodological introduction)

2. Image acquisition Scott F. Lamoureux and Jörg Bollmann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Introduction Image acquisition and paleoenvironmental research Sample preparation for image acquisition Acquisition methods Summary Acknowledgments References

3. Image calibration, ﬁltering and processing Alexandra J. Nederbragt, Pierre Francus, Jörg Bollmann and Michael J. Soreghan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Introduction Image pre-processing Colour information and calibration Image processing Metadata Summary Acknowledgments Appendix References

viii 4. Image measurements Eric Pirard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Introduction Digital imaging and sampling theory Dealing with the available information Digital image analysis strategies Intensity and color analysis Blob analysis Structural analysis Summary Acknowledgments References 5. Testing for sources of errors in quantitative image analysis Pierre Francus and Eric Pirard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87 Introduction Some useful deﬁnitions Preparation errors Integration errors (sampling) Analysis errors Future directions Summary Acknowledgments References

Part II: Application of Imaging Techniques on Macro- and Microscopic Samples

6. Digital sediment colour analysis as a method to obtain high resolution climate proxy records Alexandra J. Nederbragt and Jürgen W. Thurow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Introduction Image data collection Extracting colour data Light correction RGB to L∗ a∗ b∗ conversion and colour calibration Mosaicking Examples and comparison with other methods Summary Acknowledgments References

ix 7. Toward a non-linear grayscale calibration method for legacy photographic collections Joseph D. Ortiz and Suzanne O’Connell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Introduction What is grayscale analysis? Evaluating the nonlinear correction method Summary Acknowledgments Metadata References

8. From depth scale to time scale: transforming sediment image color data into a high-resolution time series Andreas Prokoph and R. Timothy Patterson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Introduction Wavelet analysis Image processing Methodology Testing of the method Example: Marine Laminated sediments from the west coast of Vancouver Island, NE Paciﬁc Summary Acknowledgments References

9. X-ray radiographs of sediment cores: a guide to analyzing diamicton Sarah M. Principato . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Introduction Image acquisition Image processing Image measurement Advantages of using image analysis Drawbacks to image analysis Example: case study of ﬁve diamicton units from North Atlantic continental margins Future direction Summary Acknowledgments Metadata References

x 10. Application of X-ray radiography and densitometry in varve analysis Antti E. K. Ojala . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Introduction Methods Examples from Lake Nautajärvi clastic-organic varves Summary Acknowledgments References

11. Processing backscattered electron digital images of thin sections Michael J. Soreghan and Pierre Francus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Introduction Image acquisition Image processing Image measurement Case study: grain size analysis of upper Paleozoic loessites Discussion and recommendations for BSE image analysis Future direction Summary Acknowledgments Metadata References

Part III: Advanced Techniques

12. Automated particle analysis: calcareous microfossils Jörg Bollmann, Patrick S. Quinn, Miguel Vela, Bernhard Brabec, Siegfried Brechner, Mara Y. Cortés, Heinz Hilbrecht, Daniela N. Schmidt, Ralf Schiebel and Hans R. Thierstein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Introduction Automated image acquisition Automated classiﬁcation What can be improved? Summary Acknowledgments Appendix: system description References

xi 13. Software aspects of automated recognition of particles: the example of pollen Ian France, A. W. G. Duller and G. A. T. Duller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Introduction Acquisition of microscopic images Feature extraction Example: pollen classiﬁcation using a neural network Future directions Summary References

14. Multiresolution analysis of shell growth increments to detect variations in natural cycles Eric P. Verrecchia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Introduction Spectral analysis Wavelet Transform Multiresolution analysis Application to growth increment detection Conclusion Summary Acknowledgments References Glossary, acronyms and abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

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THE EDITOR Pierre Francus is a professor in the Centre Eau, Terre et Environnement at the INRS (Institut national de la recherche scientifique), Québec city, Québec, Canada. Pierre Francus is a member of the GEOTOP (Centre de recherche en Géochimie et en Gé odynamique).

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AIMS AND SCOPE OF DEVELOPMENTS IN PALEOENVIRONMENTAL RESEARCH SERIES Paleoenvironmental research continues to enjoy tremendous interest and progress in the scientific community. The overall aims and scope of the Developments in Paleoenvironmental Research book series is to capture this excitement and document these developments. Volumes related to any aspect of paleoenvironmental research, encompassing any time period, are within the scope of the series. For example, relevant topics include studies focused on terrestrial, peatland, lacustrine, riverine, estuarine, and marine systems, ice cores, cave deposits, palynology, isotopes, geochemistry, sedimentology, paleontology, etc. Methodological and taxonomic volumes relevant to paleoenvironmental research are also encouraged. The series will include edited volumes on a particular subject, geographic region, or time period, conference and workshop proceedings, as well as monographs. Prospective authors and/or editors should consult the series editors for more details. The series editors also welcome any comments or suggestions for future volumes.

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EDITORS AND BOARD OF ADVISORS OF DEVELOPMENTS IN PALEOENVIRONMENTAL RESEARCH BOOK SERIES

Series Editors: John P. Smol Paleoecological Environmental Assessment and Research Lab (PEARL) Department of Biology Queen’s University Kingston, Ontario, K7L 3N6, Canada e-mail: [email protected] William M. Last Department of Geological Sciences University of Manitoba Winnipeg, Manitoba R3T 2N2, Canada e-mail: [email protected] Advisory Board: Professor Raymond S. Bradley Department of Geosciences University of Massachusetts Amherst, MA 01003-5820 USA e-mail: [email protected] Professor H. John B. Birks Botanical Institute University of Bergen Allégaten 41 N-5007 Bergen Norway e-mail: [email protected] Dr. Keith Alverson Director, GOOS Project Office Intergovernmental Oceanographic Commission (IOC) UNESCO 1, rue Miollis 75732 Paris Cedex 15 France Tel: +33 (0)1-45-68-40-42 Fax: +33 (0)1-45-68-58-13 (or 12) e-mail: [email protected]

LIST OF CONTRIBUTORS JÖRG BOLLMANN Department of Earth Sciences ETH and University Zurich Sonneggstrasse 5, 8092 Zurich Switzerland e-mail: [email protected] BERNHARD BRABEC Department of Earth Sciences ETH and University Zurich Sonneggstrasse 5, 8092 Zurich Switzerland RAYMOND S. BRADLEY Climate System Research Center Department of Geosciences, University of Massachusetts Amherst, MA 01003-9297, USA e-mail: [email protected] SIEGFRIED BRECHNER Department of Earth Sciences ETH and University Zurich Sonneggstrasse 5, 8092 Zurich Switzerland MARA Y. CORTÉS Department of Earth Sciences ETH and University Zurich Sonneggstrasse 5, 8092 Zurich Switzerland A.W.G. DULLER picoChip Designs Ltd. Riverside Buildings 108 Walcot Street, Bath BA1 5BG, United Kingdom e-mail: [email protected] G.A.T. DULLER ([email protected]) Institute of Geography and Earth Sciences, University of Wales, Aberystwyth, Ceredigion, SY23 3DB, Wales, UK e-mail: [email protected] xv

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I. FRANCE FCS Caerau Llansadwrn, Gwynedd LL57 1UT, Wales, UK e-mail: [email protected] PIERRE FRANCUS Climate System Research Center, Department of Geosciences, University of Massachusetts, Amherst, MA 01003-9297, USA Currently at INRS - Eau, Terre et Environnement 490 rue de la Couronne, Québec (QC) G1K 9A9, Canada e-mail: [email protected] HEINZ HILBRECHT Department of Earth Sciences ETH and University Zurich Sonneggstrasse 5, 8092 Zurich Switzerland SCOTT F. LAMOUREUX Department of Geography Queen’s University Kingston, ON K7L 3N6 Canada e-mail: [email protected] ALEXANDRA J. NEDERBRAGT Department of Geological Sciences, University College London, Gower Street, London WC1E 6BT, UK e-mail: [email protected] SUZANNE O’CONNELL Department of Earth and Environmental Sciences Wesleyan University Middletown, CT 08457, USA e-mail: [email protected] ANTTI E.K. OJALA Geological Survey of Finland P.O. Box 96 FIN-02150, Espoo Finland e-mail: [email protected]

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JOSEPH D. ORTIZ Department of Geology Kent State University Lincoln and Summit Streets Kent, OH 44224, USA e-mail: [email protected] R. TIMOTHY PATTERSON Department of Earth Sciences and Ottawa-Carleton Geoscience Centre, Herzberg Building, Carleton University Ottawa, Ontario K1S 5B6, Canada e-mail: [email protected] ERIC PIRARD Département GeomaC - Géoressources Minérales Université de Liège Sart Tilman B52/3 4000 Liège, Belgium e-mail: [email protected] SARAH M. PRINCIPATO Institute of Arctic and Alpine Research and Department of Geological Sciences University of Colorado, Campus Box 450 Boulder, CO 80309-0450, USA Currently at Department of Environmental Studies, Box 2455, 300 N. Washington St Gettysburg College Gettysburg, PA 17325, USA e-mail: [email protected] ANDREAS PROKOPH SPEEDSTAT 36 Corley Private Ottawa, Ontario K1V 8T7, Canada e-mail: [email protected] PATRICK S. QUINN Department of Earth Sciences ETH and University Zurich Sonneggstrasse 5, 8092 Zurich Switzerland e-mail: [email protected]

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RALF SCHIEBEL Department of Earth Sciences ETH and University Zurich Sonneggstrasse 5, 8092 Zurich Switzerland e-mail: [email protected] DANIELA N. SCHMIDT Department of Earth Sciences ETH and University Zurich Sonneggstrasse 5, 8092 Zurich Switzerland e-mail: [email protected] MICHAEL J. SOREGHAN School of Geology and Geophysics, University of Oklahoma, 100 E. Boyd St. Norman, OK 73019, USA e-mail: [email protected] HANS R. THIERSTEIN Department of Earth Sciences ETH and University Zurich Sonneggstrasse 5, 8092 Zurich Switzerland e-mail: [email protected] JÜRGEN W. THUROW Department of Geological Sciences University College London Gower Street, London WC1E 6BT, UK e-mail: [email protected] MIGUEL VELA Department of Earth Sciences ETH and University Zurich Sonneggstrasse 5, 8092 Zurich Switzerland ERIC P. VERRECCHIA Institut de Géologie Université de Neuchˆatel Rue Emile Argand 11 2007 Neuchâtel, Switzerland e-mail: [email protected]

1. AN INTRODUCTION TO IMAGE ANALYSIS, SEDIMENTS AND PALEOENVIRONMENTS

PIERRE FRANCUS ([email protected])

Climate System Research Center Department of Geosciences University of Massachusetts Amherst, MA 01003-9297 USA Currently at INRS - Eau, Terre et Environnement 490 rue de la Couronne, Québec (QC) G1K 9A9 Canada RAYMOND S. BRADLEY ([email protected])

Climate System Research Center Department of Geosciences University of Massachusetts Amherst, MA 01003-9297 USA JÜRGEN THUROW ([email protected])

Department of Geological Sciences University College London Gower Street, London WC1E 6BT UK Keywords: Visual information, Quantiﬁcation, Geosciences, Image acquisition, Image processing, Image measurement, Quality control, Neural networks, Recommendations

Image analysis is concerned with the extraction of quantitative information from images captured in digital form (Fortey 1995). Visual information has always played an important role in the Geosciences — indeed, many disciplines rely heavily on the content of images, whether they are sketches drawn in the ﬁeld, or descriptions of microscopic slides (Jongmans et al. 2001). Visual charts are often used in sedimentology in order to provide some semi-quantiﬁcation, such as for instance, Krumbein’s grain roundness classes (Krumbein 1941), classiﬁcation of ichnofabric (Droser and Bottjer 1986), or simply the chart of phase percentages sitting nearby every binocular microscope. However, with the noticeable 1 P. Francus (ed.) 2004. Image Analysis, Sediments and Paleoenvironments. Kluwer Academic Publishers, Dordrecht, The Netherlands.

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exception of remote sensing, compared to other disciplines image analysis has been slow to develop in the Geosciences, despite its potential usefulness. One problem with image analysis studies of geologic material is that objects are generally less homogenous than biologic or medical samples, and observation conditions are more variable. Digital imaging systems were the exception in the 80’s, because the computers needed to process sizeable images were cutting edge and expensive systems, mostly entirely tailored for that unique purpose. The decreasing price of personal computers, with their simultaneous and dramatic increase in performance, made digital image processing more accessible to researchers in the 90’s. Soil scientists, especially micromorphologists, have been very active in the development of new image analysis tools (e.g., Terribile and Fitzpatrick (1992), VandenBygaart and Protz (1999), Adderley et al. (2002)). The growing interest for image analysis in Earth Sciences is revealed by the increasing number of initiatives to bring image analysis into the spotlight. Without being exhaustive, one can mention a number of meetings on the subject (e.g., Geological Society of London, London, UK, September 1993, and Geovision held in Liège, Belgium, in May 1999), an increasing number of papers in journals such as Computers & Geosciences, and books (e.g., De Paor (1996)). In the second volume of the Developments in Paleoenvironmental Research (DPER) series, a chapter by Saarinen and Pettersen (2001) was already devoted to image analysis applied to paleolimnology. Paleoenvironmental studies of sediments can greatly beneﬁt from image analysis techniques. Because it is a low cost and high-resolution analysis method, image analysis allows sediment cores to be studied at the very high resolution that is necessary to resolve high frequency climate cycles. For instance, image analysis of varved sediments can contribute to a better understanding of past climate variability, providing that chronologies are veriﬁed and quantitative relationships are established between the sedimentary record and climate. A wide range of data can be acquired using image analysis. Visual data include counting of laminations (to build-up time scale), measurement of lamination thickness, and establishment of sediment properties (chemistry, mineralogy, density) from its color. Physical data are for instance the morphometry of microfossils such as diatom and coccoliths, grain size, grain morphometry, sediment fabric. Chemical and mineralogical data can be inferred from images of tools such as XRF-Scanning, IR-Scanning, and energy and wavelength dispersive spectrometry. Other tools used are X-radiography, core scanning, non-normal scanning, optical and electron microscopy. An international group of scientists, mainly marine and lacustrine sedimentologists, gathered at the University of Massachusetts, Amherst, in November 2001 to review this subject, and to make an update of the latest techniques available. The workshop entitled Image Analysis: technical advances in extracting quantitative data for paleoclimate reconstruction from marine and lacustrine sequences was sponsored by the US-National Science Foundation (NSF) and the International Marine Past Global Change Study (IMAGES) program. The participants of the workshop made recommendations (documented in the appendix) promoting the use of low cost image analysis techniques and facilitating intercomparisons of measurements in the paleoclimate community. This volume is the natural extension — not the proceedings — of the workshop because it addresses some of the concerns and fulﬁls some of the needs identiﬁed during the workshop. Although image analysis techniques are simple, many colleagues have been discouraged in using them because of the difﬁculty in gathering relevant

AN INTRODUCTION TO IMAGE ANALYSIS . . .

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information in order to set-up protocols and methodologies to solve a particular issue. Often, specialized papers are only comprehensible by computer scientists, mathematicians or engineers. Relevant information is scattered in the methods sections of many different research papers, and is not detailed enough to be helpful for beginners. Also, monographs on image analysis techniques (e.g., Russ (1999)) are oriented towards medicine, biology or material science. Finally, specialized lectures remain very expensive. The DPER volume 7 intends to ﬁll this gap, providing comprehensive but simple information on imaging techniques for paleoenvironmental reconstruction in a single volume. By providing such information, the user will understand every step involved in the imaging process, from the acquisition to measurements, in order to be able to evaluate the validity of scientiﬁc results obtained. This is necessary in order to allow image analysis techniques to mature as widely accepted methodologies for paleoenvironmental reconstructions. In brief, this volume intends to: - provide a compendium of image analysis techniques available for paleoenvironmental reconstruction retrieved mainly from lacustrine and marine sediment cores; - cover image analysis techniques performed at the core-scale level (macroscopic, sedimentary structure, color), and at the microscopic-scale (thin-section, and X-ray slabs); - provide comprehensive descriptions of protocols, guidelines, and recommendations for pertinent use of low cost image analysis techniques; - review and illustrate the wide range of quantitative information that can be obtained using image analysis techniques by showing case studies; - show improvements that high-resolution studies using image analysis techniques can bring about in paleoenvironmental reconstructions and in our understanding of environmental changes. In order to achieve these goals, the DPER volume 7 is divided into three parts. Part I is designed more like a textbook by making a methodological and theoretical introduction, that will allow the reader to become familiarized with the image analysis jargon, and to ﬁgure out what are the different steps required to obtain reliable results. Image analysis implies the following steps whatever the image application: image acquisition, calibration and ﬁltering (or pre-processing), image enhancement and classiﬁcation (or processing), image analysis (or image interpretation) (Jongmans et al. 2001). Part I tries to follow this logical sequence. In Chapter 2, Lamoureux and Bollmann review the different technologies (hardware) applicable for the study of lake and marine sediments, at a macroscopic and microscopic scale in order to obtain the best possible digital images. Their contribution points out issues that must be considered to account for artifacts in the acquisition process, and prior to start the acquisition of an extensive set of images. Chapter 3 by Nederbragt et al. describes software-based operations used to perform the analysis of images (sensu lato), i.e., image calibration, image ﬁltering and image classiﬁcation, as well as how to transform popular RGB ﬁles within the CIE L*a*b* systems, more useful for paleoenvironmental reconstructions. Pirard outlines in Chapter 4 the different kinds of measurements that can be retrieved from images with a particular emphasis on the analysis of image intensities (gray levels, colors) and individual objects (size, shape, orientation). Pirard also discuss the problem of statistical representativity of the pixels and advocate for caution when interpreting the results. In Chapter 5, Francus and Pirard illustrate how researchers can test the validity of the results obtained using image analysis techniques, and advocate for a systematic quality control of the results.

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Part II of the volume illustrates six applications of imaging techniques performed on macroscopic (images of surface of sediment cores) and microscopic (slabs and thinsections) samples using miscellaneous supports (digital and analog photography, X-ray, electron microscopy) in order to reconstruct paleoenvironments. Chapter 6, by Nederbragt and Thurow, outlines comprehensively how to extract color data from digital images of sediment cores, focusing on techniques to ﬁlter out artifacts due to uneven illumination. Ortiz and O’Connell explain in Chapter 7 how to retrieve quantiﬁed information from older non-digital photographs, such as photographs of sediment cores from archived OPD and DSDP cruises. In Chapter 8, Prokoph and Patterson describe an ingenious methodology applicable to annually laminated sediments that transforms digital sediment color data (recorded in a depth-scale) into a time-scale data set. Chapter 9, by Principato, describes a simple methodology to quantitatively characterize diamictons from X-ray radiographs of whole or half sediment cores. In Chapter 10, Ojala outlines how to acquire the best possible X-radiographs of thin impregnated slabs of laminated sediments in order to perform the counting and quantiﬁcation of the laminae. Then, Chapter 11, by Soreghan and Francus, reviews the issues during the acquisition of images using scanning electron microscopes in backscattered mode, and illustrates the analysis of thin-sections of an old consolidated loess deposit aiming for the reconstruction of paleowind intensity. The last Part outlines advanced techniques that may preﬁgure what the future of image analysis will be. Bollmann et al. describe in Chapter 12 robots that automatically acquire images of microscopic samples (microfossils) aiming to process these images with automated recognition systems, i.e., neural networks. The following Chapter 13, by France et al., focuses more on the software aspect of automated recognition by neural networks, providing an example for automated recognition of pollen grains. Finally, Verrecchia examples the uses of advanced mathematical tools, such as wavelet and multiresolution analysis in order to analyze and retrieve measurements on images of banded/laminated samples. To complete the book, a comprehensive glossary is included to help the reader to obtain a correct understanding of the words used through this somewhat technical volume. Computer scientists and engineers develop new powerful tools and algorithms every day. Geoscientists in general and sedimentologists in particular should take advantage of these technological advances by looking for interdisciplinary collaborations. Some accomplishments, such as the automated recognition of microfossils, are not fulﬁlled yet but are close to completion. We need to better identify our needs in order to guide the next developments, and this identiﬁcation starts with a better understanding of what image analysis can accomplish. The future of image analysis techniques in paleoenvironmental science will probably be the integration of processing algorithms within the acquisition phase, allowing the scientist to concentrate on the analysis of the data sets produced (Jongmans et al. 2001). The authors hope that this volume will trigger new ideas for the use of imaging techniques. The topic is new but the technique is very ﬂexible, in such a way that “. . . imagination is the limit” (Saarinen and Petterson 2001). Acknowledgements The authors thank the Paleoclimate Program (GEO-ATM) of United States National Science Foundation and the International Marine Past Global Change Study (IMAGES) program for funding of the workshop Image Analysis: technical advances in extracting quantitative

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data for paleoclimate reconstruction from marine and lacustrine sequences held at the University of Massachusetts, Amherst, in November 2001. Pierre Francus is supported by the University of Massachusetts, Amherst. We thank Frank Keimig (Climate System Research Center) for his help during the edition of this volume. Appendix: workshop recommendations Proceeding with image analysis involves the same three major steps regardless of the type of sample, e.g., surface of sediment core, thin-section, or the technique used to acquire an image (RGB photography, X-radiography, scanning electron microscopy). These steps are image acquisition, image processing and image measurement. Image acquisition It is emphasized that the quality of the image must be the best possible. A lot of energy should be spent on this step. Acquiring images should involve: Choice of the magniﬁcation, resolution, and size of image One needs to consider the smallest feature that needs to be detected, the largest feature that will be encountered and the representativity of the image with respect to the overall sample. Illumination Variation of light intensity needs to be checked in the ﬁeld of view, and the analyst must be aware of spatial and temporal variations. To correct for irregular illumination, we recommend acquisition of a photograph of the background (for example 18% gray sheet) at the beginning of the image acquisition session and at the end. Calibration standards Where it is possible, spatial (ruler, grids) and color (gray/color chart, density wedges) references should be acquired on each photograph. If not, the ruler and color/gray charts should be acquired at the beginning and the end of each working session, keeping in mind the need to maintain the image acquisition conditions strictly constant during the acquisition session. To maintain acquisition conditions strictly constant, it is also recommended that images should be acquired in the shortest period of time possible. It will avoid miscellaneous problems due to aging of color charts or ﬁlament, moving equipment to another location, changing hardware and software. Metadata It is critical to record as much information as possible regarding the factors that can inﬂuence the quality of images. They include among other things, the characteristics and settings of the acquisition device (e.g., depth of ﬁeld, current intensity in a SEM ﬁlament) and any event occurring during the working session such as a power failure. The calendar of working session should also be noted.

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Image processing In order to insure the intercomparability of the measurements it is necessary to document the software used and a detailed description of the ﬁlters used in the methods section or metadata section of all published work. It is also recommended to avoid software that is not explicit in explaining algorithms used for processing. For example, there are several ways to compute a perimeter. The user needs to check what is the method used to do so, to ensure comparability of different approaches. A digital master or archive version of the image should be saved for each captured image. File format involving lossy compression, such as Joint Photographic Experts Group (JPEG), should be avoided by all means since compression involved loss of information that can not be recovered. Uncompressed ﬁle formats, such as Tagged Image File Format (TIFF), are recommended. Image measurement The representativity of the measurements made on digital images should always be kept in mind because pixels are samples of an image, images are samples of the sample under investigation, the samples under investigation are a sample of the sediment of interest. Each step of the image analysis should be carefully tested using sets of calibration images or test images. As a general principle, testing can be accomplished by slightly varying a single component of image acquisition condition or processing procedure — while maintaining the others strictly identical — and monitoring the impact on the ﬁnal measurements. It is impossible to review all the tests that need to be conducted here because of the variety of procedures. However, the following steps should be carefully considered: Related to image acquisition: magniﬁcation, resolution, contrast, brightness, color coding systems (RGB, L*a*b*), hardware, image sampling representativity, illumination (spatial repartition, drift), spatial deformation (parallax effect), pixel shape, 8-bit <> 16-bit images, TIFF <> other formats imposed by hardware and software, . . . . Related to image processing: noise removal ﬁlters, contrast/brightness manipulation, image enhancement, segmentation and thresholding, edge detection, binary image manipulation, . . . . Related to image measurement: orientation, perimeters, distances, alignments, ellipse ﬁtting, and homemade indices. WEB site The workshop attendees recommended the compilation of a web site where the following information can be gathered: List of references related to image analysis. List of hardware/software providers. Documentation of computer codes or ﬁlters used in research paper. A record and archive of metadata related to imaging techniques. A place to publish things that do not work. A place to publish testing of image analysis procedures.

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There is a need for this because it is very difﬁcult to publish such information in regular research papers. The workshop participants agreed that such data are essential to insure intercomparison and reproducibility of results. They also agreed this web page should be maintained professionally. References Adderley W.P., Simpson I.A. and Davidson D.A. 2002. Colour description and quantiﬁcation in mosaic images of soil thin sections. Geoderma 108: 181–195. De Paor D.G. 1996. Structural Geology and Personal Computers. Computer methods in the geosciences, Pergamon, 15, 524 pp. Droser M.L. and Bottjer D.J. 1986. A semiquantitative ﬁeld classiﬁcation of ichnofabric. J. Sed. Petrol. 56: 558–559. Fortey N.J. 1995. Image analysis in mineralogy and petrology. Mineral. Mag. 59: 177–178. Jongmans D., Pirard E. and Marsh S. 2001. Geological application of digital imaging. Comp. Geosci. 27: 1015–1017. Krumbein W.C. 1941. Measurement and geological signiﬁcance of shape and roundness of sedimentary particles. J. Sed Petrol. 11: 64–72. Russ J.C. 1999. The Image Processing Handbook. CRC Press, Boca Raton, Florida, 771 pp. Saarinen T. and Petterson G. 2001. Image analysis techniques. In: Last W. and Smol J. (eds), Tracking Environmental Change Using Lake Sediments: Physical and Geochemical Methods. Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 23–39. Terribile F. and Fitzpatrick E.A. 1992. The application of multilayer digital image-processing techniques to the description of soil thin-sections. Geoderma 55: 159–174. VandenBygaart A.J. and Protz R. 1999. The representative elementary area (REA) in studies of quantitative soil micromorphology. Geoderma 89: 333–346.

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Part I: Getting started with Imaging Techniques (or methodological introduction)

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2. IMAGE ACQUISITION

SCOTT F. LAMOUREUX ([email protected])

Department of Geography Queen’s University Kingston, ON K7L 3N6 Canada JÖRG BOLLMANN ([email protected])

Department of Earth Sciences ETH and University Zurich Sonneggstrasse 5, 8092 Zurich Switzerland Keywords: Digital photography, Analog photography, Scanning, X-radiograph, Scanning electron microscope, Color, Light ﬁltering, Sedimentology, Image analysis, Paleoenvironmental reconstruction

Introduction With increased interest in the use of sedimentary records for paleoenvironmental analysis, considerable effort has been made to utilize various image properties and analysis techniques as quantitative and semi-quantitative environmental proxies (Hughen et al. 1996; Petterson et al. 1999; Francus 1998; Nederbragt et al. 2000; Nederbragt and Thurow 2001; Tiljander et al. 2002). For the most part, these approaches centre on the use of image information obtained from the sediments in the visible (400–750 nm) bands of the electromagnetic spectrum. Some researchers make use of near infrared and infrared (NIR, 750–1200 nm), ultraviolet (UV, 1–400 nm) and X-ray regions of the electromagnetic spectrum as well. Increasingly, available technologies have extended these investigations into image analysis based on synthetic imagery produced from electron microscopy. This type of imagery typically provides resolution of features at the micron (µm) scale but may also be used to study sediment properties at larger scales. Therefore, signiﬁcant improvements in acquisition technologies, computing power and storage capacity have made sedimentary image processing increasingly viable for many applications in paleoenvironmental analysis. An essential ﬁrst step in sedimentary image analysis research is the acquisition of high quality images that are suitable for the research objectives. The diversity of available image acquisition and processing systems reﬂects the varied interests and the resources available to individual researchers. Successful image acquisition requires substantial planning and consideration of the inherent limitations of the selected acquisition method. Clearly, poor 11 P. Francus (ed.) 2004. Image Analysis, Sediments and Paleoenvironments. Kluwer Academic Publishers, Dordrecht, The Netherlands.

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quality or substandard imagery will create signiﬁcant problems during the subsequent analysis and should be avoided where possible. This chapter is intended to provide an overview of image acquisition methods with emphasis on the issues necessary to obtain high quality images required for quantitative image analysis. Issues regarding the selection of a particular technique and major considerations related to acquisition conditions are discussed, and are followed by brief descriptions of the common types of acquisition methods currently available for sedimentary analyses. For detailed discussion of the analytical procedures used for extracting quantitative information from sedimentary images (e.g., enhancement, calibration, and segmentation), the reader is referred to the other chapters that follow in this volume. Image acquisition and paleoenvironmental research It is tempting to begin using image analysis for a variety of paleoenvironmental research with relatively little consideration of the image acquisition process. Indeed, a considerable amount of early work successfully made use of commonly available equipment to capture images. This apparent success has been largely in qualitative research, and limited to visualization and archiving of sedimentary properties, perhaps with some enhancement of image contrast or color. However, quantitative image processing requires careful attention to a variety of conditions during the acquisition process (lighting, exposure) that are frequently overlooked in qualitative analysis (Fig. 1). Therefore, it is critical to establish optimal acquisition conditions as a ﬁrst step in any quantitative sedimentary image analysis project. Despite the differences in acquisition techniques, there are many common issues in obtaining high quality images. General considerations The ﬁrst and most important issue to be considered is the nature of the research objectives and the type of image information that is required to reach those objectives.As with selection of any procedure, selection of an acquisition technique should consider the aims of the subsequent image analysis, the possible acquisition methods, and the resources available to the researcher. Two critical considerations are image scale (or magniﬁcation) and image resolution. Typically, scale is deﬁned by the ﬁeld of view of the acquisition hardware and in practice, can vary from microns to tens of centimetres. Selecting an appropriate image scale balances two purposes: a) it permits extracting appropriate spatial information from the sample and b) minimizes the number of images and processing time necessary for the study. Most photographic equipment, for instance, can provide a wide range of image scales through the use of different of lenses and by varying the working distance from the sample. Image resolution refers to the ability of an acquisition system to record sample detail in an image (Edmund Industrial Optics 2002). Resolution effectively determines the amount of detail that may be obtained from the sample of interest. Typically, the resolution of digital hardware is reported in dots (pixels) per inch (dpi) or in pixel size (usually in µm). While many inexpensive scanners and other acquisition hardware devices provide optical resolutions of 600–1200 dpi, many manufacturers of consumer products report higher resolutions

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Depth (mm) Figure 1. An example of an image of laminated sediment from Sanagak Lake, Nunavut, Canada, obtained by scanning an X-radiograph negative using a 600 dpi ﬂatbed scanner (A). The image has a gradual shift to higher gray scale values (lighter) from right to left that was in part due to uneven exposure of the original X-radiograph ﬁlm and also due to uneven acquisition by the scanner. This image defect will lead to problems when assembling two adjacent and overlapping images (B). Plotted values from two separate X-radiograph scans from the same lake reveal a prominent downward trend with depth and demonstrate an offset in gray scale values where the two images overlap.

(9600+ dpi) that are produced from interpolation of the raw, optical scan. With this type of equipment, care should be taken to limit acquisition to the maximum optical resolution of the hardware, to avoid uncontrolled interpolation by software drivers. Where the optical system can be adjusted with different lenses, the real resolution can be similarly adjusted. However, for a given camera, increased resolution will be at the expense of image scale, because the number of pixels in the camera sensor is ﬁxed. In cases where it is not clear what the resolution of the system is, or if the user wishes to test the effective resolution, specially designed targets are available (Edmund Industrial Optics 2002). The most common used is the United States Air Force (USAF) target, although other organisations (e.g., Institute of Electrical and Electronics Engineers (IEEE)) produce similar tests. The appropriate combination of scale and resolution for image acquisition depends on the subsequent analysis to be performed. For visual purposes, including illustrations for publication, lower resolutions (300–1200 dpi) are usually sufﬁcient. Stratigraphic observations and measurements at the millimetre-scale can also be carried out at these resolutions

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5 mm

600 dpi

2400 dpi Figure 2. An example of the impact of acquisition resolution. Sedimentological features and other qualitative information in laminated sediments from Nicolay Lake, Nunavut, Canada are apparent from the 600 dpi scan in the left panel. Enlargements (panels at right) of a small section containing isolated sand and silt grains shows the pixeling and degradation of sedimentological properties in the 600 dpi scan compared to the 2400 dpi scan. The enlarged area is outlined on the lower magniﬁcation image.

(Fig. 2). However, many quantitative studies (e.g., Francus (1998)) require substantially higher image resolutions with pixel sizes <5 µm. As a matter of practicality, the number of images required for a given project should be considered at an early stage. While considerable progress has been made to automate or streamline the time required to acquire images (Bollmann et al., this volume; Nederbragt et al., this volume), many systems still require substantial time to obtain images. After the images are obtained, storage capacity may be a limiting factor, although this is increasingly becoming less of an issue. However, the human resources available for a project may be the main factor that limits the number of images that can be analysed. The number of images can be controlled by the scale of images (for instance, a small number of images that each cover a large section of sample) although the resulting changes to image resolution or scale may hinder the analysis. Rapid developments in the hardware available for image capture have resulted in the widespread use of direct digital acquisition of images from sedimentary materials. Digital cameras and scanners are the most commonly available to researchers because they are relatively inexpensive and can be used for purposes other than sedimentary image analysis. While the trend towards improved features and sensor resolution is likely to continue, analog acquisition remains as a viable means to obtain high-quality images that can be subsequently digitized (e.g., Ortiz and O’Connell, this volume). Many microscopy systems are equipped with ﬁlm cameras and provide excellent results. Similarly, analog X-radiography

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and electron microscopy systems are by far the most common equipment available to researchers. Therefore, while analog approaches require an additional digitizing step, they remain important tools for many sedimentologists. Like their digital counterparts, most of the key issues in image acquisition apply to analog equipment (see the next section). Finally, quantitative assessment of image properties and development of techniques that can be transported between laboratories require consideration of the reproducibility of the image acquisition method. Image properties of many sedimentary samples change rapidly with age. For example, reduced sediment will change composition due to oxidation. Similarly, some image acquisition equipment (lights, ﬁlm) also age with unpredictable results. Many of the key issues discussed in the following section are designed to document and minimize the inﬂuence of sample and equipment aging, as well as the varying acquisition conditions. Reproducible, quantitative results depend on accounting for these changes. Key issues in image acquisition Speciﬁc details of the image acquisition process will vary with the equipment used and the sample material. Regardless, the issues that affect image quality are frequently similar. This section discusses several of the most important considerations for obtaining the best quality images, particularly sample shape, lighting and image calibration. Sample shape Depending on the type of acquisition, the shape of the sedimentary sample will affect the resultant image substantially. With sample shape, we refer to the spatial and geometric form of the object under examination. In principle, uniform geometry, particularly with respect to the imaging sensor optical system is critical to obtain clear images. In the broadest sense, shape affects focus with reﬂected light, such as camera or video systems. For example, it will be difﬁcult to focus on a sediment slab that is uneven in thickness or has an irregular surface. Systems that utilize transmitted light (e.g., microscopes or scanners) are also sensitive to image shape with respect to ﬁnal image exposure. For instance, a thin section of uneven thickness will appear as darker in the thickest areas compared to the thinnest areas. Sample shape is especially important for X-radiography as the attenuation of the X-ray beam is controlled, in part, by sample geometry (Principato, this volume). Further, lens aberrations (or imperfections), particularly at low magniﬁcation can induce geometric distortions in the ﬁnal image. Although this is typically a minor concern with high quality lens elements, this type of image distortion can be estimated by imaging a uniform grid pattern to measure distortion across the ﬁeld of view, if necessary. Image registration Like sample shape, accurate image registration is necessary to ensure that the image properties can be indexed correctly to the true sample space. Alignment of two or more overlapping images to produce a larger image requires the registration of the individual images. Misalignment can result in an offset between quantitative information from the sample stratigraphy and any related physical measurements. In practice, registration can be accomplished using one of several simple techniques, depending on the required accuracy and the type of imaging system. In the case of large-scale core imaging, inclusion of a ruler

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into the image is a common and useful registration method which permits subsequent merging of information from overlapping samples. Similarly, registration or measuring marks are used on smaller samples to obtain correct image placement. Where repeated images are taken of the same sample (e.g., thin sections), the use of alignment jigs can provide accurate and consistent placement of the samples (Protz and VandenBygaart 1998). Lighting considerations The type and arrangement of the illumination source is an important consideration for acquisition using cameras and microscopes. The selection of a particular type of lighting can enhance the ﬁnal image substantially, by improving contrast, reducing glare, or in some cases, providing an image that will require minimal or reduced post-processing. By contrast, many acquisition systems, including scanners and X-radiography systems, are limited to a single type of illumination. Regardless, it is important to note that even ﬁxed illumination sources may vary as they age during use, thus changing the amount and wavelength of light to some degree. For most imagery, illumination in the visible and near infrared (NIR) bands is commonly used. Analog camera ﬁlm and light-sensitive sensors found in digital cameras are sensitive to these wavelengths and can produce high contrast images suitable for image processing. Illumination in the ultraviolet (UV) band can also be used and is particularly useful for ﬂuorescence imaging. As most light sources used for image acquisition are intense, caution should be taken to avoid exposure that could lead to eye damage. In particular, appropriate ﬁltered safety glasses should be used with UV light sources. Similarly, the heat produced by high-wattage lights can heat ﬁxtures rapidly and contact can cause burns. Most light sources used for photography or in scientiﬁc equipment have well documented illumination bands, and are frequently referred to by their black body temperature. For instance, commercial photography ﬂoodlights (typically 300–500 watt power) with tungsten ﬁlaments emit light at 3200 ◦ K. Although most illumination products are broad-band emitters, selective ﬁltering of the light source can generate a relatively narrow bandwidth of illumination (see section below on ﬁltering). It is important to note that photographic ﬁlms that are designed for use with tungsten ﬂoodlights are available and will provide better color rendition compared with conventional commercial ﬁlms that are optimized for general lighting sources. In addition to the different sources of light, the type of sample illumination will make a substantial difference on the quality and properties in the ﬁnal image. Uneven illumination or artefacts caused by inappropriate illumination are difﬁcult to remove from images and may prevent quantitative analysis. Therefore, careful selection of the illumination can minimize or eliminate problems that are common with sedimentary materials, in particular glare from wet surfaces of sediment cores. While the full range of illumination methods are typically only available with photomicroscopy, some are readily used for larger-scale photography (Fig. 3). Typically, most image problems are associated with highly directional lighting, produced for example, by photographing a sample with two bright spotlights. In addition to the uneven illumination, directional lighting typically produces glare and shadows. While these problems can be alleviated to some degree by using multiple light sources, directional lighting is rarely satisfactory for sediment imaging. By contrast, diffuse illumination, produced by a large number of lights or by ﬁltering can minimize glare and shadows. Diffuse

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Imaging Sensor Lens Elements

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Directional

Diffuser

Diffusion Screen

Diffuse Axial

Beamsplitter

Diffuse Sample

Stage

Backlight

Diffuser

Figure 3. A schematic representation of different illumination strategies for imaging sedimentary samples. Although the ﬁgure shows different lighting conﬁgurations for photomicroscopy, many are suitable for other acquisition techniques. Note that directional and external diffuse light usually come from more than one source, but have been simpliﬁed in the ﬁgure.

light sources are typically obtained by reﬂecting the light source on a diffusion screen, a technique commonly used in commercial photography. For photomicroscopy, diffuse light sources are available for both reﬂected and transmitted light imaging. In the former case, a large number of small light sources (typically light emitting diodes (LED)) are conﬁgured in a ring around the lens and provide coaxial light (Edmund Industrial Optics 2002). In cases where glare or shadowing remain problematic, diffuse axial illumination produced using a beamsplitter in the microscope lens assembly generates very even diffuse light with minimal glare. Where transmitted light imaging is desired, a diffuse backlighting source is of critical concern. Diffusing lenses and sample stages are available to provide even, diffuse light for imaging transparent and semi-transparent samples (e.g., thin sections). Where the sample material is opaque, brightﬁeld (or backlight) illumination can provide images that eliminate surface details and have high edge contrast. This illumination technique is especially useful for counting objects such as sediment grains or charcoal and has found wide use in sedimentology (Bouma 1969). The selection of an appropriate illumination conﬁguration and source will frequently provide images with relatively uniform lighting. While many light sources appear to provide reasonably even, diffuse light during sample inspection and visual assessment of the images, quantitative image analysis requires estimation of the uniformity of the illumination. By doing so, uneven illumination can be identiﬁed and corrected (see Nederbragt et al. (this volume)). A pragmatic approach requires obtaining a control image without a sedimentary

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sample. Analysis of the control image will identify areas of reduced illumination that are inherent in the acquisition system. However, it is important to note that this technique is not suitable for accounting for uneven illumination caused by glare or shadows, as these artefacts are speciﬁc to each sample. Similarly, analysis of the control image can provide an important measure of the noise generated by the image capturing system. In theory, perfect acquisition of a uniformly colored object using a uniform light source should generate an image with identical sensor values throughout the image. The deviation from this ideal situation is an important measure of the noise introduced during the sampling process. Finally, while it is not usually possible to predict how the illumination source will age, care should be taken to provide a means to measure its impact on a series of images. Again, a pragmatic and simple approach to this problem is to include one or more color standards in each image. In this way, changing illumination properties can be quantiﬁed (see Nederbragt et al. (this volume)). Light ﬁltering Light ﬁltering can be used for a variety of purposes in image acquisition to improve the image characteristics for subsequent processing. By making use of ﬁlter properties, the reﬂection (and transmission) properties of the sedimentary material can be enhanced to improve contrast between different components or structures. Additionally, ﬁlters are typically necessary to make use of infrared and ultraviolet wavelengths. In general, ﬁlters used in image acquisition can be categorized into bandpass, polarizing, and neutral density ﬁlters. Each type of ﬁlter has speciﬁc properties that affect the spectrum of light or the quantity of light that passes through the ﬁlter. The properties and uses of the main ﬁlter types are discussed below. Bandpass ﬁlters are all characterized by reduction of light transmission in a particular range of the electromagnetic spectrum. This group of ﬁlters can be further divided into several important functional types, including: interference, bandpass, longpass and shortpass types. Speciﬁcally, shorter wavelengths correspond to ultraviolet and blue light while longer wavelengths produce red and infrared light. Bandpass ﬁlters are designed to transmit light only in a speciﬁed range of wavelengths and to absorb wavelengths outside of this range (Fig. 4). In practice, the transmission bandwidth is bounded by transition bands of partial transmission; therefore, most bandwidth ﬁlters do not produce an ideal ﬁltering effect. Interference ﬁlters are special case of bandpass ﬁlters that have very narrow absorption bands (±10 nm). These ﬁlters are used in a variety of spectroscopic analytical equipment and are available in a large range of central wavelength values. Francus and Pirard (this volume, Fig. 3) show an example of how such a ﬁlter help to discriminate between two different mineral phases. However, unlike more conventional bandpass ﬁlters, interference ﬁlters are very sensitive to placement and variations in the incident angle of illumination can impact the ﬁltration characteristics (Edmund Industrial Optics 2002). Longpass and shortpass ﬁlters are essentially bandpass ﬁlters that absorb on the upper and lower ranges of the imaging spectrum. Depending on the speciﬁed wavelength absorption characteristics of the ﬁlter in use, the illumination on the sediment sample can be varied substantially. Moreover, ﬁlters can be used in combination to further alter the illumination. Indeed, this principle is used in color photographic ﬁlm where the incident light on the ﬁlm is selectively absorbed by light sensitive materials, separated by thin ﬁlm ﬁlters that restrict the passage of different

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Figure 4. Generalized wavelength ﬁltering characteristics of common colored ﬁlters. Additive colored ﬁlters (A) allow passage of the corresponding band of light (e.g., a green ﬁlter allows the passage of only green light), while subtractive ﬁlters (B) block the transmission of one of the additive primaries (e.g., magenta blocks green light). The gray shaded area is the transition zone for the red ﬁlter.

wavelengths. Color ﬁlters are available as dichroic (surface coated) or solid substrate types and are usually available as sets using either additive or subtractive color systems. Additive primary color ﬁlters (red, green, and blue) transmit light in their respective color, and when all three are combined together, produce white light (Lillesand and Kieffer 1984) (Fig. 4). In contrast, the subtractive primary colors (yellow, magenta, and cyan) ﬁlter by removing one of the primary additive colors. For instance, ﬁltering out green light results in transmission of blue and red light with the net result of magenta. While used for different processes, additive ﬁlters are used primarily in projection applications like television and subtractive ﬁlters are used in color photographic ﬁlm. Both types of ﬁltration have application in sedimentary image analysis through enhancement of contrast between colors and for identifying mineral materials (e.g., Protz and VandenBygaart (1998)). It is important to note that color ﬁltering can also be carried out during subsequent image analysis (see Nederbragt et al. (this volume)). Polarizing ﬁlters are most frequently used to minimize glare from wet sediment surfaces and cross polarization can be used for some mineral identiﬁcation (Fig. 5). Ordinary light (random polarization) can be thought of as consisting of electromagnetic waves at right angles to one another, and occurring in all possible aspects from the light source (Edmund Industrial Optics (2002)). Polarizing ﬁlters reduce the light to a single plane, hence

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Figure 5. An example of the use of cross-polarization to distinguish sedimentary components. Laminated sediments (9–12 cm below the lake ﬂoor) from the deepest point in Baldeggersee, Switzerland contain carbonate lamina produced during diatom blooms. These layers are apparent in an image obtained from a thin section (a). Cross-polarization of the same thin section during scanning (b) improves the clarity of the carbonate layers (homogeneous, light gray lamina) for subsequent analysis. Both images were obtained using an Agfa Duoscan transparency scanner at 1440 dpi in 8-bit RGB mode. The images have been converted to 8-bit greyscale and the brightness and contrast enhanced for presentation (images courtesy of P. Francus).

substantially reducing the amount of light transmitted. If a second polarizing element is added, the amount of light transmitted is proportional to the relative transmission axes of the two ﬁlters. If the polarizers are perpendicular, no light is transmitted. If the two polarizers are parallel to each other, the transmission is considerably higher. Many microscopes have fully

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integrated cross-polarizing ﬁlter sets built into the transmitted light stage for thin section work (Fig. 5). Alternatively, polarizing ﬁlters can be added to camera and microscope lenses, and sheet ﬁlm ﬁlters can be placed on ﬂatbed scanners with sample material to obtain similar effects. Finally, neutral density (or gray) ﬁlters are designed to evenly reduce the transmission of all wavelengths of light to prevent overexposure or damage to the imaging equipment. In practice, the use of neutral density ﬁlters is uncommon in most image acquisition situations, but may be used to protect lens surfaces and sensitive sensor systems where necessary. Calibration of image density As discussed in the illumination section, calibration of the image density in photography requires the inclusion of a density standard composed of a color or grayscale pattern target in each image. Grayscale patterns are usually composed of a series of rectangles varying from white to black, typically in 15 or more density steps. Color calibration requires more specialized targets (see Nederbragt et al. (this volume)). Therefore, before acquisition begins, it is important to develop the image analysis strategy and protocols to select an appropriate calibration standard. Finally, image calibration targets also serve to indicate the impact of illumination aging, thus serving as an important quality control measure. Sample preparation for image acquisition A comprehensive discussion of sample preparation for image acquisition is beyond the scope of this chapter. Detailed descriptions of the preparation procedures can be found in the accompanying chapters of this volume. However, as many sampling procedures (for imaging and other analyses) are destructive, it is important to consider the type of image acquisition prior to extensive work with the sediment (Fig. 6). Many image acquisition methods require minimal preparation work, including whole- and half-core X-radiography and core face photography. Protocols have been developed to consistently prepare core faces for acquisition for color analysis (see Nederbragt and Thurow (this volume)) and results from these studies have produced valuable paleoenvironmental proxy records (Hughen et al. 1996; Nederbragt et al. 2000; Nederbragt and Thurow 2001). Generally, clear core face images can be obtained by carefully scraping the surface, moving the cleaning edge across the sedimentary structures. In cases where the sediment is clay-rich, an electro-osmotic knife can be used to prevent smearing (Pike and Kemp 1996). If the sediment is frozen, covering the surface with a thin ﬁlm of water can be useful to reduce reﬂections off ice crystals (Renberg 1981). Finally, in some cases, particularly with some clastic sediments, allowing the surface to partially dry improves the contrast between sedimentary structures, although this may lead to cracking, particularly in diamictons. Image acquisition at ﬁner scales usually requires some degree of subsampling. In the case of unconsolidated materials, stabilization of the sediment is also usually required. Sediments can be stabilized in blocks and slabs using a variety of techniques (see Bouma (1969)) depending on the sample texture and water content. The most difﬁcult case is clayrich, wet sediments that require dehydration using either freeze-drying or liquid-liquid method, followed by impregnation with low viscosity epoxy resin (Pike and Kemp 1996; Lamoureux 2001). The stabilized sediment samples are suitable for a variety of image

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Whole sample

X-radiography

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Reflective photography X-radiography X-radiography

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Reflective photography Brightfield photography SEM Reflective photography Reflective scanning X-radiography Backscatter SEM

Separations

Polished faces

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Transmission photography Transmission scanning Backscatter SEM

Figure 6. Flow chart showing general sample preparations required for speciﬁc acquisition methods.

acquisition methods, including high quality X-radiography (Tiljander et al. 2002) and photography of polished faces. Stabilized samples can also be thin sectioned, thus opening the potential for transmitted-light microscopy and photomicroscopy. Similarly, polished thin sections are suitable for scanning electron microscopy (e.g., Francus (1998)). Further sample preparation is necessary for acquisition from a scanning electron microscope. Due the potential for heating by the electron beam, wet samples must be ﬁrst dehydrated and, if necessary, stabilized. Additionally, the sample must be conductive and grounded to the stage to dissipate charge accumulation from the electron beam. As most sediment samples are electrical insulators, a thin layer (∼200 Å) of amorphous carbon or gold is precipitated onto the sample surface to achieve greater magniﬁcation and resolution. Environmental scanning electron microscopes (ESEM) allow the use of uncoated and wet samples, due to the low vacuum used in the chamber, and may be suitable in

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some cases. Finally, for backscattered electron (BSE) microscopy, the sample must be ﬂat and polished using a ﬁnal polishing grit of 1 µm or ﬁner (Soreghan and Francus, this volume).

Acquisition methods This section is intended to provide an introduction to some of the main image acquisition methods used for sedimentary samples (Fig. 7). Rather than presenting a comprehensive discussion of these methods, the intent is to provide information and common issues that arise in using these approaches. Detailed information regarding the theory and application of these methods is provided in accompanying chapters.

Whole sample

SEM Photomicroscopy

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Air or oven dried Epoxy resin

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Embedded Polished faces

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Thin sections

Figure 7. Flow chart showing steps in embedding unconsolidated samples of both coarse and ﬁne grained sediment. Samples with high clay content requires special handling to for undisturbed subsampling, dehydration and embedding (after Bouma (1969), Pike and Kemp (1996), Lamoureux (2001)).

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Analog techniques Several analog techniques (photography, X-radiography) are the most common means used to acquire images from sedimentary sources. Analog techniques pose signiﬁcant challenges for quantitative image analysis due to image variability introduced by development. This is particularly the case with commercial developers, as most equipment automatically adjusts exposure and other properties for each image, making it difﬁcult to compare multiple images quantitatively. However, as most researchers are likely to have access to analog equipment, these methods are likely to remain in use for some time to come. Additionally, a large amount of archival material is available in analog form that was collected from sedimentary materials that are no longer intact. The conversion of these analog products to digital images is readily accomplished by scanning the original ﬁlm negative or prints. Scanning is discussed further in the digital acquisition techniques section that follows. Photography By far, analog photography is the most common image acquisition method, largely due to widely available, high quality equipment and the relatively low cost of obtaining images. Photography depends on the controlled exposure of light sensitive chemicals (silver iodide) carried on a plastic ﬁlm medium. Color photographic ﬁlm is composed of three lightsensitive layers separated by bandpass ﬁlter layers that record image information during exposure. A system of optical elements is used to provide primary magniﬁcation and the aperture controls the amount of exposure. Additionally, small aperture openings provide a large depth of ﬁeld, or the range of focus. The ﬁlm is isolated from light by a shutter that is opened for a short interval during exposure. Although both print (negative) and slide (positive) ﬁlms are widely available, slide ﬁlms are typically used due their ﬁner silver iodide crystals that produce better image detail. Acquisition with a typical single lens reﬂex (SLR) camera requires minimal setup: a stable mount for the camera and sample, and sufﬁcient lighting. The camera system must be able to focus relatively close to the sample. Macro-lenses are most suited for this task and are widely available. While personal preference plays an important role in building a practical setup, stability is particularly important to obtain sharp images and lighting must be appropriate for the sedimentary material. Wet samples, including many sediment cores, usually require diffuse light to minimize glare. Note that the light spectrum of ﬂuorescent and incandescent light bulbs results in poor color rendition in photographs. The best results are normally obtained from high-power lamps designed for photography, synchronised ﬂash units, or diffuse sunlight through a window or outdoors. Regardless of the conditions used, it is crucial that care is taken to maintain identical settings and lighting during a session. In particular, automatic camera settings that vary exposure and aperture should be avoided. A ﬁnal point to consider is that most modern ﬁlm processing laboratories scan negatives to produce photographic prints and automatically adjust scanning settings (e.g., contrast and brightness). As these settings are not documented, it is very difﬁcult to use these images for quantitative analysis. In many instances, the scanning resolution is lower than what can be obtained by scanning an analog print. The use of slide ﬁlm avoids this issue potentially, as images can be scanned with control over resolution and acquisition settings by the researcher.

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X-radiography While outwardly similar to conventional photography, X-radiography makes use of the high-energy X-ray bands of the electromagnetic spectrum and generates a fundamentally different type of sedimentary image. Image acquisition requires a source that is generated by high voltages applied to an X-ray tube. The X-ray emissions are directed towards the sample and, due to their high intrinsic energy, pass through the sample with varying degrees of attenuation. The attenuation of the beam is primarily determined by the density of the material: higher material density increases X-ray absorption. X-ray sensitive ﬁlm is placed under the sample and an image is formed that corresponds to the net incident beam. Thus, materials that are dense (e.g., metals) produce decreased exposure on the ﬁlm and result in lighter areas on the resulting negative image. This principle has been widely utilized for medical and industrial imaging where subsampling is not possible. For sedimentary imaging, the non-destructive nature of X-radiography is highly advantageous. Moreover, the density image produced can reveal subtle variations in composition and structure, which in many cases, are not visible otherwise (Fig. 1). A variety of industrial and medical X-radiograph equipment can be used to generate images suitable for sedimentary image analysis. Prior to any work with X-radiograph equipment, users should be fully versed with all safety features and cautions. Further, safety interlocks that prevent the operation of the X-ray equipment when a safety conditions are not met (e.g., a door is open) must be checked for proper operation. Users should consult documentation supplied with the X-ray equipment for speciﬁc details. It is important to note that the character of the X-ray source is considerably different for these applications, and hence, requires different exposure times and precautions. Medical X-ray systems utilize lower voltages (c. 40–60 KV), higher currents (c. 100 mA), and are usually designed for short exposure times (<1 second). Medical facilities generally have automatic development systems that can accelerate the process of determining the optimal exposure settings. By contrast, industrial systems are designed for imaging metals and other dense materials. These systems use higher voltages (c. 50–70 KV) and lower currents (c. 1–5 mA). The higher voltage is more suitable for dense mineral materials, however, the exposure times may exceed several minutes. Moreover, as many small facilities, particularly those in educational settings, have low demand for X-ray imaging, developing exposed ﬁlms is usually carried out manually and is time-consuming. Manual ﬁlm development requires a dark room and can slow determination of the optimal exposure time substantially. The development chemicals also have a short shelf life, and must be replenished on a monthly basis. Hence, infrequent users of industrial or research X-ray equipment are often faced with a cumbersome and expensive means of image acquisition. In some systems, the X-ray image is captured directly with a video camera and digitized by computer equipped with a frame grabber, therefore eliminating the ﬁlm manipulation and development difﬁculties and expense. A ﬁnal consideration for imaging pertains to X-ray beam path. Most available systems have relatively short beam paths (1 m). Because of the short path, the X-ray beam is not fully collimated (parallel) and can lead to edge parallax. For general imaging (for instance, sediment cores) parallax is visible but of minor concern. However, when ﬁne sedimentary structures are of interest, the parallax produces edge blurring that can impose limits on the subsequent image analysis. The solution to this problem is to utilize a long (several metres or more) X-ray source path to obtain as parallel of a beam as possible. In practice however,

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the expense and large space required by these facilities can only be justiﬁed by frequent use by specialized users. As discussed previously in the sample shape section, the shape of the sample is of primary importance for X-radiography. Samples must be as uniform as possible in thickness to obtain consistent exposures. Unlike visual illumination, it is not possible to determine uneven exposure caused by sample thickness variations. In some cases, it is not possible to obtain uniform sample thickness without some subsampling. In the case of round sediment cores, the core edges will over-expose due to the non-linear thinning of sediment thickness. However, many researchers (e.g., Tiljander et al. (2002)) have obtained excellent X-radiographs by subsampling core sediments into uniform rectilinear dimensions. Further, considerable information can be obtained by avoiding the over-exposed portions of the images during analysis (see Principato (this volume)). Finally, it is important to note that the use of metal sample holders and core tubes can drastically reduce the quality of the sediment images by reducing the overall beam strength. Where possible, the sediment should be removed from metal casings and care should be taken to also remove any metal fragments produced during splitting. Calibration of X-radiographs is readily carried out by utilizing density wedges that vary in thickness either continuously or in ﬁxed steps (Axelsson 1983; Ojala, this volume). Most wedges are made of precision machined metal and placed adjacent to the sample on the X-ray ﬁlm. Precise standards are available from scientiﬁc and industrial tool suppliers. Digital techniques Recent and ongoing technological advances have resulted in a wide range of available equipment for direct digital acquisition of sedimentary images. In addition to avoiding the extra step of scanning required by analog images, direct digital acquisition can provide increase sample spatial and color resolution. Moreover, rapid previewing assures that correct exposure and sample registration are obtained — a critical step when samples are subsampled immediately after imaging. Most of the principles that apply to analog acquisition also apply to digital systems. The researcher must also be aware of how the digital information is stored and what type of ﬁle compression or intrinsic ﬁltering is applied to the image. This issue and other considerations are discussed below for the three main digital systems used to acquire images for sedimentary analysis. Scanning Scanning is perhaps the most important and widespread digital acquisition method, in part due to the frequent use of analog cameras and X-radiograph systems, as well as the suitability of many sedimentary samples for direct scanning (De Keyser 1999). Although they vary substantially in appearance and capabilities, most scanning systems utilize an array of light-sensitive photodiodes to collect the image information. The diode array is moved precisely across the sample to construct a composite of the image properties. In principle, the movement of the scanning sensor increases the complexity of the hardware. However, the mechanical movement permits the use of a small, high resolution sensor head that signiﬁcantly reduces the equipment cost. Scans can be obtained using either reﬂected or transmitted light, depending on the hardware. Reﬂected light is used for opaque samples and photographs, but sample dimensions

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are frequently constrained by the size of the scanner. More commonly, transmitted light scanning is used to obtain images from ﬁlm negatives, slides, and thin sections. Highresolution slide scanners that are used for photographic slides and negative strips have mechanisms that will scan only a small area. Flatbed scanners can scan page-sized or larger areas and are suitable for large photographs, X-radiographs and thin sections. However, note that the transmitted light scanning area of ﬂatbed scanners can be substantially smaller than the area available for reﬂected light images. Due to the constraints of the scanning process, most scanner optics are designed to operate with a ﬁxed, narrow depth of ﬁeld. Moreover, exposure and lighting conditions are frequently preset to optimize the speciﬁc scanning sensor response characteristics. The lighting source, often a high intensity ﬂuorescent bulb, is also rarely customizable by the user. While these constraints may seem restrictive, software compensation of light and exposure is available for all scanners, but should be used with caution and consistency. Scanning resolution is determined by the density of the sensor head and the precision of the mechanical stage. While it is not uncommon to obtain resolutions of 1200 pixels per inch (or dpi) or higher, many scanners specify signiﬁcantly higher resolutions obtained through interpolation of the raw scan data. As the interpolation algorithm is rarely documented, the higher interpolated resolutions should be avoided for image analysis. Similarly, the color resolution of many commercial scanning systems exceeds 24 bits (that is, 224 different colors). However, like spatial resolution, these sensor values represent the upper limit of actual color differentiation in the image and the beneﬁts of high color depths should be weighed before image acquisition. High color depth substantially increases image ﬁle size and processing times, leading to storage problems and reduced productivity. Finally, scaling (or enlargement) of an image should be performed during the scanning process, and not after, since modifying the size of an image electronically alters both the image and color details through pixel interpolation during scaling. Image ﬁle formats vary substantially and represent varying degrees of compression and loss of information. Many ﬁle formats are optimized to adequately represent images for visual purposes (e.g., Joint Photographic Experts Group (JPEG)) and represent signiﬁcant alteration of the raw image. Many scanners use compressed ﬁle formats by default; hence, the user must take care to select raw data formats. It is important to note that although these ﬁle formats maintain image ﬁdelity, they are not necessarily the best format or color representation for image processing. One particularly useful color format used in sedimentary image analysis is the L*a*b* type. For details regarding this system and transformations from other color formats, the reader is directed to Nederbragt et al. (this volume). Finally, image calibration during scanning is important to maintain consistency of image properties and to account for light source aging. Color and grayscale density targets can be included during the acquisition in a manner similar to conventional photography. In addition calibrating for light aging affects, many scanning systems carry out automatic calibration before each scan. The impacts of the hardware calibration can be unpredictable, particularly if the scanner uses a particular area to carry out this procedure. If the sample is located in the calibration area, the calibration can be signiﬁcantly altered. Although details are not always clearly documented, users should make an effort to determine the nature of hardware calibrations prior to image acquisition. Several good quality scanners provide scientiﬁc calibration material for this purpose. Finally, as is the case with analog

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photographic prints, commercial scanning services may be unsuitable for image analysis work because scanning adjustments (e.g., contrast, brightness) are made automatically and are not documented. Digital photography Digital cameras have become commonplace in recent years and many researchers have access to handheld and microscope models. Like analog cameras, digital versions consist of two major subsystems: optics and a light-sensitive sensor array. Exposure settings may vary from fully automatic to manual. As with most acquisition systems, users are advised to avoid the use of automatic settings as they may vary image properties unpredictably. Compared to scanners, the rectangular charge coupled device (CCD) in most digital cameras generates the image simultaneously, eliminating the need for a moving scanning mechanism. The exceptions to this case are line scan cameras that utilize the same principle as a scanner to build a larger, high resolution image (e.g., Schaaf and Thurow (1994)). Line scan cameras were commonly used for scientiﬁc image acquisition prior to the availability of cost-effective megapixel CCD sensors, but have become less common. The CCD sensors vary by size, pixel count, quality (number of “dead” pixels) and light sensitivity. Most cameras contain rectangular CCD sensors 1/4–1/2 inches long (note that the industry typically uses the nonSI units). Increased CCD sensor size provides a larger number of light-sensitive pixels, and hence, higher resolution for a given optical magniﬁcation. Indeed, many cameras are sold by the number of pixels (2+ million pixels) rather than the chip size. Higher resolution can also be obtained using optical magniﬁcation. Therefore, selection of an appropriate digital camera must account for the combination of both the CCD size and optical system. The majority of digital cameras capture color images although monochrome cameras are available for microscopes. Monochrome cameras are characterized by higher signal to noise ratios, improved light sensitivity and greater contrast (Edmund Industrial Optics 2002). Moreover, for visualization, the human eye perceives spatial variations more clearly in black and white than in color. Color CCD arrays have the disadvantage of requiring three different pixels (the additive primaries red, green and blue) to generate one color pixel. This results in reduced camera resolution and greater numbers of “dead” or non-functional pixels due to the greater complexity of the sensor. To avoid these limitations, three-CCD cameras that optically split the incoming image into red, green and blue bands that are captured by separate CCD arrays are available, although these cameras are expensive and available from a limited number of manufacturers. As with analog cameras, the optical characteristics vary between digital cameras. As the optical system is the primary means of adjusting the image ﬁeld of view, the quality and ﬁdelity of the lenses should be as important a consideration as the CCD array size. File storage and compression on digital cameras is frequently more problematic than with scanners, as many cameras are designed to be operated without external ﬁle storage. Hence, most handheld cameras do not have the provision for the storage of uncompressed ﬁles. For example, a 2.1 megapixel camera requires approximately 5 Mb of memory to store an uncompressed Tagged Image File Format (TIFF) image compared to approximately 500 Kb for a high-quality JPEG format ﬁle. As previously discussed, image compression results in loss of image information and should be avoided for acquisitions intended for quantitative image analysis. Digital cameras intended for use with microscopes usually have uncompressed, raw ﬁle format support.

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Scanning electron microscopy In recent years, scanning electron microscopy (SEM) has been used to acquire images for a variety of detailed sedimentological analyses (Fig. 8) (e.g., Dean et al. (1999)). Scanning electron microscopes use electrons to generate an image through progressive surface scanning. When the electron beam hits the sample, the interaction of the beam electrons and the sample atoms generates a variety of signals that include secondary electrons (electrons from the sample itself), backscattered electrons (beam electrons from the ﬁlament), X-rays, light, heat, and transmitted electrons (Lee 1993). Secondary electrons are used solely for imaging the surface of a sample and secondary electron images are obtained most frequently with the SEM. Backscattered electron images also provide information on specimen composition and topography. Backscattered electrons vary in their amount and direction with the composition, surface topography, crystallinity and magnetism of the specimen. The contrast of a backscattered electron image depends on (1) the amount of backscattered electron generated, which depends on the mean atomic number of the specimen, (2) the angle dependence of backscattered electrons at the specimen surface, and (3) the change in the backscattered electron intensity when the electron probe’s incident angle upon a crystalline specimen is changed. Backscattered electrons are generated in

200 µm Figure 8. A backscattered electron image of laminated sediment from Sawtooth Lake, Nunavut, Canada, acquired with a JEOL JSM-5410 scanning electron microscope. The sediment was freeze-dried, embedded with epoxy resin prior to preparation of a polished face. Image magniﬁcation is 100X. Note the clear deﬁnition of individual sand and silt grains (image courtesy of P. Francus).

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a larger region than secondary electrons, that is, several tens of nm compared to nm. Therefore, backscattered electron images give lower spatial resolution than secondary electron images. Signals generated with an SEM are recorded with various detectors that generate an electrical signal that can be digitized (Lee 1993). Most modern SEMs are already equipped with digital imaging units for digitizing secondary electron images and backscatter electron images. There are two basic image acquisition modes in a SEM: slow scan and TV. In TV mode, an image is acquired at TV frequency (50/60 Hz) to rapidly generate and image. However, the image quality is often poor. Image geometry is often distorted and the signal to noise ratio is low (Fig. 9a). The signal to noise ratio can be improved with the use of autocorrelation and stacking ﬁlters (Fig. 9b) (Krinsley et al. 1998). However, registration of the image geometry usually cannot be improved. Therefore the quality of the built-in TV mode needs to be conﬁrmed using images of a calibration grid (see also Nederbragt et al. (this volume)). Image acquisition in slow scan mode produces much better image geometry and signal to noise ratio (Fig. 9c). With increasing line time, the signal to noise

A

B

C Figure 9. Varying signal to noise ratios in different acquisition modes of a scanning electron microscope. A: image acquired in TV mode (50 Hz) without noise ﬁltering (note the low signal to noise ratio); B: image acquired in TV mode (50 Hz) using an autocorrelation ﬁlter (averaging of 64 images) to reduce the noise (note the improved signal to noise ratio); C: image acquired in a slow scan mode (line time of 20 ms) to reduce the noise. The images of the checkerboard pattern on a disk out of a single crystal of silicon were taken with a Philips LaB6 scanning electron microscope.

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ratio and the quality of image geometry increases and the scanning time can be adjusted to suit particular needs. Images from older analog SEMs can often be digitized using the TV output in combination with a video capture system. However, the signals commonly do not use PAL or NTSC video standards used with video capture systems. Slow scan images can also be digitized using external scan control (see Soreghan and Francus (this volume)). The time needed to acquire an image with the SEM can vary considerably from TV frequency to several hours in slow scan mode (see also Bollmann et al. (this volume), Soreghan and Francus (this volume)). However, this requires several instrument and external conditions to be constant while acquiring an image. Internal to the SEM instrument, the most important parameters are stage and beam stability, as well as stability of electron emission. Stage drift occurs in every SEM and is caused by factors such as overall quality of the stage, momentum after stopping the stage, vibration and temperature changes. Drift can be characterized simply by measuring the drift (movement of the stage) versus time at high magniﬁcation. This gives an indication for the most suitable acquisition time. Details about measuring the stage drift are described by Vladár (1999). Movement of the ﬁlament/gun during acquisition reduces illumination. Electron gun shift and tilt occurs in every SEM and is usually adjusted by the operator. However, movements can also occur during acquisition due to thermal drift of the ﬁlament, contamination of the column causing interior charge-up, and external magnetic stray ﬁelds (see below). The electron emission can vary during acquisition due to ﬁlament aging or power supply instabilities, although the latter are rare in modern instruments. Aging of the ﬁlament is a major concern, particularly for automated image acquisition over a time frame of 24 hours. Currently, the two types of electron sources used for SEMs are thermionic electron sources equipped with Tungsten or LaB6 ﬁlaments and ﬁeld emission sources equipped with a Schottky Field Emitter (warm ﬁeld emission) or a cold ﬁeld emitter. The most commonly used and most economical type is the Tungsten ﬁlament, which has a lifetime of 100 to 150 working hours (about one week in 24 hour operating mode). Tungsten systems are very robust and unlike a LaB6 ﬁlament or a ﬁeld emission gun, do not require high vacuum (10−7 to 10−8 mbar) to operate. The lifetime of a LaB6 ﬁlament and Schottky Field Emitter is about 1000 and >2000 hours, respectively (approximately six weeks to three months in 24 hour operating mode, respectively). Cold ﬁeld emitters are not suitable for automation of image acquisition because they are very unstable. The most suitable systems, for example, for automated operation over several hours (see also Bollmann et al. (this volume)), are Schottky Field Emitters because of their stability and the long ﬁlament lifetime. LaB6 systems are also suitable for automated applications. However, the degree of spatial ﬁlament drift in LaB6 systems varies by batch and manufacturer. Therefore, we strongly recommend extensive tests of the stability over several weeks before deciding which SEM or gun system to invest in. Important external factors include vibrations, acoustic noise and stray electromagnetic ﬁelds that may result in image geometric distortion and unfocused images (Fig. 10). Most modern SEMs are already equipped with shock absorbers and they are often located in the basement of buildings on massive concrete blocks. However, it might be necessary to compensate for vibration with an active (computer controlled) compensation system. The most common source of disturbance is external stray magnetic ﬁelds. Alternating current (AC) ﬁelds are generated by poorly shielded building wires and power supplies.

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Direct current (DC) ﬁeld sources include: high-current electromagnets found in massspectrometers, elevators, subways, and the earth magnetic ﬁeld. AC ﬁelds result in sawtooth patterns in the SEM image whereas DC ﬁelds cause beam shifts, often resulting in image striae (Fig. 10). Room shielding and active ﬁeld compensation are approaches that can effectively reduce stray ﬁelds for SEM work.

Figure 10. Image distortion due to AC electromagnetic ﬁelds (saw tooth pattern) and DC electromagnetic ﬁelds resulting in striae in the image (middle and lower part). This image of a polycarbonate membrane ﬁlter was acquired with a Philips LaB6 scanning electron microscope.

Summary High-resolution digital photography and acquisition equipment is becoming widely available and cost-effective. Additionally, SEM and related acquisition technologies provide the means for obtaining images with resolution containing both structural and elemental information. Despite the development of new acquisition techniques and hardware, selecting an appropriate imaging solution for a research problem remains a critical issue for sedimentary research. Moreover, despite the differences between acquisition technologies, all share common approaches and considerations in order to obtain the highest quality images for quantitative sedimentary analysis. Consideration should be made to account for artefacts in the acquisition process, particularly that sample shape and illumination variations are accounted for. Additionally, color or equivalent image standards should be included in each image to permit quantifying the properties between images. Finally, image resolution and ﬁle storage protocols should be appropriate for the research objective and preserve the original image information (i.e., no compression). Technological advances will undoubtedly create new image acquisition opportunities for sedimentary researchers. Additionally, evolving approaches for the automation of image acquisition will provide increasingly efﬁcient methods to obtain data from long sedimentary sequences or with higher spatial resolution.

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Acknowledgments The authors wish to thank the editors for their efforts that have improved the manuscript. Reviews by A. Nederbragt and A. Rochon signiﬁcantly improved the presentation of the text. Ursula Brupbacher helped proof read the manuscript.

References Axelsson V. 1983. The use of X-ray radiographic methods in studying sedimentary properties and rates of sediment accumulation. Hydrobiologia 103: 65–69. Bouma A.H. 1969. Methods for the Study of Sedimentary Structures. John Wiley & Sons, New York, 458 pp. Dean J.M., Kemp A.E.S., Bull D., Pike J., Patterson G. and Zolitschka B. 1999. Taking varves to bits: scanning electron microscopy in the study of laminated sediments and varves. J. Paleolim. 22: 121–136. De Keyser T.L. 1999. Digital scanning of thin sections and peels. J. Sed. Res. 69: 962–964. Edmund Industrial Optics 2002. Optics and Optical Instruments Catalogue. Barrington, NJ, 325 pp. Francus P. 1998. An image-analysis technique to measure grain-size variations in thin sections of soft clastic sediments. Sed. Geol. 121: 289–298. Hughen K.A., Overpeck J.T., Peterson L.C. and Trumbore S. 1996. Rapid climate changes in the tropical Atlantic region during the last deglaciation. Nature 380: 51–54. Krinsley D.H., Pye K., Boggs S., Jr. and Tovey N.K. 1998. Backscattered Scanning Electron Microscopy and Image Analysis of Sediments and Sedimentary Rocks. Cambridge University Press, Cambridge, United Kingdom, 193 pp. Lamoureux S.F. 2001. Varve chronology techniques. In: Last W.M. and Smol J.P. (eds), Developments in Paleoenvironmental Research (DPER) Volume 2-Tracking Environmental Change Using Lake Sediments: Physical and Geochemical Methods, Kluwer, Dordrecht, pp. 247–260. Lee R.E. 1993. Scanning Electron Microscopy and X-ray Microanalysis. Prentice Hall, Englewood Cliffs, New Jersey, 458 pp. Lillesand T.M. and Kiefer R.W. 1984. Remote Sensing and Image Interpretation, 2nd ed. John Wiley and Sons, 721 pp. Nederbragt A.J. and Thurow J.W. 2001. A 6000 year varve record of Holocene climate in Saanich Inlet, British Columbia; from digital sediment colour analysis of ODP Leg 169S cores. Mar. Geol. 174: 95–110. Nederbragt A.J., Thurow J.W. and Merrill R.B. 2000. Color records from the California margin: proxy indicators for sediment composition and climatic change. Proceedings of the Ocean Drilling Program, Scientiﬁc Results 167: 319–329. Petterson G., Odgaard B.V. and Renberg I. 1999. Image analysis as a method to quantify sediment components. J. Paleolim. 22: 443–455. Pike J. and Kemp A.E.S. 1996. Preparation and analysis techniques for studies of laminated sediments. In: Kemp A.E.S. (ed.), Palaeoclimatology and Palaeoceanography from Laminated Sediments. Geological Society Special Publication No. 116, pp. 37–48. Protz R. and VandenBygaart A.J. 1998. Towards systematic image analysis in the study of soil micromorphology. Sci. Soils 3: 11. Renberg I. 1981. Improved methods for sampling, photographing and varve-counting of varved lake sediments. Boreas 10: 255–258. Schaaf M. and Thurow J. 1994. A fast and easy method to derive highest-resolution time-series datasets from drillcores and rock samples. Sed. Geol. 94: 1–10.

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Tiljander M., Ojala A., Saarinen T. and Snowball I. 2002. Documentation of the physical properties of annually laminated (varved) sediments at a sub-annual to decadal resolution for environmental interpretation. Quat. Int. 88: 5–12. Vladár A. 1999. Time-lapse scanning electron microscopy for measurement of contamination rate and stage drift. Scanning 21: 191–196.

3. IMAGE CALIBRATION, FILTERING, AND PROCESSING

ALEXANDRA J. NEDERBRAGT ([email protected])

Department of Geological Sciences University College London Gower Street London WC1E 6BT UK PIERRE FRANCUS ([email protected])

Climate System Research Center Department of Geosciences University of Massachusetts Amherst, MA 01003-9297 USA Currently at INRS - Eau, Terre et Environnement 490 rue de la Couronne, Québec (QC) G1K 9A9 Canada JÖRG BOLLMANN ([email protected])

Department of Earth Sciences ETH and University Zurich Sonneggstrasse 5, 8092 Zurich Switzerland MICHAEL J. SOREGHAN ([email protected])

School of Geology and Geophysics University of Oklahoma Norman, OK 73019 USA Keywords: Image analysis, Calibration, Size, Colour, Grey-scale, Contrast and brightness, Filtering, Edge detection, Segmentation, Metadata

Introduction The previous chapter dealt with the acquisition of the best possible image. This chapter reviews the two next following steps: (1) Pre-processing includes spatial and density 35 P. Francus (ed.) 2004. Image Analysis, Sediments and Paleoenvironments. Kluwer Academic Publishers, Dordrecht, The Netherlands.

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calibration, as well as correction for imperfect image acquisition. (2) Image processing involves modiﬁcation of the original image in such a way that the required numerical data can be extracted. Both steps are a prerequisite for the actual image measurements that are discussed in the following chapter (Pirard, this volume). This chapter presents and discusses a selected set of pre-processing and processing techniques that are the more commonly used in sedimentary palaeoenvironmental applications. The order in which the techniques are presented corresponds to a typical progression of operations, but it can be changed according to speciﬁc research needs. Both pre-processing and processing involve three main types of operations. The ﬁrst type applies a transformation to the image as a whole, changing the intensity of each pixel in the original image in a way that depends only on the original value of that particular pixel. Examples include mathematical operations like adding a value to each pixel, or multiplying pixels by a constant. Such operations usually do not result in loss or gain of information, and applying the reverse operation allows retrieval of the original image data. In general, this type of operation is used in image pre-processing, mostly for calibration. The second type of operation transforms the value of a pixel based on the value of adjacent (or neighbouring) pixels. This type of operation permanently alters the content of the image and the original data cannot be retrieved. Such operations are usually related to image processing operations (image ﬁltering, enhancement, classiﬁcation and segmentation; Jongmans et al. (2001)). The third and last type of operation involves the simultaneous manipulation of two or more images or using the values in one image to modify the content of another image. Image pre-processing Spatial calibration Accurate and reliable measurement of size and geometry is a crucial aspect of Geosciences. However, geometric measurements in digital images (or photographs) taken with a camera, light microscope (LM) or Scanning Electron Microscope (SEM) can be biased by various factors. These include distortion resulting from the optical properties of a lens, perspective, the process of digitisation, as well as erroneous size speciﬁcation (for details see Russ (1999), Hecht (1998)). Calibration of geometric measurements is therefore required to optimise reproducibility and accuracy. If measurements are not corrected, data are difﬁcult to compare and may become useless for quantitative analysis. In order to produce scaled measurements (in SI units), the pixel size has to be determined by measuring the number of pixels along a selection that corresponds to a known distance. Spatial calibration functions are included in all image analysis software packages, including the correction for the pixel ratio when the horizontal and vertical resolutions are not the same. In the following section, several major sources of error are described and the procedures for size and shape measurements with SEM and LM are outlined, but the same principles are also applicable to other types of images. SEM measurements Because of inherent technical uncertainties, the accuracy of size measurements carried out with an SEM should be controlled regularly with calibration standards such as a chequerboard or microbeads (Figs. 1 and 2). The accuracy of the magniﬁcation reading

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Figure 1. SEM Image of a latex calibration microbead with a diameter of 15 µm ± 0.3 µm (Dynospheres , Product No.: SS-15-PX6 Particle size standard, Batch No.: Q-639) taken in BSE mode with a Philips XL30 LaB6 microscope at 16 KV.

often changes with different magniﬁcations and the degree of distortion varies over time depending on various factors (for details see ASTM Committee E-4 (1993), Lee (1993)). Therefore, it is advisable to keep the settings such as working distance, spot size, high tension, line time (scan speed), magniﬁcation, focus, and resolution constant during a measurement campaign to reduce the source of errors (Lamoureux and Bollmann, this volume). For example, some SEMs exhibit strong non-linear distortion in television (TV) mode. Images of a chequerboard captured in TV mode clearly demonstrate that the width of a singe ﬁeld increases non-linearly from the left to the right and the top to the bottom of the image (Fig. 2C, Table 1). According to the speciﬁcations provided by the manufacturer, all ﬁelds are square, and both length and width of a single ﬁeld on a chequerboard are 10 µm ± 0.2 µm. However, the ratio of X and Y measurements shows that this is true for only for one ﬁeld, i.e., number 9 in Figure 2C (Table 1). Furthermore, the average length and width of all ﬁelds is 9.48 µm and 10.45 µm respectively. Only the size measurements of ﬁeld number 9 are within the given error of ±0.2 µm (Table 1). Measurement in TV mode is therefore not recommended. In general, image distortion increases with faster line scan times and there is consequently a trade-off between image quality and the time needed for image acquisition. Light microscope measurements Geometric distortion occurs in images obtained with a light microscope system due to irregularities in the lenses (Hecht, 1998). In contrast to measurements obtained with the SEM, distortion of LM images is constant over time. The extent of distortion should be determined prior to performing geometric measurements. Calibration is performed with a micrometer or reticule grid of known size. Distortion is usually less in the centre of the ﬁeld of view and measurements from this area reduce the degree of error. In addition, it is sensible to keep the light intensity, magniﬁcation/objective and digital image resolution constant during a measurement campaign.

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B.

C.

Figure 2. SEM images of a chequerboard pattern on a disk out of a single crystal of silicon. The size of a single square is 10 µm ± 0.2 µm and the accuracy of angle measurements is 0.5 arcsecs; A) Overview image in slow scan; B) Close-up of A; C) as A, but in TV mode. The resolution is 700 × 574 pixels. Numbers and lines refer to measurements listed in Table 1. Note the non-linear distortion along both the X and Y axis. For panel A and B, acquisition conditions similar to Figure 1. The image in panel C has been taken using an Hitachi S2300 microscope in BSE mode at 20 KV. 32 images have been averaged for noise reduction.

Calibration for optimal reproducibility and accuracy Calibration procedures for the SEM and LM are available from the American Society for Testing and Materials (ASTM Committee E-4, 1993, 2002; ATSM Committee F-1, 1997). The accuracy of image measurements depends on the standard target that was used for the calibration, as well as the size of the pixels in the digitised image. For example, the precision of the length of one ﬁeld on a chequerboard is 10 µm ± 0.2 µm. Therefore, all measurements have a minimum error of ±2% if only one ﬁeld was used for calibration. If the calibration was done over 10 ﬁelds of the chequerboard (100 µm length) on a digital image with a resolution of 100 × 100 pixels all subsequent measurements can not be more accurate than ±1 µm because one pixel is 1 × 1 µm in size. For the measurement of individual sedimentary particles (e.g., microfossils or grains) with an SEM or LM, the addition to the sample of calibration microbeads in the size range of the particles to be measured provides an effective way to calibrate the size measurements. It also allows recalibration of the measurements with another system in the future. Measurement of the length and width of a statistically signiﬁcant number of microbeads (e.g., 30

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39

Table 1. List of X and Y measurements done on an image of a chequerboard calibration target taken with a SEM in TV mode; numbers given in the column ﬁeld refer to the ﬁelds on the chequerboard in Figure 2C. W/H is width/height ratio of the ﬁelds; stdv stands for standard deviation. Bold values indicate measurements within the given error of 10 ± 0.2 µm. Width µm

Height µm

W/H

Field

Width µm

Height µm

W/H

1

8.76

9.88

0.89

17

9.88

10.29

0.96

2

9.04

9.88

0.92

18

10.15

10.43

0.97

3

9.74

10.15

0.96

19

8.62

10.57

0.82

4

10.15

9.74

1.04

20

9.46

10.71

0.88

Field

5

10.43

10.02

1.04

21

9.60

10.85

0.88

6

8.76

10.43

0.84

22

10.02

10.71

0.94

7

9.46

10.43

0.91

23

10.43

10.57

0.99

8

9.60

10.29

0.93

24

8.62

10.43

0.83

9

10.15

10.02

1.01

25

9.18

10.85

0.85

10

8.76

10.43

0.84

26

9.60

10.85

0.88

11

9.32

10.43

0.89

27

9.88

10.43

0.95

12

9.46

10.29

0.92

28

8.35

10.85

0.77

13

10.02

10.29

0.97

29

9.04

10.99

0.82

14

9.88

10.29

0.96

30

9.60

10.71

0.90

15

9.04

10.43

0.87

31

9.04

10.57

0.86

16

9.46

10.57

0.89

32

10.02

10.85

0.92

Min.

8.35

9.74

0.77

Mean

9.48

10.45

0.91

Max.

10.43

10.99

1.04

Stdv

0.56

0.32

0.07

or more) is advisable to correct for apparent size offsets (Bollmann et al. 2002). In order to test the accuracy and the reproducibility of measurements obtained with automated systems (see Bollmann et al. (this volume)) measurements of particle standards with different mean diameter should be taken at regular intervals. Intensity calibration Each pixel records a numerical value (intensity) that corresponds to some property in the original sample. Pixel intensities can be calibrated against known standards to produce a quantitative estimate for that property. The type of calibration standard will depend upon the kind of imaging technique used, e.g., a colour or grey chart for sediment photographs (Nederbragt and Thurow, this volume), a density wedge for X-radiographs (Ojala, this volume), or a mineral standard for tomography (Boespﬂug et al. 1994) and Backscatter Electron (BSE) images (Soreghan and Francus, this volume). The process of creating a calibration function for a particular type of data or application might be complex (Ortiz and O’Connel, this volume; Russ 1999). However, the calibration rationale remains identical. From a set of intensity measurements of several objects of known properties, one can establish a calibration curve to estimate the composition of the sample. Colour information

40

NEDERBRAGT, FRANCUS, BOLLMANN AND SOREGHAN

and calibration, as a particular case of pixel intensity, are discussed later in this chapter. Colour images are the standard output of many digital cameras and imaging systems, and intensity calibration will therefore involve processing of colour data in many applications. Light distribution correction The importance of using a good quality light source for image acquisition, one that produces an even light distribution, is discussed by Lamoureux and Bollmann (this volume). However, some variation in light intensity within the ﬁeld of view will usually be present. Depending on the application, such an uneven light distribution may require ﬁltering. For example, when different phases are classiﬁed based on their intensities, some objects in a lighter/darker area in the ﬁeld of view may be incorrectly identiﬁed. In many cases, effects of an uneven light distribution can be ﬁltered out of the image sufﬁciently well to allow further image processing. Here we address two common techniques that can be applied to the image directly. Other approaches exist, such as rank levelling (Russ 1999), to take care of non-uniform illumination and the reader should refer to reference textbooks for more details. A further discussion of ﬁltering data after they have been extracted from uncorrected images is given in Nederbragt and Thurow (this volume) and France et al. (this volume). In some cases, the actual light distribution across an image can be measured directly, by imaging a uniform card or surface. The image of this card is ﬁrst smoothed, to remove irregularities, and then subtracted from all the images in the data set. However, ﬁnding an appropriate card for this purpose can be a matter of trial and error, and testing if the resulting correction is adequate. In practise, the spatial variation in colour values registered by the camera is not only dependent on the strength and type of illumination (Lamoureux and Bollmann, this volume), but also on the reﬂectivity and the colour intensity of the imaged objects (Nederbragt and Thurow, this volume). An alternative approach is to estimate the light distribution from the images themselves. The example in Figure 3 shows how a background pattern of large-scale changes in colour can be estimated, and subtracted from the image, leaving ﬁne scale features virtually intact. Such functions to subtract a background pattern are available as a built-in function in image analysis software packages. However, there are abrupt jumps in colour values in the background pattern, which are not related to the uneven distribution of the light source, but are produced by real changes in sediment colour (Fig. 3C). The results can be reﬁned, by selecting those images from a set that show the least variation in real sediment colour, and calculating an average image from that subset. The background of such an average image is more likely to be sufﬁciently smooth and representative for the whole data collection (Fig. 3D). It can then be subtracted from all individual images in the data set. Contrast and brightness Visual inspection of the images is usually an important part of image analysis, to determine the most suitable method for the processing of the data set. However, visual identiﬁcation of the relevant features can be difﬁcult if the image is dark, or if the difference in colour between the various components is small. If this is the case, contrast and brightness can be

IMAGE CALIBRATION, FILTERING, AND PROCESSING

41

Figure 3. Example of correction for uneven light distribution using a built-in function in the image analysis package NIH image v1.61 to subtract a background pattern from an image. A) Image of laminated sediments collected with the grey scale camera described in Schaaf and Thurow (1994); darker values towards top and bottom of the image are the result of uneven illumination. B) Result after background subtraction. C) Difference between image A and B, i.e., the background pattern estimated from the single image in A; note that the algorithm captures the general trend of darker values towards the edges, but also shows abrupt breaks that are unrelated to light distribution. D) A smoother background, one that is more representative of the light distribution, was generated by calculating an average image from the one in A together with 23 other images, and estimating the background pattern in that average image.

enhanced after acquisition, in such a way that the required information remains unchanged while features of interest are made more clearly visible. The concept of contrast and brightness is best illustrated in a histogram of intensities, or grey-values, of all the pixels in a ﬁeld of view (Fig. 4). The position of values in the histogram along the intensity axis represents brightness information, and the dispersion of the histogram along the same axis represents contrast information. It is easier for the human eye to distinguish multiple phases, i.e., two populations in the histogram of intensities, when the full range of the available intensities is used, i.e., 256 values for 8 bits images, instead of a small portion of the available range. There are different ways to correct or enhance the intensity distribution in an image. The reader is referred to image analysis textbooks

42

NEDERBRAGT, FRANCUS, BOLLMANN AND SOREGHAN

Figure 4. Histogram of grey scale values in the image shown in Figure 5D, class width is one unit. The histogram was generated with the image analysis package NIH image v1.61; note that in this package, 0 = white, and 255 = black. Dark shaded area is the histogram of grey values in the original image after the camera noise is ﬁltered out, the minimum value found is 162, the maximum is 214. Light shaded area represents grey scale values after scaling to increase contrast and brightness. Note that after scaling the distribution of grey values is no longer continuous, i.e., values in between the spikes in the histogram do not occur within the image.

(e.g., Seul et al. (2000)) for a more comprehensive discussion. Here we outline a simple method, which is sufﬁcient for many applications, and which does not result in loss of colour information in the image. The following transformation has been applied to the images in Figures 2, 5, and 6, for illustration purposes, as the original images were too dark to see the relevant features. The minimum value found in the histogram is subtracted from every pixel in the image (Fig. 4). All pixels are then multiplied by 255/(maximum-minimum), or a slightly smaller value. The effect is that the original colour values are scaled throughout the range of values that can be depicted (0 to 255), without any pixel going out of gamut. As a result, the original colour values can be reconstructed again, by applying the inverse transformation. It can be preferable to ignore those parts of the image for which colour information is not essential. For example, the image enhancement in Figure 6 is based on the maximum and minimum values within the area of the image where the sediment is displayed, ignoring the much lighter colour values in the tape measure alongside the core. If the purpose of the analysis is to compare a set of images to each other, then it is probably better not to use the maximum and minimum in an individual image, but to ﬁnd the maximum and minimum for the data set as a whole. Using those values for scaling ensures that originally identical colour values in different images are still comparable after the transformation.

IMAGE CALIBRATION, FILTERING, AND PROCESSING

43

Loss of information would occur if the enhancement operation produces pixels with values that are negative or larger than 255. Such values are replaced with 0 and 255 respectively, i.e., several light colours are all transformed into white, or several dark colours into black. Note, however, that contrast enhancement only changes the perception of the image but does not produce more information. Stretching a histogram will result in “empty values” (Fig. 4), which might be a problem for further processing, or imply additional processing. Colour information and calibration Introduction Colour can be expressed in a number of different co-ordinate systems that are designed for various applications. Colour in digital images is expressed in red, green, and blue (RGB) colour co-ordinates, which is the system used for televisions and computer screens. However, the RGB system is not the most suitable for presentation of palaeoenvironmental colour data. Indeed, the two important features for visual classiﬁcation of a colour are hue or tint (e.g., green) and lightness (e.g., dark green or light green). In RGB, each of the three co-ordinates is a combination of lightness and hue. Shades of grey are expressed by R = G = B, with black (R = G = B = 0) and white (R = G = B = 255) as the two extremes. The hue of a colour is determined by difference between the values of R, G, and B. As a result, it is difﬁcult to interpret the actual colour of an object from a plot of R, G, and B values (Fig. 7). The L∗ a∗ b∗ colour co-ordinate system is more appropriate to present colour information (or lightness/grey-scale) in numerical values, because it is designed to match human colour vision (Fig. 7). The L∗ a∗ b∗ colour system is deﬁned by the Commission Internationale de l’Éclairage (CIE L∗ a∗ b∗ ), the asterisks differentiate this system from its predecessor CIE Lab. A comprehensive discussion of this and other colour systems can be found in Berns (2000). We present the equations needed to translate RGB into grey-scale and L∗ a∗ b∗ coordinates, and describe a procedure to obtain calibrated colour values. The advantage of L∗ a∗ b∗ for interpreting colour data is that it distinguishes between light intensity and actual colour. L∗ describes lightness, its values can range between 0 (black) to 100 (white). The other two variables describe the actual colour, with a∗ representing green (negative values) or red (positive) and b∗ representing blue (negative) or yellow (positive values). Both a∗ and b∗ are zero when a colour is grey. Non-linear R G B An initial point to note is that many cameras use a non-linear version of RGB (R G B ) to render colour. In linear RGB, all values are a linear function of the amount of light (energy) received by the camera. In non-linear R G B , R = Rmax (R/Rmax)b , in which b is a constant, and Rmax is the maximum value that R can have (usually 255). G and B are similarly deﬁned. The value of the constant b depends on the speciﬁc camera. In display devices, the relation between input energy and brightness of the output on the screen is non-linear. The above transformation, or gamma-correction, is therefore applied to the

44

NEDERBRAGT, FRANCUS, BOLLMANN AND SOREGHAN

input signal, to ensure that the displayed image has the proper contrast and brightness. In theory, gamma correction should be done entirely within the computer. In practice, many cameras already perform a (partial) gamma correction on the images they produce. Such corrections are not necessarily unique to colour images. Digitising systems that produce grey-scale images can apply a similar non-linear transformation to the input light/energy intensity. The main problem for the purpose of this chapter is that the speciﬁcs of the RGB system used by a given camera are usually not provided by the manufacturer. However, a cameraspeciﬁc colour calibration function can be estimated by imaging a series of colour chips or tiles with pre-determined colour values. Figure 8 shows an example, how measured colour values in images of a Munsell soil colour chart have a non-linear relation with the known RGB values of those speciﬁc Munsell colours. The colour chart that was imaged in this case was a work-copy, in which colours have darkened with age. Similar data for a pristine chart can provide an estimate of the gamma-correction used in a speciﬁc camera, to allow translation of R G B values into linear RGB. Converting linear RGB to grey-scale and L∗ a∗ b∗ To translate linear RGB to both grey-scale and CIE L∗ a∗ b∗ , the RGB values are converted ﬁrst into CIE XY Z tristimulus values. In this system, Y (Luminance) represents lightness or grey-scale. X and Z contain the actual colour information. The XY Z system is a linear transform of RGB:       R X Xr Xg Xb  Y  =  Yr Yg Yb  · G , (1) B Zr Zg Zb Z where Xr , Yr , Zr , etc. represent camera-speciﬁc constants. Equation (1) is valid under the condition that a white-point calibration has been performed, to ensure that white as measured by the camera corresponds to a reference white. The most commonly used reference white is CIE D65 (viewed under a 2◦ angle), which was designed to represent pure white as seen by natural daylight (Appendix 1). Default constants can be inserted into equation (1), which are based on guidelines for colour representation in television-broadcasting (ITU-R 2002). They can be used when the constants cannot be determined more accurately for a speciﬁc camera, hoping that the camera was designed to adhere to the guidelines. Published defaults constants do not apply to the X, Y , and Z tristimulus values directly, but use the derived x, y, and z chromacity coordinates: x = X/(X +Y +Z), y = Y/(X +Y +Z) and z = Z/(X +Y +Z) = 1−(x +y). Only x and y are listed, as z is then determined (Table 2). Inserting the default constants into equation (1) and incorporating the translation from x and y into XY Z tristimulus values yield the following:       X 0.4124 0.3576 0.1805 R/Rmax  Y  = 0.2126 0.7152 0.0722 · G/Gmax . (2) Z 0.0193 0.1192 0.9505 B/Bmax The derivation of equation (2) is explained in SMPTE RP 177-1993 (1993). Note that the X, Y , and Z resulting from equation (2) are scaled to unity. The reference white point

IMAGE CALIBRATION, FILTERING, AND PROCESSING

45

Table 2. Constants used for translation of RGB values into XY Z tristimulus values, as recommended in ITU-R Recommendation BT.709-4 (ITU-R 2002). x

y

reference white (D65 2◦ )

xw

0.3127

yw

0.3290

primaries:

Red

xr

0.640

yr

0.330

Green

Xg

0.300

yg

0.600

Blue

xb

0.150

yb

0.060

(R = G = B = 255) yields X = 0.9505, Y = 1.00, and Z = 1.089 instead of the 95.05, 100, and 108.9 respectively, which are the values deﬁned for CIE White D65 (2◦ ). Only the Y -value obtained by equation (2) is used to transform a colour image into grey-scale. By deﬁnition, grey-scale is the Y -tristimulus value, or luminance, obtained from the RGB to XY Z transformation. Colour information is discarded by ignoring X and Z. Scaling Y to the range 0–255 needed for display on the screen, the transformation becomes: Y = 0.2126R + 0.7152G + 0.0722B.

(3)

Grey-scale values are thus a weighted average of the three RGB colours. The reason is that, at the same light intensity, green is perceived as brighter than red, which in turn is brighter than blue. Equation (3) yields a value of 255 for pure white. Note, however, that some software packages invert the scale for grey-value images, and use 0 for white, and 255 for black. One example of such a package is the image analysis program NIH image (developed at the U.S. National Institutes of Health and available on the Internet at http://rsb.info.nih.gov/nih-image/), which was used to generate several of the illustrations in this chapter (see Fig. 4). For applications where the full colour information is needed, the XY Z values can be translated further into CIE L∗ a∗ b∗ . The deﬁnitions are as follows (Berns 2000): 16 Y − (4.1) L∗ = 116 f Yn 116 Y X −f (4.2) a∗ = 500 f Xn Yn Z Y b∗ = 200 f −f (4.3) Yn Zn with f (Y /Yn ) = (Y/Yn )1/3 for Y/Yn > 0.008856 and f (Y /Yn ) = 7.787(Y/Yn )+16/116 for Y /Yn ≤ 0.008856; f (X/Xn ) and f (Z/Zn ) are deﬁned similarly. Xn , Yn , and Zn are the tristimulus values of a reference-white. The reference white to use in practice are those of D65, but scaled to unity, i.e., the XY Z values obtained from equation (2) for pure white in the RGB system (255, 255, 255). Note that the L∗ a∗ b∗ conversion can be applied to colour images directly, to create three separate grey-scale images that each render one of the co-ordinates. However, L∗ , a∗ , and

46

NEDERBRAGT, FRANCUS, BOLLMANN AND SOREGHAN

b∗ values will have to be scaled before they can be depicted on a computer screen. The equations can yield values in the range 0 to 100 for L∗ , −86.2 to 98.2 for a∗ , and −107.9 to 94.5 for b∗ . These values are not compatible with the range that computer images can have (0 to 255). Negative a∗ and b∗ values need to be scaled to positive values before they are assigned to an image, e.g., by adding 127 to all pixels (see contrast and brightness discussion earlier in this chapter). Colour calibration The colour transformations of equations 2, 3, and 4 yield relative values that are sufﬁcient in many applications to document patterns of change in colour. However, colour information in images that were collected over a longer period of time will show variation due to drift in camera calibration or ageing of the light source. It may therefore be necessary to calibrate colour values for precise comparison of different images. Examples of applications for which colour calibration is important are discussed in Nederbragt and Thurow (this volume) and Ortiz and O’Connel (this volume). The basis for colour calibration is that the data are in linear RGB. Colour calibration is then incorporated into the translation of linear RGB into XY Z tristimulus values. It requires that four chips with known colour values are imaged regularly, providing the information needed for calibration (see Appendix 1). Instead of using the default constants of equation (2), the actual constants are estimated for a particular camera using the colour values of the four colour chips. Modifying equation (1), the equation to translate RGB into XY Z becomes:         Xr Xg Xb X a R  Y  = b  +  Yr Yg Yb  · G , (5) c Z B Zr Zg Zb where the vector of constants a, b, and c is added to allow for an offset in the white-point calibration. In this equation, Xr , Yr , Zr , etc. represent a combination of camera speciﬁc constants and the aperture and speed of the camera. The twelve constants in this equation can then be solved, using the measured RGB values and the known XY Z values of the four colour chips. Standard photographic practice would suggest to use bright red, green, blue, and white colour chips or tiles. However, for the purpose of most palaeoenvironmental applications, it is better to use colours that are more similar in intensity to the actual objects that are measured. In particular, the use of a white chip creates the risk that the measured RGB values, which should be close to 255, run out of gamut (i.e., out of the range of values that can be depicted). If that is the case, information is lost that was needed for colour calibration. Writing out the matrix multiplication in equation (5), and rearranging the sets of linear equations yields, for the X-values of the four colour chips used:       a X1 1 R1 G1 B1 X2  1 R2 G2 B2   Xr   =  ·  , (6) X3  1 R3 G3 B3  Xg  X4 1 R4 G4 B4 Xb

IMAGE CALIBRATION, FILTERING, AND PROCESSING

47

where the numbers refer to one each of four different colour chips; R1 , G1 , B1 , R2 , G2 , etc., are the measured RGB values, and X1 , X2 , X3 , and X4 are the known X-tristimulus values of those four colours; and a, Xr , Xg , and Xb are 4 of the 12 constants in equation (5) that need to be solved. equation (6) represents a set of four linear equations with four unknown parameters, which can be solved with standard methods (Davis 1986). The Y and Z constants are solved in an equivalent manner (replace all X-s in equation (6) with Y and Z). Image processing Image enhancement Enhancement methods deal with highlighting some portions or components of an image. It involves modiﬁcation of pixel values to make the image easier to interpret visually and (or) to prepare it for measurement. In that respect, ﬁltering noise and modifying contrast and brightness of an image is part of image enhancement. However, making some feature of interest more evident is often performed at the expense of other features, and hence some information is lost. There is no standard enhancement method, because the choice of method will depend primarily upon the nature of the image and its subject, as well as the task needed to be performed by the imaging technique. Noise removal In addition to noise introduced by the instrument itself (hardware noise), most geologic materials are non-homogeneous, even within single phases. The strategy to remove hardware noise, which can be systematic in nature, might be different from the one to smooth nonhomogeneous material, i.e., parts of the image with variable intensities that are presumably part of the same phase. In ﬁltering noise from images, the underlying assumption is that a single pixel in an image is much smaller than any important detail within that image, hence a neighbouring pixel is likely to belong to the same domain (e.g., a grain, Russ (1999)). This allows for some form of averaging of neighbouring pixels to reduce random noise (Fig. 9). A number of studies have evaluated various types of ﬁlters to determine optimal noise reduction while maintaining the most details of interest (e.g., Starkey and Samantary (1991), Russ (1999)). In most cases the ﬁlters consist of a square array of numbers (a kernel, with dimension 3 × 3, or 5 × 5, etc.), which forms a multiplier that is applied to each pixel and its adjacent neighbours. This array is moved pixel by pixel across the entire image (Fig. 10). The ﬁlter replaces the intensity of the central pixel with the average of the values speciﬁed by multiplying kernels. Filters can also have various or non-uniform multipliers, such that the range of possible ﬁlters is extremely large (Russ 1995). Averaging ﬁlters, however, have disadvantages, particularly when grain boundaries or lamination morphology are of interest. Because several pixel values are averaged, boundaries are typically blurred and can be displaced relative to the original position, while the noise is still visible (Fig. 5B). Further, these types of ﬁlters can also create “pseudo resolution” in that the ﬁltering process produces artiﬁcial domains, or connections between

48

NEDERBRAGT, FRANCUS, BOLLMANN AND SOREGHAN

Figure 5. An example of ﬁltering to remove camera noise. A) Image of a laminated sediment with dark and light, one-pixel wide vertical streaks; shown is a grey scale translation of an image originally acquired in colour. Note that contrast and brightness were enhanced to illustrate the lamination pattern more clearly. B) After four applications of a 3 × 3 average ﬁlter, the streaks are still visible while the image as a whole is becoming blurred. C) One application of a 3 × 3 median ﬁlter removes the noise successfully. D) A 1 × 3 horizontal median ﬁlter is also sufﬁcient to remove the noise, while at the same time minimising alteration of the original image.

originally discrete regions (Russ 1999). Therefore, smoothing of the image, which is one of the basic operations offered in image analysis software, is usually the least desirable solution, because it is a irreversible operation. Related ﬁlters, called median ﬁlters and hybrid-median ﬁlters, ﬁnd the median value of a pixel and its adjacent neighbours after ranking these values. The ﬁlter then replaces the original pixel value with the median value (Fig. 9). This process is particularly good for removing pixel-scale noise (“shot noise”) and has the added advantage of not displacing or blurring distinct boundaries, such that the ﬁlters can be applied repeatedly (Huang et al. 1979; Russ 1999). Because it discards the extreme values, a median ﬁlter is often more successful in removing noise without substantially altering the information in the image.

IMAGE CALIBRATION, FILTERING, AND PROCESSING

49

Figure 6. Filtering of an image of laminated sediments, which was collected by a line-scan camera in an experimental stage of development. A) Grey scale translation of an image originally collected in colour, note that contrast and brightness were enhanced to illustrate the lamination pattern more clearly. B) Enlargement showing the detailed structure of the noise. C) Same image after ﬁltering. Horizontal black lines, which represent failure of the camera during the occasional line scan, are ﬁltered out with a 3 × 1 vertical median ﬁlter. In the grey bands, which represent systematic camera noise, pixels in odd columns are persistently darker than their neighbours. The grey bands were removed by replacing pixels in odd columns with the average of their horizontally adjoining neighbours.

Finding the optimum ﬁlter may require some experimentation (Francus and Pirard, this volume). Here, we illustrate in Figures 5 and 6 how hardware noise can be ﬁltered with minimum effect on the information in the image. The image in Figure 5 contains vertical streaks that the camera produced occasionally, possibly due to overheating. A three-point horizontal median ﬁlter is actually sufﬁcient to remove the streaks, which are vertical and only one pixel wide. The advantage of a horizontal ﬁlter in this case it that there is no change of information along the vertical axis, i.e., in the stratigraphic direction. The example in Figure 6 was taken with a line scan camera that was still in an experimental stage. The one pixel wide black lines across the image, which represent camera failure during the occasional single line scan, are removed with a vertical 3-point median ﬁlter. However, neither average nor median ﬁlters will work to remove the dark banding in the image. In those dark bands, every other pixel is darker than average. Used in this case is the fact that the dark pixels always occur in the odd columns. A macro was written to replace the pixels in odd vertical lines by the average of the two horizontally adjoining pixels, leaving the even columns as they were. The removal of the noise intrinsic to a non-homogeneous sample is technically conducted in a similar way. In hardware noise removal, one took care to keep the alteration of the original image to a minimum. However, the aim here is to make features of interest more visible (or to enhance them). This time it can be done at the expense of other characteristics of the image. For instance, a powerful smoothing ﬁlter (e.g., Gaussian blur) (Fig. 10) could be the only option to make uniform the intensities of the pixels belonging to an nonhomogeneous phase. We have seen before that such a ﬁlter can obliterate the boundaries of features of interest. However, the original image, or its duplicate, still contains pristine information about the position of the edges of these features.

50

NEDERBRAGT, FRANCUS, BOLLMANN AND SOREGHAN

Figure 7. Digital image of a core section of Albian sediments collected by ODP (Section 1049C-13X-1; Norris et al. (1998)) with sediment colour expressed in RGB and L∗ a∗ b∗ co-ordinates. The image is a grey-scale translation of a colour original; the sediments vary in colour from light brown (medium-grey in this ﬁgure) to very light grey or white. The RGB data were collected from the colour version of the image using NIH-image v1.60, and translated into L∗ a∗ b∗ with equation (2) in the main text. In RGB, the three colour co-ordinates show a very similar pattern, which mainly reﬂects dark-light ﬂuctuations; it is virtually impossible to read from the plot that there is a change in actual colour from brown to grey. In L∗ a∗ b∗ , L∗ shows the ﬂuctuations between light and dark, while the colour change can be read from a∗ and b∗ . Dark intervals (low L∗ ) have more strongly positive values for a∗ (more red) and b∗ (more yellow), which together represent brown (or orange). See text for further discussion of the RGB and L∗ a∗ b∗ co-ordinate systems.

IMAGE CALIBRATION, FILTERING, AND PROCESSING

51

Figure 8. Cross plot of RGB values of the colour chips in a Munsell soil chart as measured in a set of digital colour images and the RGB values that are deﬁned for those speciﬁc colours. Note that the non-linear relation between measured and theoretical RGB values is the result of a gamma-correction performed by the camera.

Edge detection Edge detection operations are useful to outline a grain in a matrix, to delineate the limits between two phases, or to reveal structural boundaries such as those between laminae. There are several techniques that allow for edge detection. An edge detection function is built in all image analysis packages, and the software documentation should specify which technique is used. Here we outline three of the most common edge detectors but the reader is referred to image analysis textbooks (e.g., Russ (1999), Seul et al. (2000)) for further discussion. Sobel edge detection (Sobel 1970) generates derivatives in two perpendicular directions, which are combined subsequently, e.g., by taking the square root of the sum of the squared derivatives (Fig. 10). Laplacian operators (Russ 1999) subtract the intensity value of each neighbouring pixels from the central pixel. In a region of the image that is homogenous the result of applying this kernel is to reduce pixel intensities to 0. If a discontinuity is present, the

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Figure 9. Result of the application of ﬁltering operations on an original array (A) in an 8-bits image; (B) result of an averaging ﬁlter: the central pixel is turned to the mean of all nine pixel values; (C) result of a median ﬁlter: the central pixel is replaced with the median intensity value of all pixel values; (D) result of a hybrid median ﬁlter: the ﬁlter compute ﬁrst the median of the 5 pixels making an X; then the median of the 5 pixels making an +. Finally, it attributes to the central pixel the value of the median of the central pixel and the two previously computed medians. Note that the hybrid-median ﬁlter does somewhat preserve the light diagonal line present in the original (pixels with values 96, 10, 15 in A).

result is a value different from 0, either positive or negative. The resulting values must be “normalised” between 0 and 255 after the operation to make the detection visible (Fig. 10). Kirsch operators (Kirsch 1971) apply each of the eight possible orientations of a derivative kernel and keep the maximum value (Fig. 10). Derivatives are obtained using kernels as shown in Figure 10. As with ﬁltering kernels, a wide variety of derivative kernels is possible by varying the coefﬁcients. Large kernels are less sensitive to noise by averaging several pixels and reduce image shift. Image math In image math, the intensity of a pixel in an output image is computed from the intensities of the corresponding pixel in two or more input images. Because the operation is performed on a pixel-by-pixel basis, images need to be exactly identical in terms of number of pixels in each row and column. In general, image math is used on images of the same ﬁeld of view, imaged with different detectors (e.g., in remote sensing), with different lighting (Fueten et al. 1997), or from the same original image, processed differently to enhance different features of the image, and ﬁnally recombined together (Soreghan and Francus, this volume). Possible operations are numerous and the most usual include addition, subtraction, multiplication, division, as well as logical operations (Boolean operators). Image segmentation Segmentation refers to the identiﬁcation and selection of features of interest (Russ 1999). Thresholding, or binary segmentation, refers to the subsequent process of eliminating all features except those of interest for ease of analysis. It transforms a grey-level image into a binary (i.e., black and white) image, in which black pixels represent the features of interest and white pixels are the background (or vice versa).

IMAGE CALIBRATION, FILTERING, AND PROCESSING

B.

53

B1

+1 +2 +1

0 0 0

-1 -2 -1

+1 0 -1

+2 0 -2

+1 0 -1

B2

-1 -1 -1

-1 8 -1

B3

+1 +1 +1

0 0 0

-1 -1 -1

+1 +1 0

+1 0 -1

0 -1 -1

+1 0 -1

+1 0 -1

+1 0 -1 etc...

B4

1 1 2 2 2 1 1

2 2 4 8 4 2 2

1 2 2 4 2 2 1

1 2 2 4 2 2 1

2 2 2 4 4 8 8 16 4 8 2 4 2 2

-1 -1 -1

1 1 2 2 2 1 1

Figure 10. Example of kernels used for image ﬁltering. A. Contrast kernel: each pixel value is set to the mean of its value and those of the 8 nearest pixels, weighted by the coefﬁcients of the kernel. In this case (−204 − 177 − 96 − 151 + 90 − 155 − 15 − 246 − 168)/9 = −124.6, which is set to 0 as the minimum value of the gamut. Note that a mean ﬁlter is simply the result of the multiplication of a kernel having all coefﬁcients = 1. B. Examples of other kernels. B1. Vertical and horizontal convolution used for Sobel Edge detection; B2: Laplacian Operator; B3: three of the eight kernels used to calculate a Kirsch operator; B4: 7 × 7 Gaussian blur.

The thresholding value is usually selected subjectively, by adjusting a slider along a grey scale that marks interactively which pixels are selected in the ﬁeld of view. The selection can also be done directly on an intensity histogram. Since peaks usually represent the homogeneous regions in the image, threshold level is often set in the trough between two populations of pixels in the intensity histogram. Automated methods to adjust threshold settings (e.g., entropy, factorisation, compacity and moment techniques) analyse the histogram of intensities or the image itself (Sahoo et al. 1988). The reader is referred to more specialised textbooks for further information on automated methods (e.g., Gonzalez and Woods (2002)). In the case of multiple-band images, such as colour images, it may be possible to classify features of interest based on differences in intensities in each band: objects that are indistinguishable in one colour band, maybe fully distinct in another (Pirard and Bertholet 2000). Another segmentation technique is the maximum likelihood classiﬁer, which is used mainly in remote sensing, but has been used successfully to distinguish different mineral

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phases in BSE images (Tovey and Kringsley 1991). Finally, classiﬁcation procedures based on the internal texture of the features of interest are also possible (see Soreghan and Francus (this volume)). Processing binary images Once the image is thresholded (made binary), it may still be necessary to perform additional operations before it is possible to proceed with measurements. The type of operations that is applied most extensively to binary images is referred to as morphological procedures (Serra 1982). They change pixels from black to white (or from white to black) based on the value of adjacent pixels. They are essentially similar to the neighbour operations used in kernel ﬁltering, but they are simpler because the pixel values can be 0 or 1 only. Hereafter our convention is to equate black with object and white with background. Erosion, dilation, opening and closing Erosion. Erosion turns a black pixel to white when the black pixel has n white neighbours (n is between 1 and 8). By varying n, one can change the efﬁciency of the erosion, n = 1 being the strongest erosion. Erosion allows for elimination of spurious pixels, particularly at grain boundaries or pixels that occur as isolated noise (i.e., isolated pixels or small group of pixels). It can also separate grains that have been joined artiﬁcially through other ﬁltering processes (Fig. 11). Dilation. Dilation whereby a white pixel is changed to black when it touches n black neighbours, is the opposite process. Dilation is performed to connect discontinuous objects and ﬁll in holes (Fig. 11). Since erosion and dilation are processes that eliminate or add pixels from object boundaries, they alter the surface area of the object. To account for that modiﬁcation of size, many authors use opening and closing. Opening is erosion followed by dilation, which smoothes objects and removes isolated pixels. Closing consists of dilation followed by erosion, and smoothes objects and ﬁlls small holes. However, after opening and closing, objects do not revert to their original shape. The resulting shape is strongly inﬂuenced by the shape of the kernel (square) used in the operation. For instance, a circle will turn to an octagon after several openings. It is therefore advisable not to use such operations if the ﬁnal goal is to study the shape of the features of interest. A classic example of using morphological methods is provided by Ehrlich et al. (1984; 1991) who describe the application of a series of erosions, dilations and openings to estimate size distributions and porosity in sandstones. Euclidean distance maps and watershed segmentation It is usually also necessary to separate touching objects in a binary image. This is probably the most difﬁcult task in image analysis, especially when the objects are variable in size and shape. We outline here one separation method, but the reader is also referred to specialised papers (e.g., van den Berg et al. (2002)). From a binary image, it is possible to create an euclidean distance map (EDM): each pixel of an object is replaced by an intensity value proportional to the distance between that pixel and the nearest boundary (Fig. 12). When two features are touching each other, the EDM will display two maxima, or two peaks (Fig. 12b). After that, a watershed segmentation

IMAGE CALIBRATION, FILTERING, AND PROCESSING

55

A. B. i

g

i

C.

i

D.

g

g erosion

dilation

Figure 11. Effect of erosion and dilation on binary images. A. Binary image of a Pleistocene sediment from Lake Vico at 335 cm core depth, scale bar is 100 µm; black pixels represents clastic grains. Image of a 25 µm thick covered thin section with a petrographic microscope @ 100 magniﬁcation, crossed-polarised light. Digitised on a Kodak Photo-CD, resolution is 0.94 pixel/µm. The original grey-scale image has been processed using NIH-Image v1.61, with the following functions: enhance contrast, apply LUT, median, sharpen, median, add constant (1), Autothreshold, Invert, Make Binary, Apply LUT to obtain the binary image displayed in A. B. Zoom in of A. C. Erosion with n = 4 and 2 iterations: grains (g) have been separated, and irregularities (i) at the boundary of grains are disappearing; note the change in the size of the grains. D. Dilation with n = 4 and 2 iterations: grains (g) have been joined, and irregularities (i) have been ﬁlled in.

algorithm will ﬁnd the low between the two maxima and draw a cut between the touching objects, turning 1 line of pixels to white. Watershed segmentation works well for rounded and convex objects. However, it performs erroneous separations with elongated objects (Fig. 12). Metadata The examples above illustrate clearly that there are many different approaches to obtain results in image analysis procedure. Results may often look similar even when they are not the same in detail. Therefore, in order to ensure reproducibility of the results, we advocate a

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Figure 12. Example of a binary image with black grains on a white background (A), and a euclidean distance map (B) and subsequent watershed segmentation (C) performed on (A). Note that the watershed segmentation separates round and convex object effectively, but performs erroneous cuts on elongated objects.

detailed speciﬁcation of the algorithms used in the procedure. For example it is not sufﬁcient to state “we used an edge detection algorithm”, but rather “a Sobel edge detection with a +1 0 −1 +2 0 −2 +1 0 −1

kernel”. The caption of Figure 11 provides another example of a comprehensive

description of the methods that were used to generate results. Summary In this chapter we discussed image calibration, ﬁltering, and processing techniques, which are used to prepare an image for subsequent data extraction and analysis. Size measurements from a digital image are calibrated by imaging objects with a known size. Pixel intensity is a measure for the composition of the imaged object and can be calibrated by imaging objects with known composition. Methods depend on the type of material and imaging technique. We discuss colour calibration, as colour is one of the most widely used types of data in image analysis. Filtering is performed on an image to remove artefacts that are unrelated to the object of study. The challenge is to ﬁnd the best ﬁlter, one that removes all noise with minimum change to the actual information in the image. Described are techniques to remove the effects caused by uneven illumination during imaging, and methods to ﬁlter camera related noise. Image processing involves modiﬁcation and/or enhancement of the image in such a way that the required numerical data can be extracted more easily. Processing techniques that are outlined include edge detection, segmentation, and processing of binary images. Acknowledgments Thanks are due to H. Lamb, S. Lamoureux, and A. Pepper for helpful suggestions to improve the manuscript. The methods described in this paper have been developed as part of research by AJN that was supported by various grants from the Natural Environmental Research Council. PF was supported by the University of Massachusetts.

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Appendix. Colour calibration tools The most accurate tools for colour calibration are purpose made ceramic tiles with a very accurately determined colour composition. We know of only one organisation from which such tiles can be obtained, i.e., British Ceramic Research Ltd (trading name CERAM, web address www.ceram.co.uk, formerly named British Ceramic Research Association Ltd). They can provide tiles in various reference whites (e.g., CIE D65) as well as sets of tiles in various colours. Another service they provide is to measure the colour of objects sent to them. A reference card with the “four colour chips with known colours” discussed in the text can be constructed, e.g., from pieces of four sheets of coloured cardboard which were sent to CERAM to have their colour determined. References ASTM Committee E-4, 2002. Standard Guide for Calibrating Reticles and Light Microscope Magniﬁcation, Designation E 1951-01, Annual Book of ASTM Standards, Vol. 03.01: 1182–1188. ASTM Committee F-1, 1997. Standard Practice for Preparing an Optical Microscope for Dimensional Measurements. Annual Book of ASTM Standards, Designation F 728-81, Vol. 10.05: 325–329. ASTM Committee E-4, 1993. Standard Practice for Calibrating the Magniﬁcation of a Scanning Electron Microscope, Designation E 766-93, Annual Book of ASTM Standards, Vol. 03.01: 614–61. Berns R.S. 2000. Billmeyer and Saltzman Principles of Color Technology. Wiley, New York, 247 pp. Boespﬂug X., Ross N., Long B.F.N. and Dumais J.F. 1994. Tomodensitométrie axiale: relation entre l’intensité tomographique et la densité de la matière. Can. J. Earth Sci. 31: 426–434. Bollmann J., Henderiks J. and Brabec B. 2002. Calibration of Gephyrocapsa coccolith abundance in Holocene sediments for paleotemperature assessment. Paleoceanography 17: 7–1 to 7–9. Davis J.C. 1986. Statistics and Data Analysis in Geology. John Wiley & Sons, New York, 646 pp. Ehrlich R., Kennedy S.K., Crabtree S.J. and Cannon R.L. 1984. Petrographic image-analysis 1. Analysis of reservoir pore complexes. J. Sed. Petrol. 54: 1365–1378. Ehrlich R., Crabtree S.J., Horkowitz K.O. and Horkowitz J.P. 1991. Petrography and reservoir physics 1. Objective classiﬁcation of reservoir porosity. AAPG Bull.-Am. Assoc. Petrol. Geol. 75: 1547– 1562. Fueten F. 1997. A computer-controlled rotating polarizer stage for the petrographic microscope. Comp. Geosci. 23: 203–208. Gonzalez R.C and Woods R.E. 2002. Digital Image Processing. Addison-Wesley Pub Co, 793 pp. Hecht E. 1998. Optics. Addision Wesley, Bonn, 717 pp. Huang T.S., Yang G.J. and Tang G.Y. 1979. A fast two-dimensional median ﬁltering algorithm. IEEE Trans. Acoust. Speech Signal Process. ASSP-27: 13–18. ITU-R. 2002. Recommendation BT.709-4: Parameter Values for the HDTV Standards for Production and International Programme Exchange. International Telecommunication Union Radiocommunication Sector, Geneva, 32 p. Jongmans D., Pirard E. and Marsh S. 2001. Geological application of digital imaging. Comp. Geosci. 27: 1015–1017. Kirsch R. 1971. Computer determination of the constituent structures of biological images. Comp. Biomed. Res. 4: 315–328. Norris R.D., Kroon D. and Klaus A. 1998. Proc. ODP, Init. Repts., 171B, College Station, TX (Ocean Drilling Program). Lee R.E. 1993. Scanning Electron Microscopy and X-ray Microanalysis. Prentice Hall, Englewood Cliffs, New Jersey, 458 pp.

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Pirard E. and Bertholet V. 2000. Segmentation of multispectral images in optical metallography. Rev. Metall.-Cah. Inf. Techn. 97: 219–227. Russ J.C. 1995. Thresholding images. J. Comp.-Assist. Microsc. 7: 141–164. Russ J.C. 1999. The Image Processing Handbook. CRC Press, Boca Raton, 771 pp. Sahoo P.K., Soltani S., Wong A.K.C. and Chen Y.C. 1988. A Survey of Thresholding Techniques. Comp. Vis. Graph. Image Process. 41: 233–260. Schaaf M. and Thurow J. 1994. A fast and easy method to derive highest-resolution time-series data sets from drillcores and rock samples. Sed. Geol. 94: 1–10. Serra J. 1982. Image Analysis and Mathematical Morphology. Academic Press, London, 610 pp. Seul M., O’Gorman L. and Sammon M.J. 2000. Practical Algorithms for Image Analysis: Description, Examples, and Code. Cambridge University Press, Cambridge, New York, 295 pp. SMPTE RP 177-1993 1993. Derivation of Basic Television Color Equations. Society of Motion Picture and Television Engineers, White Plains, NY, 4 pp. Sobel I. 1970. Camera Models and Machine Perception. AIM-21. Stanford Artiﬁcial Intelligence Lab, Palo Alto. Starkey J. and SamantarayA.K. 1991.An evaluation of noise reduction ﬁlters, with particular reference to petrographic images. J. Comp.-Assist. Microsc. 3: 171–188. Tovey N.K. and Krinsley D.H. 1991. Mineralogical mapping of scanning electron-micrographs. Sed. Geol. 75: 109–123. van den Berg E.H., Meesters A., Kenter J.A.M. and Schlager W. 2002. Automated separation of touching grains in digital images of thin sections. Comp. Geosci. 28: 179–190.

4. IMAGE MEASUREMENTS

ERIC PIRARD ([email protected])

Département GeomaC - Géoressources Minérales Université de Liège Sart Tilman B52/3 4000 Liège Belgium Keywords: Statistics, Color, Diameter, Mathematical morphology, Stereology, Size, Shape, Roundness, Covariance

Introduction Following the previous chapters dealing with image acquisition and image processing, this contribution makes an overview of the image measurements that are mostly relevant for paleoenvironmental studies. After having explained basic notions of sampling theory linked to the ﬁeld of image acquisition, this chapter reviews some of the most essential parameters available for proper characterization of the image content. A particular emphasis is put on the analysis of image intensities (grey levels, colors) and individual objects (size, shape, orientation). More advanced concepts related to structural or textural analysis could not ﬁnd place in this chapter and are only brieﬂy commented. Digital imaging and sampling theory It is not well recognized that statistical considerations are central to image based measurements. However, considering that pixels are picture elements and, as such, samples of a real picture, and considering moreover that images are very often only but a part of the scene under study, it appears obvious that digital imaging somehow conceals a sampling strategy. The basic requirement for any sampling procedure to be representative cannot be neglected, and it is therefore useful to start by trying to bridge the gap between the statistical vocabulary and the image processing terminology. For more detailed discussions, the reader can refer to basic textbooks in statistical analysis, but he should be aware that images deal with samples in space and as such do refer to the ﬁeld of spatial statistics (Cressie 1993). This ﬁeld is rarely found in introductory textbooks, but is well worth reading for those who want to investigate the statistical nature of images in depth. 59 P. Francus (ed.) 2004. Image Analysis, Sediments and Paleoenvironments. Kluwer Academic Publishers, Dordrecht, The Netherlands.

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Deﬁning the scope of the study Statisticians often refer to a bag with black and white marbles when having to introduce the basic concepts of sampling. This is however an oversimpliﬁed situation for geologists dealing with the analysis of a sediment or the characterization of a given fossil. Indeed, the very ﬁrst questions to be answered are “What is the object of my investigation? What do I want to characterize with my measures?”. Hence, two concepts have to be clariﬁed before even building the experimental setup: Field and Universe. The ﬁeld of study The ﬁeld is the spatial extension within which measures have to be taken. The dimensions of the ﬁeld may appear explicitly (a single fossil specimen, a black lamina of sediments, . . .) or may rely on a more subjective deﬁnition (a 3 cm thick varve sequence, . . .). Sometimes the ﬁeld of study is clearly limited by commercial or technical constraints (a given sedimentary sequence within a limited mining concession, that part of a sedimentary sequence that can be recovered without loss, . . .). The universe under study The universe is the source of all possible measures within the ﬁeld of study. In that sense a universe is deﬁned by the nature of the measure to be performed. Hence, considering measures of biogenic carbonates in a given sedimentary sequence, the universe is the set of all possible measures of biogenic carbonate contents. A logical consequence of this deﬁnition is that porosimetry on the same sedimentary sequence shares the same ﬁeld but refers to another universe (the set of all possible porosimetric measurements). Dealing with the available information Whatever the ﬁeld of view, digital images are made out of pixels. These picture elements are the elementary building blocks of a digital image, and as such, represent samples of the original scene. Obviously information has been lost during capture and digitization of the video signal so that each pixel only refers to a limited region of space. The support In the classical terminology of spatial statistics the support refers to the spatial extension on which a measure is performed. The support is often very small and almost always negligible with respect to the ﬁeld of study. In the particular case of digital imaging, the spatial extension (support) of a picture element is clearly related to the resolution of the imaging device and to the magniﬁcation that is being used. Taking digital pictures of a 2 mm large ﬁeld of view with a 1300 columns CCD means working with a theoretical resolution of about 1.54 µm. The support, in the sense that it refers to the region emitting light integrated by a single element of the CCD, is an important notion in digital imaging.

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The sample In the present context, the word sample will be used for indicating the measure itself as performed on the support. Typically, with CCD cameras, we refer to the amount of photons emitted by the sample. Depending on the mode of observation this can be, of course, transmitted white light or diffuse reﬂectance at 639 nm etc. For the sake of clarity, we will speak in this chapter of “intensity” in a broad sense when referring to the measure carried by a pixel. Nested sampling Considering that most problems in image analysis do not deal with the characterization of a single image, it becomes evident that image analysis often implies nested sampling strategies. In other words, pixels are samples of an image, images themselves are samples of a thin section, thin sections are samples of a core and cores are samples taken from a sediment (Fig. 1). The reader should therefore be aware that all comments made on sampling and representativity at the pixel level should be extended to each one of these four nested sampling strategies. If this does not completely ruin the accuracy of the analytical results, it must at least produce humility in every scientist who interprets the results.

Figure 1. Image analysis is always a multiple sampling problem. A piece of core is sampled into several thin sections, sections are sampled into a series of images and digital images themselves are the result of a sampling process at the pixel level.

The population The population is best deﬁned as the set of all possible measures in the universe. This explicitly refers both to the nature of the measure and to the support used for sampling. In other words, distributions of intensities measured on the same ﬁeld of view but taken at different magniﬁcations with the same camera will indicate differences (thus underlining the existence of different populations). The modiﬁcation of distribution laws with magniﬁcation is as essential in image analysis as it is in most geological problems. The major consequence of this is that one cannot mix samples with different supports (e.g., images of different magniﬁcations) unless it has been demonstrated that the difference in sample distribution is negligible. This problem is designated as the “change of support” problem and is too often underestimated. By deﬁnition, the whole population is never accessed and it is the main goal of statistics to infer properties at the population level from a limited collection of samples. In the following paragraphs, we will mainly focus on the problem of estimating properties at the

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image level from observations at the pixel level. The next steps, from images to samples and samples to sediments are left to the reader. Digital image analysis strategies Blobs, textons and textures A central step in image analysis is to decide from the beginning, whether the description of a scene can be decomposed into the spatial arrangement of elementary objects and what these objects are. For many quantitative petrologists (Grifﬁths 1988), a sediment can be described conceptually by specifying the nature, size, shape, orientation and dispersion of individual grains. However, it is not hard to imagine situations where nothing such as a grain, a crystal, a fossil. . . or, in generic terms, a blob appears in the image. This is particularly evident at macroscopic scale with very ﬁne-grained material (consider chalk, lava, mudstone, micritic limestone, etc. . . .). By taking a closer look at such material it might appear however that the texture as observed at a given scale is somehow statistically repeated at regular intervals to produce the global texture. This situation is characteristic of all wallpapers and applies to a certain extent, and in a statistical sense, to natural objects. In the latter case, one would speak about texton arrangements. A texton being a textural primitive not necessarily corresponding to a geological event or body. Finally one also has to face problems where neither blobs nor textons emerge from the image. In that case the description of a texture cannot rely on the arrangement of primitives, and it has to start from the spatial relationships existing between pixels or arbitrary groups of pixels (e.g., 3 × 3 neighborhoods). Typology of digital image analysis tools A systematic presentation of image analysis techniques is not as straightforward as it may seem, particularly because the image content may be very diverse. However, from the above discussion about blobs and textures and by limiting ourselves to most problems dealt with in sedimentology, it appears judicious to split analytical problems into the following groups: -

Intensity analysis: statistical computations of parameters from pixel intensities (e.g., average color within an image, variance of light transmittance within a single crystal, . . .).

-

Blob analysis: computation of geometrical descriptors (size, shape, . . .) for selected geological objects (e.g., size of sand grains, width of fractures, . . .).

-

Structural analysis: computation of spatial relationships between geological objects (e.g., preferential orientation of grains in a sediment, average distance between pores, . . .).

-

Textural analysis: computation of spatial relationships within geological objects (e.g., characterization of gray level patterns within spores, identiﬁcation of zonation patterns within grains, . . .).

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Some of the most important image analysis tools will be exempliﬁed in the following paragraphs with the notable exception of textural analysis. For this important and still challenging ﬁeld of work, the reader is referred to more specialized papers (Haralick and Shapiro 1985). Intensity and color analysis Global vs. local vs. regional analyses It appears rather exceptional that the image frame exactly corresponds to the limits of the ﬁeld whose properties have to be analyzed (global analysis). More often, the analysis will have to be performed at a local or regional level. By local, we mean a neighborhood whose limits are deﬁned by the user himself (subjective), whereas by regional we mean the limits of a geometrical domain delimited by the characteristics of the image content (objective) (Fig. 2).

Figure 2. Backscattered electron image of a chalk aiming to visualize micron sized pores. Global average gray level of the entire image: 138; Local gray level averages within selected neighborhoods from top to bottom: 136, 132, 88; Regional gray level average within a given mask: 132.

Estimating mean and variance of intensities A collection of pixel intensities {p1 , p2 , . . . , pN } is best represented by a gray level histogram. Such a representation can be described at ﬁrst glance by a magnitude parameter (position of the histogram along the intensity axis) and a dispersion parameter (scattering of observations with respect to the magnitude). The most popular ways to quantify these

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parameters are: - the arithmetic mean: p¯ =

i=N 1 pi N

(1)

i=N 2 1

pi − p¯ . N

(2)

i=1

- the variance: σp2 = σpp =

i=1

It is not superﬂuous to remind the reader that both parameters are particularly suited for normal (Gaussian) distributions, but start to become less adequate when dealing with skewed distributions. For asymmetric distributions, the geometric mean or the median are often a better choice. Estimating mean and variance for colors Color can be considered as the human perception of a spectral reﬂectance/transmittance curve in the visible wavelength range. Due to the limitations of human vision, color is rendered in video imaging using three basic ﬁlters in the red (R), green (G) and blue (B) regions of the spectrum, hence delivering a triplet of intensities for each pixel {ri , gi , bi } (Fig. 3). Obviously means can be computed from the set of intensities within each channel, delivering the following triplet of means:

r¯ , g, ¯ b¯

with

r¯ =

i=N 1 ri N

etc.

(3)

i=1

and variances: {σrr , σgg , σbb }

with

σrr = σr2 =

i=N 1 (ri − r¯ )2 N

etc.

(4)

i=1

The ﬁrst triplet can be regarded as the center of gravity of the cloud of pixels within the RGB space, whereas each variance term must be thought of as the expression of a dispersion along each axis. Intuitively a third measure can be derived to express the trend of the cloud of pixels to form an elliptical shape rather than being scattered randomly in the RGB space. This term is the covariance triplet: {σrg , σrb , σgb } with

σrg =

i=N 1 (ri − r¯ )(gi − g) ¯ etc. N

(5)

i=1

Again, the reader is referred to basic textbooks in multivariate statistics to get an indepth understanding of these theoretical concepts. It is worth, however, insisting on the fact that such parameters are best suited for ellipsoidal geometries of pixel distributions and will not work properly if two or more distinct clusters do exist in the color space.

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Figure 3. A color image as perceived by the human eye can be split into its three components Red, Green and Blue. Each pixel can be mapped in an RGB space wherein pixels belonging to a similar mineral specie plot as clusters.

Comparing intensities and colors of objects Testing similarities in color or intensities between objects is an essential topic in image analysis that relates to the classical statistical test between samples. For the sake of simpliﬁcation we will again assume normality of intensity distributions and brieﬂy recall the tests that apply in such situations. Basically, comparing gray level intensities of objects is like comparing two histograms with different shapes. The simple difference between means expresses how distant they are from each other without taking into account their spreading. A more valuable expression of the distance between histograms should take the variance into account. Considering the simple case where gray level distributions of two objects have different mean intensities p¯ 1 and p¯ 2 but have the same variance σ , the distance between the object’s intensities can be expressed by testing: |p¯ 1 − p¯ 2 | t< √ (6) σ/ 1/N1 + 1/N2 against the Student t distribution with N1 + N2 degrees of freedom. N1 : number of pixels (area) of object 1 N2 : number of pixels (area) of object 2. When dealing with colors of pixels, a generalization of this leads to the concept of Mahalanobis distance to express the distance (discrimination) between objects in color space: Dp = (µ1 − µ2 )T · −1 · (µ1 − µ2 ) (7) µ1 : mean vector of the ﬁrst population µ2 : mean vector of the second population : covariance matrix for all variables. In RGB space, this becomes:    T r¯1 r¯2           Dp = g¯ 1  − g¯ 2   b¯1 b¯2



−1     r¯1 r¯2            σgb  · g¯ 1  − g¯ 2   . b¯1 b¯2 σbb

σrr σrg σrb

 · σgr σgg σbr σbg

(8)

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Nevertheless, the mathematical qualities of such distance measure are only one aspect of the qualities required for a quantitative measure. It is essential to relate to the physical signiﬁcance of such a measure. In practice, distances between objects in an {R,G,B} space are easily computed, but they cannot be interpreted in terms of human perception. In other words, the same value of a Mahalanobis distance in the purple region or in the light green region does not express the same visual perception of a difference. Color transforms have been proposed to take this into account and notably the L∗ -a∗ -b∗ transform (Hunt 1991; Nederbragt et al., this volume). Applying such a transform does not affect the contrast between objects in terms of image analysis, but makes it more suitable for computation if the goal is to measure a perceptual difference. A classical measure of the perceptual difference between two pixels in the L∗ a∗ b∗ space is given straightforwardly by the Euclidean distance: E =

(L1 ∗ − L2 ∗ )2 + (a1 ∗ − a2 ∗ )2 + (b1 ∗ − b2 ∗ )2 .

(9)

It must be clear to the reader that computations of color transforms are not required if the goal is to differentiate objects without any reference to the human perception of a difference in color. Spatial trend analysis of variances and means In the previous paragraph, we have been dealing with the comparison between two objects with different mean and variance values. The same question could arise for a large number of objects scattered throughout the entire ﬁeld of study (e.g., from top to bottom of a sedimentary column). Questions to be answered then are related to spatial trends in the intensity characteristics of objects or regions: Are regions becoming more and more rich in organic matter when moving from bottom to top? Are we moving from reduced to oxidized regions (increase in red component)? Are sedimentary layers more and more homogeneous in gray level? etc. The simplest example is the systematic plot of mean intensities computed within moving windows along an axis. Such a graphic, given the assumption that no calibration and section thickness problems do arise, readily indicates a trend in the intensity values that can be modeled with linear or polynomial regression if desired. A similar graphic could be plotted with moving variances, but its interpretation is more delicate. A constant variance (called homoscedasticity in the statistical jargon) probably identiﬁes a very homogeneous medium. A gentle trend in the variances might signify a progressively more homo/heterogeneous medium, but this trend should be compared to the trend expressed by the means as eventual correlations between means and variances could indicate problems in instrumentation. When dealing with parameters computed on objects rather than on moving windows, it is essential to remember the change of support problem and to detect spurious spatial correlations in variances that would be generated by a progressive change of size of the objects rather than signiﬁcant differences in intensities.

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Blob analysis The limits of traditional geometry Traditional Euclidean geometry does not strictly apply to digital image analysis. To convince oneself, it sufﬁces to realize that the area of a disc will depart from π r 2 in digital image analysis! To make things clear, it is interesting to consider the intriguing problem of estimating the area of an irregular shape. The ﬁrst method to solve the problem is to convert the measure of the surface into the measure of another more accessible physical entity. This is exactly what microscopists used to do until recently, by drawing shapes on tin sheets and weighting them. The second method is to cover the irregular surface with a ﬁnite number of simple shapes of known area. This is in a certain sense how digital imaging based technology will explore unknown geometries. Exploring bodies with spatial probes Stereology is the mathematical discipline for estimating properties in an N -dimensional space from measures in a space of lower dimensionality (typically N −1). The fundamental concept in stereology is the idea of number of intersections (or connectivity) between a set of probes and the object under study. There is theoretically no restriction on the geometry of the probes. However, for practical purposes, one will limit ourselves to discussing the intersections with points (0-D), lines (1-D) and planes (2-D). Let us consider a set of points scattered randomly, or systematically, in 3-D space. In such a case, the so-called number of connectivity N0 for a given object is the number of points hitting that object (Fig. 4a). If instead of points one uses lines, the number of connectivity N1 becomes the number of segments deﬁned on the lines by the limits of the object (Fig. 4b). An additional measure can also be deﬁned: the length L1 of each segment. Finally a 3-D object can be cut by planes, giving rise to blobs that can be characterized in terms of the perimeter L2 of each blob, the surface S2 of each blob and number of connectivity N2 . This last number is equal to the number of blobs delimited on the respective planes minus any holes within these blobs (Fig. 4c). From a purely statistical point of view random probes are essential for stereological formulae to give unbiased estimators. At this stage, the reader might wonder how to put stereology into practice. Indeed, even if we have at our disposal punctual probes (i.e., electron beams), linear probes (i.e., drill holes), planar probes (i.e., thin sections) it is very hard, if not impossible in most cases, to handle the geological body in order to ensure perfect randomness. Most often, scientists are accustomed to working with systematic sampling probes instead of random ones. Common examples of this include serial sectioning of bodies or digital imaging technologies based on systematic scanning (i.e., scanning electron beam microscopy) (Cruz-Orive 1993). One must be aware that switching from random sampling to systematic sampling is a dangerous step towards biased estimation. . . except if the object itself could be considered as random! (Fig. 5). In the future, geologists dealing with quantitative imaging in microscopy should consider their thin sections as systematic or random planes and digital images as systematic

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A.

B.

C.

Figure 4. Stereology explores the number of intersections between objects and probes thrown at random or systematically. A systematic grid of points (A) overlaid on the image of random sets gives the number of intercepts N0 . A line thrown at random through a set of objects (B) determines the number of intercepts N1 , which is the total number of outputs along the line. Finally, the number of intercepts N2 is computed as the number of connected sets cut by the image plane (C) minus the number of holes. In the above examples N0 = 50; N1 = 4 and N2 = −1.

Figure 5. Systematic sampling as is often practiced leads to biased estimators, unless the medium itself is randomly structured (A). Systematic cuts through sedimented particles is a frequent cause of bias (B).

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arrays of points intersecting their planar sections. Understanding this is essential to somehow relate the property of a pixel to an estimation of the real world. Practical computation of connectivity numbers in digital images Any digital image delivered by a video system or a scanning beam system is built as a systematic arrangement of punctual probes. However, by taking advantage of higher order arrangements of pixels, it will be possible to access information about linear intercepts and even planar intercepts. The estimation of the number of connectivity N0 in a digital image after conversion into a binary image is a straightforward job as it amounts to summing up all pixels at value PI = 1. The estimation of the number of connectivity N1 for a systematic set of parallel lines in a given direction is possible by identifying and counting all pixel conﬁgurations corresponding to “exits” in this direction. For example, all sets of possible conﬁgurations within a 2 × 2 neighborhood can be grouped into 0◦ , 45◦ , 90◦ and 135◦ intercepts (Fig. 6): • • 0 • , N1 (X, π/2) = N , N1 (X, 0) = N 1 0 1 • • 0 0 • N1 (X, π/4) = N , N1 (X, 3π/4) = N , (10) 1 • • 1 where • means indifferent (either 1 or 0). Extending the same reasoning to 3 × 3 or 4 × 4 neighborhoods will allow multiplying the number of possible intercept directions. In the later paragraphs, we will see how these basic measurements of N0 and N1 will lead to important estimations of properties in 2-D and 3-D. For the moment, we just summarize by saying that for probing volumes it sufﬁces to sample with points (N0 ) and for probing surfaces (or envelopes) it sufﬁces to sample with lines (N1 ).

Figure 6. Linear intercepts in a digital image are counted by identifying special neighborhood conﬁgurations as illustrated here for some vertical (90◦ ) and oblique (45◦ ) intercepts. (Grey pixels are part of the object, white pixels are part of the background).

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The reader is referred to the classical textbooks in stereology for more in depth discussion of the theoretical and practical aspects of this science (Weibel 1980; Stoyan et al. 1995; deHoff and Rhines 1968; Gundersen 1986). He should be aware however that some of these textbooks focus on mathematical discussions which might be difﬁcult to understand and implement, while others address biological applications, often taking advantage of the transparency of the medium and relying on manual measurements. Nevertheless, it would be unwise to neglect this scientiﬁc heritage and to try to ﬁnd out new measurements from a purely intuitive approach. Area measurements Area is deﬁned as the measure of a planar surface in 2-D space. It has long been proven by Minkowski (1903) that this measure is readily accessible without bias by counting N0 on a systematic grid. The grid spacing in the horizontal (a0 ) and vertical (a90 ) directions deﬁne the elementary surface or support (si ) to be associated with each pixel. Hence, we get: A = N0 · si .

(11)

Area measurements deﬁned in this way are robust against translation and rotation of the grid of pixels, which is a very important property. Obviously, the precision of the estimation is a function of the density of the pixel grid. For most practical needs, it can be shown that a few tens of pixels per object is already sufﬁcient (Fig. 7).

Figure 7. The area estimator evolves when taking pictures of a given shape by doubling the resolution at each step. A few tens of pixels often appear sufﬁcient for practical applications.

Diameter measurements Area measurements expressed in squared metric units are often cumbersome to deal with. Therefore, many authors prefer to deal with diameters. Unfortunately, the notion of diameter is not a single concept, and sedimentologists know it better than others having faced an

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inﬁnity of proposals in the scientiﬁc literature. We will review here the main deﬁnitions used for diameters, trying to draw the attention of the reader to those that are the most useful for practical purposes. Equivalent disc diameter For the sake of comparing areas by making an abstraction of any reference to the shape of the object, it is convenient to convert any area into the diameter of a disc having the same area. The equivalent disc diameter D0 is obtained by reverting the classical formulae for computing the surface of a disc into: 4·A D0 = . (12) π The main practical advantage of D0 is that it does not require any additional computation with respect to A. But, the reader should understand that it would √ have been exactly the same to consider all particles as being squares and to use D⊥ = A as the computation of an equivalent square side. In practice, the use of an equivalent diameter should be restricted to the analysis of a set of objects with very similar shapes (Fig. 8).

Figure 8. Arbitrary set of particles having identical areas and thus identical equivalent disc diameters (D0 = 147.2 µm)!

Equivalent inertia diameters Another diameter estimation based on a simpliﬁed shape model is the one proposed by Medalia (1970). This is no longer a transformation of the area value, but it relies on the computation of the real inertia moments of the object and the mathematical derivation of an ellipse sharing the same inertial properties. This ellipse can be characterized by its major and minor diameters, by its center of gravity as well as by its orientation. Covariance matrix or inertia moments of the shape coordinates: 1 · (xi − x) ¯ 2, σXX = N 1 σY Y = · (yi − y) ¯ 2, N 1 σXY = · (yi − y)(x ¯ i − x). ¯ N

(13)

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(14)

Axes of the ellipse of equivalent inertia: α + β, = 4 · α − β.

Ell DMax =4· Ell Dmin

(15)

Major axis orientation: θ = 90◦ −

180◦ σXX − α − β , · arctan π σXY

(16)

Ell , the longest axis of the ellipse of equivalent inertia. where θ is the orientation of DMax θ = 0◦ when the particle is oriented according to the horizontal frame of the image. As seen from Figure 9, the interest of the equivalent inertia method is to lead to a fast estimate of the major and minor axis of any object as well as its elongation and orientation, but the main drawback is that it is not a precise measure of the particle itself.

Figure 9. Equivalent inertia ellipses overlaid on the set of arbitrary shapes from Figure 8.

Feret diameters Intuitively, when dealing with diameters one often thinks about the distance between the teeth of a grip used to pick up an object. This concept is closely related to the notion of Feret diameter or caliper diameter. The Feret diameter is the projection length of the convex envelope of a particle in a given direction. A Feret diameter is thus always associated to a direction α, that is the direction of the line onto which the shape is projected. In practice, such a dimension has to be computed for a discrete set of orientations (typically 8 or 16) and from this a Feret distribution is obtained. The general trend of the distribution is a poor description of the shape. Most often, only the Maximum Feret and eventually the minimum Feret diameters are retained (Fig. 10). Some authors do prefer to combine the Maximum Feret diameter with the measure of the Feret perpendicular to it, which might be different from the Minimum. This should be

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Figure 10. Maximum and minimum Feret diameters overlaid on the set of arbitrary shapes from Figure 8.

avoided, since the direction of the Maximum Feret is not a robust notion. A very slight perturbation is capable of turning the Maximum Feret direction by 90◦ ! An alternative and robust approach is to use the orientation of the inertia ellipse and re-compute Feret diameters along the conjugate directions (Pirard 1990). Intercept / chord length distribution As stated before, the intersection of a shape with a regular network of parallel lines leads to a distribution of intercept length or, in other words, to a chord length distribution in a given direction. This used to be a popular measure in the very primitive image analysis systems, and it has been thoroughly investigated by stereologists together with the parent notions of spectrum of linear erosions and linear openings (Serra 1982; Soille 1999). However, considering even simple shapes, it does appear that the chord length distribution is a rather complex function. The best way to identify a square shaped object in a scene will probably never be to ﬁt any experimental chord length distribution with the model distributions for a square. The power of the chord length distribution is better expressed by its applications in texture analysis rather than in blob analysis. Diametric variation Instead of measuring the individual intercept length, stereologists use the number of intercepts in a given direction (Nα ) as a way to get the total length of intersection. This measure is called the Diametric Variation (Lα ) and will be very useful to develop a stereological estimator of the perimeter. Considering a square grid of pixels, the diametric variation for the N 45◦ E direction is written as: √ 2 · a0 , (17) L45 = N45 · 2 where a0 is the unit distance between pixels in the horizontal (0◦ ) direction. Inscribed and circumscribed disc diameters Until this point, an important concept is still missing to adequately address the measure of a diameter: the narrowest region of a particle has not been correctly identiﬁed and measured. The requested measure is the diameter of the maximum inscribed disc (DIN ).

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Figure 11. A concave particle with its associated maximum inscribed square (ultimate erode set). Results may vary as strongly as 41% with rotation of the image grid (A). The same particle with its associated maximum inscribed disc using a Euclidean metric for erosion (B).

Such a measure is of interest in sedimentology (Wadell 1933), as well as in any study about reactivity or crystal growing. As seen from Figure 11, the minimum Feret diameter is not the right concept, and the minimum diameter of the inertia ellipse is not a solution either. For those familiar with mathematical morphology, it should be clear that the desired measure is the value of the ultimate eroded point. In other words the number of iterations of a unitary erosion to completely dissolve an object (Nederbragt et al., this volume). Since most image analysis softwares still use square (or possibly octagonal) neighbourhoods the result is sensitive to orientation and might overestimate the true inscribed disc diameter by as much as 41%! To get an unbiased and precise estimation, one must rely on perfectly circular structuring elements as implemented in the holodisc distance function (Pirard 1996). The circumscribed disc diameter (DOUT ) is given by the maximum Feret diameter, but clearly there is no reason for this disc to share the same center as the inscribed disc diameter. Aspect ratio measurements Among the most useful and most widespread expressions of shape we ﬁnd the aspect ratio or elongation factors. Sedimentologists are used to working with charts representing a so-called sphericity index, most often as deﬁned by Riley (1941) and expressed as: DIN R = . (18) DOUT This formula, referring to a three-dimensional measure of an object, is not accessible through classical image analysis, but many 2-D equivalents relying on ratios of diameters have been proposed. Unfortunately, computations of elongations will depend on the nature of the diametric measure and on the method of computing elongations. Some authors use: DMax El = (19) Dmin which is probably the most intuitive formula.

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Figure 12. Relative evolution of various aspect-ratio formulae for ellipses with 1:1 to 10:1 axes.

Others prefer: El =

Dmin DMax

or

El = 1 −

Dmin DMax

(20)

because the results are normalized between [1, 0] or [0, 1] Still others propose: El =

DMax − Dmin DMax + Dmin

(21)

which is also constrained between [0, 1] but with a more gentle slope. This will probably sufﬁce to make the reader aware that, even for such a simple concept as aspect ratio, there is no universal concept and that inter-laboratory comparison must be undertaken with extreme care (Fig. 12). Alternatively, elongations can be computed from the minimum and the maximum of a Feret diameter distribution provided enough, typically sixteen, directions have been computed. It could also be derived from the ratio between the inscribed and the circumscribed disc diameters. Each one of these methods and each of many other proposals in the literature has its advantages and disadvantages. Perimeter measurements The perimeter often appears as a classical concept whose formula is very well known to everybody for simple geometries. But, when dealing with natural objects seen through a systematic pixel sampling process the story turns out to be one of the most complex problems of quantitative estimation. The interested reader should refer to original work by Minkowski (1903) and might follow the trace of perimetric measures up to the most recent fractal theories of Mandelbrot (1982). However, in the present chapter, we will draw the attention of the reader to the various digital perimeter concepts and suggest practical formulae for its estimation without entering the problem of scale dependency.

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Inner and outer perimeter We have seen in the previous paragraphs that systematic sampling by pixels is an unbiased method for estimating the size (area) of an object. However, it seems evident that it has dramatically reduced the information about the original contour of the object. Even worse, there is no such thing as a contour of an object unless we deﬁne what border pixels are and how they are connected to each other. By deﬁnition, border pixels are those lying at the transition between an object and its background. So, one possible deﬁnition is to retain those pixels at value pi = 1 having at least one neighbor at pi = 0 (inner perimeter). But, there is no reason not to consider the dual situation of retaining pixels at pi = 0 having at least one neighbor at pi = 1 (outer perimeter) (Fig. 13).

Figure 13. The polygonal approximation of an inner (outer) eight-connectivity perimeter is obtained by linking the black (white) border pixels using horizontal, vertical or oblique edges. The alternative inner four-connectivity perimeter is shown as a dotted line.

Four or eight connectivity (4-c or 8-c) Summing up the border pixels as a measure of the perimeter length would be equivalent as to considering that all pixels are at equal distance from each other. An obviously more realistic alternative is to consider eight-connectivity, thus allowing connections in oblique directions. In the latter case, the right perimetric estimate has to differentiate elementary steps in the oblique directions that are 1.41 times longer than the horizontal or vertical edges. Such perimetric estimates can be grouped under the term polygonal approximation of the contour (Fig. 13). It is important to realize that both the 4-c and the 8-c estimates are models, and although it is very much probable that the 8-c is closer to reality, there is nothing to demonstrate this. The original contour length has been lost and could have been as low as the 8-c inner perimeter, but could have been much longer too. In any case, there is no reason to say it is an average between the 8-c inner and 8-c outer contours. Cauchy-Crofton formula A poorly known, though mathematically indisputable formula is the estimation of the perimeter using a rotational average of the diametric variation. It has long been proven by Cauchy that this is the best way to recover the perimeter of a circle (2π r) sampled by

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parallel lines (Serra 1982). The expression of the Cauchy-Crofton perimeter is as follows: √ π π 3π π 2 L2 (X) = · N1 (X, 0)+N1 X, + N1 X, + N1 X, · ·a0 , (22) 4 2 4 4 2 where the numbers of intercepts N1 (X, A) to be used in this formula correspond to the counting of the pixel neighbourhood conﬁgurations shown in formula (10). Theoretically, this formula is unbiased for convex shapes and gives the best results with reasonably isometric objects (i.e., objects having similar diametric variations in all directions). In practice however, it proves to be a robust measure of a perimeter for many natural quasiconvex shapes such as sand grains, fossils, etc. Important remark on scale dependency of perimetric estimates Any measure of a perimeter is very sensitive to the scale of observation. This means that the more one magniﬁes the object or the higher the resolution of the digital image, the more details will appear along the contour. The practical implication of this is that it makes no sense to compare particles pictured in different conditions or to compare particles of different sizes in terms of perimeter or speciﬁc surface. Roughness and roundness measurements The potential of image analysis for shape characterization is emerging with the development of new and powerful algorithms. However, most systems available today are still suggesting simple shape factors such as 4πA/P 2 for addressing roughness characteristics. Not only is such a parameter very sensitive to the kind of perimetric estimator that is used for P (and then squared!), but it simply lacks a clear physical signiﬁcance as was already pointed out by Serra (1982) (Fig. 14). Possible alternatives of roundness and roughness measurements do rely on mathematical morphology, fractal analysis or Fourier shape spectrum analysis (Pirard and Hoyez 1995). A good example is given by the perfect automation of Wadell’s early concepts (Wadell 1933). Figure 15 illustrates how a parameter derived from the succession of openings with increasing radii (Pirard 1994) correlates perfectly with the famous Krumbein (1941) visual chart used in sedimentology.

Figure 14. All three shapes share the same value of 4π A/P 2 (0.436) even in a Euclidean space. But obviously, there is no application at all that might consider these three shapes as being equivalent.

Structural analysis After having described individual blobs by computation of their most prominent geometrical properties, the next step in image analysis is to analyze the presence of eventual groups or

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Figure 15. Krumbein’s visual chart has been drawn from former concepts introduced by Wadell (1933) and is widely used in sedimentology. The same concept is perfectly correlated to an “equivalent roundness” parameter computed as a weighted average of successive openings (Pirard 1994).

populations of blobs sharing the same properties and to analyze the way these blobs are distributed into space. These kinds of problems are grouped here under the generic term of structural analysis. Describing populations of blobs Modal analysis Modal analysis designates the description of a ﬁeld in terms of the fraction of that ﬁeld occupied by its various constituents. In other words, once pixels or blobs have been given a nature by the classiﬁcation / segmentation process, it is possible to describe the ﬁeld in terms of relative frequency of each kind of blob. The most familiar computation is the description of an image in terms of surface fraction occupied by the constituent X. This is classically denoted AA (X) in stereological notation. Considering the spatial distribution of phases as a random process, the proportion of a phase in the image is simply: Pr{pi ∈ X} =

N(pi = X) A(X) = AA (X), = NTot A(I )

(23)

where X designates one of the possible phases that has been attributed to the pixel by the classiﬁcation / segmentation process. In practice, provided the density of pixels is high enough (several tens of pixels falling within X) the estimation of AA (X) is precise and unbiased. It is the authors responsibility to choose a resolution such that even the smallest blobs of phase X can be captured by the digitizer. If not, then a signiﬁcant fraction of X might be overlooked and generate a bias in the estimation of AA (X). On the other hand, if phases cannot be considered as randomly dispersed, one must keep in mind that the systematic grid sampling of a digital image does not observe the criterion of equiprobability and that a bias might also occur.

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Figure 16. Image analysis is a unique tool for computing modal analysis within individual crystals or user-deﬁned regions. In this example, the user-deﬁned region is a single ilmenite crystal outlined in back. Within this area, the hematite exsolution (light curly vertical stripes) abundance gives an estimate of 11.06%.

At this point, it is important to remember that AA (X) is the estimation of the surface fraction of phase X in image I . For estimating the surface fraction in a whole thin section, it is essential to pick up a collection of images (typically 10 to 30) without changing the magniﬁcation from one to the other! Interested readers are referred to the ﬁrst principle of stereology to understand how the estimation of AA (X) in a sufﬁcient number of sections taken at random in a 3-D material lead to an unbiased estimation of VV (X): the volumic fraction of X in the sample (deHoff and Rhines 1968). Clearly modal analysis can be computed for ﬁelds that do not necessarily correspond to the limits of the image frame. An interesting example of this is given by hemo-ilmenites for which the interesting ratio is Hematite/Ilmenite+Hematite on an individual crystal basis (Fig. 16). Size distributions The grouping of size measurements into synthetic histograms or size distribution curves is a central topic in image analysis. Blobs can be grouped into classes on the basis of their observed 2-D size. Such distributions can be computed for all particles or for user-deﬁned subsets of particles. Examples of this include: the computation of the size distribution of all grains in a sediment, the size distribution of only neoformed calcite, the size distribution of hematite exsolutions within ilmenite, the size distribution of ﬂuid inclusions within a single grain, etc. The deﬁnition of histogram classes is entirely left to the reader and there is no deﬁnite recommendation as testiﬁed by the various professional practices in this domain. Some are used √to an arithmetic progression (175-250-325. . .), others to a geometrical progression by 2 (175-250-350. . .) and so on. But in image analysis not only is the choice of sieve meshes left to the reader, but also the relative weighting method. In other words, considering size distribution classes as virtual sieves, it is possible to weight the content of the sieve or to count the number of particles in a given sieve. Such size distribution curves are called by weight or by number and lead to very different interpretations (Fig. 17). Logically the weight parameter is most often the area, but it could be replaced by another measure.

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Figure 17. Size distributions can be displayed either as a relative number of particles or a relative apparent volume. Fine powders (40 µm) in a coarse material (1 mm) may represent less than a 1% in volume but almost 90% in number.

The unbiased estimation of a size distribution curve for particles extending over more than a single image is not as straightforward as it may seem. In particular, it is mandatory to take into account the probability of inclusion of a particle within the image frame. Evidently, the larger the particle the higher the probability to hit the frame and to be excluded from the blob analysis procedure. This probability can be expressed as the fraction of the total image area remaining after erosion of the frame by the particle under consideration. Clearly, the probability is inversely proportional to the size of the particle. Taking the simple case of a square image frame of size F and a round particle of diameter D, the probability of inclusion is readily computed as: (D) =

(F − D)2 . F2

(24)

In practice, only particles ﬁtting entirely within the image frame are considered for measurement and the relative amount of particles of a given size class (Di ) is weighted inversely proportional to (Di ). This probabilistic correction is known as the Miles-Lantuejoul correction (Serra 1982). Another, yet more important bias is the one linked to the estimation of a 3-D distribution from the observation of a 2-D distribution. This problem, ﬁrst solved by Wicksell (1926) for random sections in a population of perfect spheres is known as the second principle of stereology. Since then, many authors (e.g., Exner (1972), Cruz-Orive (1976), Cruz-Orive (1978)) have tried to extend this estimation to a larger range of shapes, but the practical applications of such theories remain rather limited. . . in particular when considering that no such thing as a random section really exists. Essentially, for 2-D size distributions observed from sections, the reader should be aware that he is strongly overestimating the amount of ﬁne particles. Shape distributions The problem of representing a histogram of shape factors is rarely addressed in the literature. The deﬁnition of shape classes and the relative weighting of the classes are not very intuitive. A probably more convenient representation of the shape properties of a population of blobs is to compute the average shape parameter within a restricted size class and to plot it as a series of box-plots (Fig. 18). When shape parameters have been carefully selected as

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Figure 18. The Box-Plot representation is convenient for comparing statistics (mean, std. dev., and min-max) computed within single size classes. In this case, a natural quartz sand, no signiﬁcant difference in terms of roundness does exist between the size classes.

Figure 19. A roundness vs. elongation scatter plot helps to visualize a signiﬁcant difference between two sand samples. Thumbnail images correspond to particles at the center of gravity of both populations (courtesy of Occhio S.A.).

mathematically independent, it might be useful to consider scatter plots in shape-space (Fig. 19). Orientation Among the possible measures on individual blobs we have mentioned the orientation of the major axis. Be it through the measure of a series of Feret diameters or more efﬁciently through the analysis of the inertia moments, every particle will be given an orientation in the [0◦ ; 180◦ ] range. The set of all measures can be plotted onto a classical rose or kite diagram. Here again the relative weighting can be by number or by surface, but whatever the choice, it is advisable to use a radius length equal to the square root of the relative frequency (Swan and Sandilands 1995). It is worth mentioning that such representation of

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Figure 20. Both images correspond to isotropy if one considers the rose diagram of the absolute orientation of individual particles. The evident anisotropy in the second image could only be revealed by studying the relative spatial arrangement of the blobs.

individual orientations is blind to any kind of preferential alignment of blobs in the image (Fig. 20). Describing the spatial relationship between blobs The binary covariance function The problem of analyzing the relationship between objects in space is a very large topic that is commonly addressed in textbooks on spatial statistics (Cressie 1993). It is out of the scope of this chapter to try to make an inventory of all possible techniques. Instead, we have chosen to give a very basic introduction to practical uses of tools based on mathematical morphology and stereology. A central concept in spatial statistics is to measure the correlation between two points that are a distance h apart. If one restricts the discussion to a binary image where pixels can take either value 1 or value 0, this amounts to counting the number of pairs of points that show the following conﬁgurations: 1 . . .. . . 1

1 . . .. . . 0

0 . . .. . . 0

0 . . .. . . 1.

h

h

h

h

The reader will understand that much redundancy does exist in those various countings and that it is possible to simplify the study of dispersion of a single phase to the study of the covariance function C(h) giving the number of 1 . . . h . . . 1 pairs for a distance h going from 0 to L (width of the image). By adding a constraint on the direction α of the 1 . . . h . . . 1 pair of points, one adds to the covariance function a capacity of directional analysis that will be useful for studying privileged orientations within the image. At this point, it is important to realize that the value of C(h) in a given direction, can be straightforwardly obtained from the intersection of the image with itself translated a distant h apart (Fig. 21). Interesting features of the covariance function are given by the tangent at its origin (which is mathematically the diametric variation), the slope of this tangent giving an idea of the average size of objects, the existence of periodicities expressing the reappearance of spatial correlation for certain distances (Fig. 22).

IMAGE MEASUREMENTS

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Figure 21. The value of the binary covariance function for a given distance h is best understood as the intersection between the original image and itself after a translation of h. Two images (A and B) of blobs (gray and black pixels) have been both horizontally translated by h = 39 pixels. The black pixels represent the non null intersection between the image and its translated (original images from MicroMorph “Centre de Morphologie Math´ematique” Paris). The covariance C(39) is calculated from these images and plotted in Figure 22.

C.

D.

Figure 22. Binary covariance functions C(h) in the horizontal direction corresponding to the images of Figure 21a and 21b.

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Covariances and other spatial auto-correlation functions are the logical extension of basic statistical tools in space. They have known statistical properties allowing to develop adequate tools and theories. From a practical point of view however, it is obvious that such functions are often too simplistic with respect to the problem of describing natural textures. The frustration comes when realizing that by computing a covariance function, one has reduced the dimensionality from a 2-D image to a 1-D signal. . . and the image processing problem has become a signal processing problem not necessarily easier to deal with! Analyzing properties of dilated images An alternative technique to the computation of covariances is to perform successive dilations and to observe the evolution of a geometrical property such as the number of connected particles, the total area, the total perimeter, etc.

Figure 23. Image of blobs dispersed into a matrix (A) and its corresponding skeleton by zone of inﬂuence (B).

Figure 24. Shadow image (A) of sixteen successive Euclidean dilations performed on the blobs from Figure 23a. Diagram of the evolution of the total perimeter length with successive dilation steps (B).

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This is somehow similar to a popular technique in Geosciences known as the Thiessen or Voronoï polygonation attributing to each blob the area of its region of inﬂuence (the set of all points closer to that blob than to any other). This function is designated in image analysis by the SKIZ (skeleton by zone of inﬂuence) function (Fig. 23). From the size distribution of Voronoï polygons, it is possible to determine, for example, whether the centers of blobs respect a random (Poisson) or non-random dispersion (Stoyan et al. 1995). Another example for testing the randomness of spatial dispersion of particles is given by ﬁtting the evolution of a perimeter measure with successive dilations of the image. The perimeter increases with dilation until coalescence appears. At that moment the perimeter starts to decrease, thus giving a measure of spatial dispersion (Bosco 1995) (Fig. 24). All these techniques have important border effects that should be carefully demystiﬁed before drawing conclusions. Summary Image analysis is probably among the most innovative tools of recent years and has gained major importance because of its wide circulation. A large set of tools for addressing image quantiﬁcation problems is now available and helps solve problems in quantitative sedimentology, such as in the analysis of grains, matrices and porous networks. Nevertheless a sound use of the technique requires better education and a wider circulation of the mathematical background that is behind most concepts. Of particular interest are Stereology, Mathematical Morphology, Stochastic Geometry, Spatial Statistics, etc. This chapter explained basic notions of sampling theory linked to the ﬁeld of image acquisition, and reviewed some of the most essential parameters available for proper characterization of the image content. A particular emphasis was put on the analysis of image intensities (grey levels, colors) and individual objects (size, shape, orientation). More advanced concepts related to structural or textural analysis could not ﬁnd place in this chapter and are only brieﬂy commented. The readers are referred to more specialized publications for the discussion on microstuctural analysis, 3-D measurements or stereological estimations. Acknowledgments Thanks to Frank Keimig for smoothing the English language. The author is particularly indebted to Joëlle Riss and Pierre Francus for their valuable comments and relevant suggestions. References Bosco E. 1995. Perimeter-area laws for a random agglomeration of particles. Phys. Rev. E 52: 4681. Cressie N. 1993. Statistics for Spatial Data. Wiley, New York, 900 pp. Cruz-Orive L. 1976. Particle size-shape distributions: the general spheroïd problem I. J. Microsc. 107: 235–253. Cruz-Orive L. 1978. Particle size-shape distributions: the general spheroïd problem II. J. Microsc. 112: 153–167.

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Cruz-Orive L. 1993. Systematic sampling in stereology. Bull. Int. Statist. Inst. 52: 451–468. DeHoff R.T. and Rhines F.N. 1968. Quantitative Microscopy. Mc Graw Hill, New York, 422 pp. Exner H.E. 1972. Analysis of grain and particle size distributions in metallic materials. Int. Metal. Rev. 17: 25–42. Grifﬁths J.C. 1988. Measurement, sampling and interpretation. In: Chung C.F. et al. (eds), Quantitative Analysis of Mineral and Energy Resources. Kluwer, NATO series, pp. 37–56. Gundersen H. 1986. Stereology of arbitrary particles. J. Microsc. 143 Pt 1: 3–45. Haralick R. and Shapiro L. 1985. Image segmentation techniques. Comp. Vis. Graph. Image Process. 29: 100–132. Hunt R.W.G. 1991. Measuring Colour. Ellis Horwood, 313 pp. Krumbein W.C. 1941. Measurement and geological signiﬁcance of shape and roundness of sedimentary particles. J. Sed. Petrol. 11: 64–72. Mandelbrot B. 1982. The Fractal Geometry of Nature. Freeman, San Francisco, 424 pp. Medalia A. 1970. Dynamic shape factors of particles. Powder Technology 4: 117–138. Minkowski H. 1903. Volumen und Oberﬂäche. Math. Ann. 57: 447–495. Pirard E. 1990. Applications of Shape Analysis in Ore Beneﬁciation. In: Petruk W. et al. (eds), Process Mineralogy IX. The Minerals Metals and Materials Society, New York, pp. 205–218. Pirard E. 1994. Shape processing and analysis using the calypter. J. Microsc. 175: 214–221. Pirard E. and Hoyez B. 1995. A comparative study of quantitative shape analysis techniques in sedimentology. Zbl. Geol. Paläont. Teil I, H11/12: 1061–1066. Pirard E. 1996. The holodisc distance transform and its applications in image analysis. Microsc. Microanal. Microstruct. 7: 453–460. Riley N.A. 1941. Projection sphericity. J. Sed. Petrol. 11: 94–97. Serra J. 1982. Image Analysis and Mathematical Morphology. Academic Press, New York, 610 pp. Soille P. 1999. Morphological Image Analysis: Principles and Applications. Springer-Verlag, Berlin, 316 pp. Stoyan D., Kendall W. and Mecke J. 1995. Stochastic Geometry and its Applications. Wiley, New York, 436 pp. Swan A. and Sandilands M. 1995. Introduction to Geological Data Analysis. Blackwell, Oxford, 446 pp. Wadell J. 1933. Sphericity and roundness of rock particles. J. Geol. 41: 310–331. Weibel E.R. 1980. Stereological Methods. Vol. 2. Academic Press, London, New York. Wicksell S.D. 1926. The corpuscle problem II. Biometrika 18: 152–172.

5. TESTING FOR SOURCES OF ERRORS IN QUANTITATIVE IMAGE ANALYSIS

PIERRE FRANCUS ([email protected])

Climate System Research Center Department of Geosciences University of Massachusetts Amherst, MA 01003-9297 USA Currently at INRS - Eau, Terre et Environnement 490 rue de la Couronne, Québec (QC) G1K 9A9 Canada ERIC PIRARD ([email protected])

Département GeomaC - Géoressources Minérales Université de Liège Sart Tilman B52/3 4000 Liège Belgium Keywords: Quality control, Errors, Robustness, Image analysis, Phase analysis, Size analysis, Shape analysis, Classiﬁcation

Introduction Image analysis, like other analytical techniques, is subject to errors. In the previous chapter (Pirard, this volume), we learned that errors accumulate at each individual step of sampling and analysis. There are numerous steps between the time a sediment core is collected and the arrangement of few digital pixels is measured. To comprehend these errors it is necessary to make some validation. However, this is not always possible. Therefore, prior to generating a long series of images that contain valuable paleoenvironmental information, it is necessary to test the quality of the images acquired and estimate the errors made. The quality of measurements obtained using image analysis is rarely evaluated in research papers, the authors claiming, often improperly, that measurements are “representative” to avoid discussion about the pertinence of the method. This is mainly due to the fact that it is difﬁcult to include such testing in research papers, because journal space is limited. However, some authors pioneered such testing, e.g., the quality of classiﬁcation techniques 87 P. Francus (ed.) 2004. Image Analysis, Sediments and Paleoenvironments. Kluwer Academic Publishers, Dordrecht, The Netherlands.

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under different conditions (Tovey and Krinsley 1991), the reproducibility of results within the same bed (Francus and Karabanov 2000), and validation with other measurements (Ojala and Francus 2002). Such evaluations are naturally more widespread in method papers (e.g., Starkey and Samantaray (1991), van den Berg et al. (2002)). This chapter aims to awaken scientists to the importance of such controls in order to allow image analysis techniques to mature as a widely accepted methodology. Testing images will also allow the users to be aware of their method’s weaknesses and strengths. They can then improve the quality and the efﬁciency of the methods by focusing their efforts where they are mainly needed, while leaving the most robust operations as they are. The purpose of this chapter is not to present a comprehensive review of the parameters that need to be tested, but rather to illustrate, through some examples, how such testing can be accomplished by slightly varying image acquisition conditions and monitoring their impact on the ﬁnal measurements. We will discuss three groups of errors (Gy 1992) in image analysis: preparation errors, i.e., errors involved during acquisition, integration errors (or sampling errors), and analysis errors, i.e., errors due to image analysis. The focus of this chapter will be on errors that relate to measurement of the image properties, i.e., on errors that propagate in the building of the image and in the measurement of the pixels. Some useful deﬁnitions Deviation and error When performing quantitative analyses, it is impossible to obtain perfect results. A dispersion of the results always exists. This dispersion may be due to two very different reasons: (1) Incompressible dispersion of the results inherent to the nature of the analyzed material (the material is heterogeneous by nature), called deviation. (2) Dispersion due to the methodology used for analysis (analytical lack of reproducibility), called error. Practically, dispersion (or variance) of results is always the sum of deviation and error. One can attempt to evaluate the deviation but one cannot reduce it. On the contrary, errors blur the quality of the results, and one needs to keep them at the lowest level possible. Precision and accuracy Precision describes a small dispersion of measures with respect to a central tendency (small variance). Accuracy describes the correspondence between the real value and the measure deduced from the central tendency (Fig. 1). A systematic bias implies inaccuracy. A technique can be very precise but inaccurate in the sense that the results produced are reproducible (weak dispersion of the results) but systematically biased. A major problem is to reveal a bias when no alternative validation method is available, such as for complex shape analysis. For example, we outline here some results of modal analysis obtained on polished sections and the corresponding bulk chemical analysis (Table 1). A quick calculation based on densities and simpliﬁed stoechiometric formulae allows the validation of the results obtained using the imaging technique and the continuation of the analysis of the material (Pirard 1991). However such validation is often tricky to perform,

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Real

Imprecise but accurate

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Real Bias

Precise but Inaccurate

Measured

Measured

Figure 1. Graphical representation of precision and accuracy. Table 1. The chemical analysis validates the modal analysis performed on a sample of an Ottoman slag from Turkey (from Pirard (1991)). Chemical analysis (% weight) FeO SiO2 Al2 O3 S Cu Co

59.7% 23.5% 11.6% 1.8% 0.76% 0.38%

Modal analysis (% volume) Fayalite Wüstite Glass Hercynite Pyrrhotite Cu sulﬁdes

71% 11% 8% 5% 3.15% 0.85%

because it is very difﬁcult to obtain perfectly comparable samples for both chemical and image analysis (Petterson et al. 1999). A good example of systematic bias is provided by the measure of the shape parameter commonly provided in image analysis software. By deﬁnition, we know that 4π A/P 2 (A being the surface area, and P the perimeter) should be equal to 1 for a perfect circle in Euclidean geometry. However, measuring images of perfectly circular objects at different scales, i.e., at different pixel resolution, we obtain a strong variability of this parameter and a central tendency sometimes of 0.9 instead of 1! (Fig. 2). The dispersion of the results obtained while computing the shape parameter for a series of discs at different magniﬁcations is due to the apparent roughness generated by pixelization of the contour. Sensitivity and robustness The apparent accuracy of a method and its exactness are not sufﬁcient criteria of quality. A weak dispersion of the results could exist for different reasons: 1) the method is very precise, and the samples are homogenous, or 2) the samples are heterogeneous, but the method used for characterization is not able to differentiate them. As a consequence, a technique should be sensitive enough, i.e., it is able to differentiate signiﬁcantly between different samples. But, at the same time it should be robust, i.e., the measurement is weakly affected by a signiﬁcant modiﬁcation of operating conditions. Robustness can be tested in

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0.86

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0.82 10

100

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Figure 2. The measurement of the shape factor F = 4π A/P 2 for perfectly circular objects at different scales (circles of 20 to 20000 pixels) reveals the strong variability of this parameter and a central tendency sometimes of 0.9 instead of 1.

practice by slightly varying image acquisition conditions and monitoring their impact on the ﬁnal measurements.

Errors in image analysis Digital images are the results of the systematic sampling of a scene by pixels covering an area of a given size. As for any other sampling processes, the transformation of a real scene into a digital image implies a succession of errors that can be classiﬁed into three groups following a terminology inspired by Pierre Gy’s pioneering work in sampling of granular materials (Gy 1992): Preparation errors: these are all errors involved in the image acquisition procedure that affect the quality of representation of objects in a scene (saturation, shadowing, etc.). Integration errors: these are errors linked to the number, density and location of discrete pixels used to build the digital image (in practice this is essentially linked to magniﬁcation and Charge Coupled Device (CCD) resolution). Analysis errors: these are all biases generated by the segmentation and measurement algorithms themselves (impact of variable thresholds, choice of diameter estimators, etc.). Hereafter, we review these different types of errors, showing how it is practically possible to identify their causes, and showing what precaution is needed to keep the cumulative error reasonable.

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Preparation errors Selecting the best imaging device It is better to spend additional time optimizing the use of the hardware and improving the conditions of acquisition of images, than to hope that sophisticated algorithms will compensate for bad image quality. The information that is not captured at the moment of image acquisition will never be recreated by further processing. An example is provided by the separation between major sulﬁde minerals from the nickel ore of Sudbury. A trained person will easily distinguish minerals such as Arsenopyrite, Pyrite, Pentlandite or Chalcopyrite in an image like Figure 3. It seems logical to tackle this problem by using a 3-CCD color camera, because the Red, Green and Blue (RGB) channels provide a representation close to the one perceived by human vision. In fact, another imaging solution emerges in microscopy: multispectral imaging (Pirard and de Colnet 2000). In our example, a series of images can be acquired from an identical scene using a succession of different ﬁlters. As opposed to RGB channels, which have a wide spectral band (100 nm), it is possible in microscopy to use interference ﬁlters with a bandwidth of

A.

B.

Mi

Pn

C.

Py

D.

Figure 3. Images of a nickel sulﬁde ore taken with a blue (∼ 400–500 nm) ﬁlter (A) and the same scene viewed at 438 nm (B). Scale bar = 100 µm; the images scatter plots of color values shows clearly that the 438 nm allows a better discrimination of the phases: Mi = Mispickel; Pn = Pentlandite; Py = Pyrite.

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FRANCUS AND PIRARD Table 2. Mahalanobis distances indicate the superior discrimination between phases when using multispectral imaging (Pirard and de Colnet 2000). Mineral pairs

RGB Mahalanobis distances

438 nm - 498 nm - 692 nm Mahalanobis distances

10.98 70.62 85.05

33.11 78.69 188.42

Pentlandite - Pyrite Pyrite - Mispickel Pentlandite - Mispickel

only 10 nm. This subtle difference allows for discrimination between the different phases of the image. Figure 3 compares the efﬁciency of the RGB imagery with multispectral imagery at 438, 498, and 692 nm. Figure 3 shows how the scene looks under a blue ﬁlter with 3000 ms integration time as compared to the same scene with a 438 ± 5 nm ﬁlter and 700 ms integration time, and displays the scatter plots for the same 400 pixels selected as representative of each phase. In order to quantify the improvements of multispectral imaging over conventional RGB imaging, Mahalonobis distances have been computed between the minerals for both spectral spaces. Values are given in Table 2 (Pirard and de Colnet 2000). Controlling image acquisition conditions Once the best hardware option is determined (for a comprehensive review, see Lamoureux and Bollmann (this volume)), it is still wise to check the quality of the images. In that respect, taking photographs of a well-known object, i.e., a calibration grid, or a color chart, is often helpful in detecting systematic errors (Nederbragt et al., this volume; Ortiz and O’Connell, this volume). Even using a monospectral (black and white) imaging technique, the operator faces a wide variety of adjustments. Integration time, gain, offset, image depth (grey level resolution), etc. are also important with respect to the perspective of further automatic image analysis. These may appear trivial adjustments to human vision, e.g., addition of a ﬁlter under the microscope, increasing light intensity, etc., but they are not for the digital camera. It is relatively easy to test for the robustness of a modal (or composition) analysis procedure by applying reasonable variations to acquisition parameters such as the intensity of light, focal distance, and others. In the next example, we explore the robustness of several automated thresholding techniques applied on the very same image acquired with various settings in the focus conditions (Fig. 4 and Table 3). It is important to proceed with such testing if one desires to develop an automated procedure to analyze a large series of microscopic preparations. Indeed, during the motorized scrolling of the sample, it would be nearly impossible to avoid changes in focusing, unless an ideal autofocus system is available. For digital image acquisition, any increase in quality leads to a relative decrease in processing time, and inversely. Testing images for noise is useful in deciding the optimum acquisition conditions in terms of the number of averaged frames (digital camera) or integration time / speed of the scan for the Scanning Electron Microscope (SEM). The amount of hardware noise can be estimated by taking two successive images of the same

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Figure 4. Images of sulfur grains (white grains) taken at different focal length. From left to right: Focus −−, in focus, Focus ++. The results of modal analysis are reported in Table 3.

Table 3. Surﬁcial proportion of the sulﬁde phase estimated using several automated thresholding techniques with respect to positive (+) and negative (−) out of focus. One notes that the method that provides the median values (in bold) is also the one that displays the strongest variability. Hence, factorization is the method that provides the least biased results, but its precision is noticeably degraded when the picture is positively out of focus.

Focus −− Focus − Reference Focus + Focus ++ Standard deviation Average

Entropy1 39,85 40,15 40,95 41,50 42,69 1,07 41,32

Moments1 40,78 40,94 41,11 43,75 45,69 2,28 42,87

Factorization1 43,44 43,35 43,03 46,08 48,78 2,69 45,31

Compacity1 48,05 51,08 46,34 49,17 51,34 2,31 49,48

Min. Histo1 49,84 51,08 47,45 51,83 51,34 2,01 50,43

1 Entropy, Moments, Factorization, Compacity, Minimum Histogram are thresholding techniques reviewed in Sahoo et al. (1988).

ﬁeld of view under strictly identical conditions, and computing their difference (Fig. 5). Testing a series of acquisition settings will allow you to decide which setting produces an acceptable level of noise. Here again simple tests can lead to a better compromise between accurate but productive imaging, because averaging additional frames or slowing down the scan speed further is not necessary.

Integration errors (sampling) This section illustrates integration errors relative to phase (composition), size and shape measurements. The reader is referred to geostatistical textbooks for a general discussion on errors relative to spatial sampling (Pirard, this volume). Integration errors include those problems related to the inﬂuence of image enlargement (image support) on the dispersion of phase ratios in thin-sections.

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C. Figure 5. Two images (A. and B.) of the same view of detrital sediment of lake El’gygytgyn using BSE, acquired successively at a magniﬁcation of ×100, and the difference between them (C.). In C. the contrast has been expended to show details. This provides a measure of acquisition noise.

Phase The ﬁrst example (Fig. 6) is two images of a neoformed calcite crystal in a sediment layer of Baldeggersee, Switzerland, taken at the very same location but using different magniﬁcations. By changing the magniﬁcation, the distribution of the phase ratio is modiﬁed but it’s mean is not. In the case of image analysis, magniﬁcation changes imply modiﬁcation of the resolution. This modiﬁcation can be more or less important according to the dispersion of the phase that is under investigation, but it always tends towards an asymmetric spreading of the phase ratio when enlargement increases. Even though the real phase ratio of the sample has not, of course, changed, the consequence√of this is that the precision of the phase ratio is roughly degrading proportionally to σ/ N as predicted by the conﬁdence interval of the mean of a Gaussian distribution. The resolution of the image also has an inﬂuence on the surface area. Figure 7 illustrates that it is impossible to obtain similar phase ratio measurements, in spite of a careful search for an optimal threshold in both cases. The main reason for this is the disappearance of the smallest calcite grains and the decrease in surface size of the largest ones due to the diffusion of light. For the 1 µm per pixel resolution, the mean phase ratio is about 9.21%, whereas it drops to 4.37% for the 5 µm per pixel resolution.

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Figure 6. Two images of a neoformed calcite layer in Baldeggersee are taken at the SEM in BSE mode at 35× (left) and 350× (right). In a series of images of the same layer, the phase percentage of calcite grains in the low magniﬁcation images ﬂuctuates between 6.5% and 9%, while they comprise between 0.74 and 20.86% in the ones at strong magniﬁcation. It shows that phase estimation is magniﬁcation dependent.

Figure 7. Phase analysis is performed on two identical scenes of BSE images of calcite layers in Baldeggersee, using identical light settings, and image processing. The resolution on the left image is 1 µm/pixel and 5 µm/pixel on the right one. Calcite content is 9.21% on the high resolution image, but is only 4.37% on the low resolution right image. Phase percentage is 8.54% of calcite on 2.5 µm/pixel image (not displayed here). Phase estimation is dependent on resolution.

Size (granulometric analysis) By deﬁnition, it is only possible to measure the size of a grain if it is entirely located within the boundaries of the image. It is clear that the probability of seeing a grain in an image is related to its size: the larger the grain, the more chance it has to touch the border of the image, and hence to be excluded from measurements. The probability of intersecting large objects is very small in high magniﬁcation images, because the ﬁeld of view is very small. At the opposite end, in low magniﬁcation images, the size of the pixels limits the size of the particle that can be detected. Intuitively, it is necessary to apply a correction for the frequency related to the grain size. For very large windows compared to the size of the

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mD0 (µm)

60

40

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0 0

250

500 750 Magnification

1000

Figure 8. Median of equivalent disk diameters (mD0 ) from 50 images of hemipelagic sediments versus the magniﬁcation at which images have been taken at the microscope. There is an exponential relationship between the variables. Image resolution has been maintained constant as well as the minimum number of pixels used to consider a group of pixels as an object.

largest grain in the image (i.e., image width greater than 10 times the largest grain diameter), the correction becomes negligible, as for the low magniﬁcation (×35) images in Figure 6. The correction will be more signiﬁcant for the ×350 magniﬁcation. This correction is known as the Miles-Lantuéjoul correction (Serra 1982; Pirard, this volume). The example of Figure 8 illustrates this inﬂuence of the magniﬁcation on size results. In order to characterize hemipelagic sediments in Lake Baikal, we collected a set of samples from miscellaneous hemipelagic settings and ages. We obtained several images from thinsections at the SEM and the petrographic microscope, and processed them as outlined in Francus and Karabanov (2000), to obtain size information using the median equivalent disk diameter, mD0 (Francus 1998; Pirard, this volume). Even if one expects some heterogeneity of the samples, Figure 8 indicates that the magniﬁcation deeply inﬂuences the size results. Testing a preliminary set of images, such as the one in Figure 8, allows one to determine a working magniﬁcation that does not imply the Miles-Lantuéjoul correction. Shape (morphometric analysis) The measure of an aspect ratio is always obtained by dividing a longest diameter by a shortest one. It can be obtained using several techniques, including the Feret diameters or the Equivalent Inertia Ellipse method (Medalia 1970). These methods do not necessarily provide identical aspect ratio values, and results can be substantially different according to the shape to be analyzed, especially for the most concave shapes. Figure 9 illustrates how the aspect ratio measurement can vary with the scale factor. Another way to reveal this bias

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B. 2.9

0 7 15 22 30 37 45

2.8 Elongation

2.7 2.6 2.5 2.4 2.3 2.2 2.1

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10000

Figure 9. In panel A., a synthetic elongated rough sand grain has been reproduced at different scales according to a geometric progression (×2) from 24 pixels to 12000 pixels, as well as rotated at 7◦ increments. Panel B. displays the elongation measurements using moments of inertia for each of the objects in panel A. It is clear that the dispersion of results is larger for small objects.

Equivalent disk diameter (µm)

10

7.5

5

2.5

1

0.75 0.5 0.25 Aspect Ratio

0

Figure 10. Aspect ratio (long/short axes of the best ﬁtting ellipse) versus size of the grains in a single image. The smallest grains are less elongated (closer to 1).

is a plot of the aspect ratio of each grain of an image versus its size (Fig. 10). It reveals that objects represented by a small number of pixels erroneously look more circular. They may need to be removed from the set of data to ensure shape measurements without bias. In practice, it can be said that particles should be at least >150 pixels (Fig. 9) in surface in order to estimate their aspect ratio without bias.

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FRANCUS AND PIRARD Table 4. Variation of the phase percentage P % according to 3 multispectral segmentation techniques of RGB images (Pirard and Bertholet 2000). Mineral

Multigaussian

Convex Hull

Behavioral

Sphalerite Arsenopyrite Pyrite Chalcopyrite Pyrrhotite

25.29 9.37 4.80 33.26 5.56

24.27 9.07 5.36 35.76 1.10

21.78 8.86 3.87 31.30 0.53

Chalcopyrite Stannite Sphalerite Galena

11.74 41.28 30.23 3.16

11.03 42.31 32.58 2.84

10.13 38.48 31.36 2.56

Analysis errors The choice of a threshold by a human operator creates some inaccuracy of the measurements that are useful to know. The same rationale is applicable for automated thresholding techniques or multivariate classiﬁcation (Table 4). Each technique has its own criteria, and one needs to choose the best suitable one for a given problem. In another example, our purpose is to quantify the amount of the detrital versus the organic input from a lake in Central Spain. Some sections of the sequence are believed to be varves. We used Backscattered Electron (BSE) images from thin-sections in order to perform a phase analysis at the lamina scale. In the method used here, and described elsewhere (Francus 1998; Francus et al. 2002), the threshold level is usually ﬁxed by a low in the density histogram that separates the pixels representing the matrix and the ones that represents the grains. However, because some sediment facies in the sequence are grain-supported (Lowe and Guy 2000), the minimum in the histogram is absent (Fig. 11). An operator needed to decide on a threshold level in a more subjective way. Therefore, it was necessary to test how much the phase results were inﬂuenced by a varying threshold level. We varied the threshold level by increments of 10 grey level values, i.e., 4% of the whole range, with a maximum of 24% around the value that was chosen by the operator. Table 5 reports that the phase percentage (P %) here is very sensitive to slight changes in the threshold value. Therefore such measurement should be taken very cautiously. From the identical example from Central Spain we also tested the robustness of size analysis. One can see that the median apparent equivalent disk diameter, mD0 , is weakly affected by threshold variations, at least in the range between 60 and 140 grey level value, i.e., 31% of the whole density depth. This means that for size analysis, there is room for imprecision in deciding the threshold level. Testing ﬁltering Many different transformations are, in general, applied to images to enhance and to allow the measurement of features of interest. Some widely used ﬁlters, such as erosions and dilations,

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Figure 11. (A.) BSE image of sediment from Laguna del Hornillo, central Spain (photograph J. Vegas Salamanca). Scale bar is 200 µm. (B.) is the grey level value histogram of image A. Image A., a 0-255 grey-level image, has been binarized into a series of black and white images using threshold values from 40 (C.) to 140 (H.), at 10 grey-level increments (odd tens not shown here). (I.) displays variations of the apparent disk diameter µD0 with varying threshold from 40 to 160. (J.) displays variations of the grain shape (mean of all the grain long to short axes ratios) with varying threshold from 40 to 160.

100

FRANCUS AND PIRARD Table 5. Variation of the size (Median D0 ) and the phase percentage P % of Figure 5 with a varying threshold value. Threshold value

Median D0 (µm)

Phase %

40

20.39

0.94

50

20.894

1.25

60

23.248

1.61

70

23.471

2.02

80

23.909

2.64

90

23.248

3.4

100

22.451

4.38

110

22.568

5.69

120

22.797

7.57

130

23.248

10.34

140

24.763

14.33

150

26.389

19.67

160

29.194

26.31

can have very surprising unwanted results on the ﬁnal measurement. Figure 12 displays the frequency histogram of the orientation of detrital grains in an image of sediments of Lake Vico (Italy), before and after the application of an opening, which is a ﬁlter that smoothes object boundaries in binary images (Nederbragt et al., this volume). In the raw image, most of the grains are horizontally disposed, i.e., their long axes have an angle with the horizontal between 0 and 20◦ and 150 and 180◦ . The application of an opening substantially increases the frequencies of the 0◦ and 90◦ classes. This is due to the fact that grains represented by a small number of pixels, i.e., <20 pixels, are very sensitive to the square nature, i.e., the 3 × 3 or 5 × 5 array, of the morphological test operated by the opening (Nederbragt et al., this volume). The orientations corresponding to the geometry of this array (vertical and horizontal) are favored. This example shows that orientation results can be biased by ﬁltering operations if the smallest object to be measured is not resolved by a sufﬁcient number of pixels. Future directions A systematic review of potential errors when using image analysis should be conducted in order to allow image analysis techniques to mature as a widely accepted methodology. However, the range of problems encountered is very wide, and it would be impossible to perform here a comprehensive review. Hence, we think that the next step toward a better use of image analysis techniques in paleoenvironmental science will be a set of comprehensive reviews of more speciﬁc and emerging topics, such as the quantiﬁcation of sediment composition from color pictures of a sediment core or grain size analysis from microphotographs.

TESTING IMAGES FOR ERRORS

A. Raw binary image

B. Binary image after an opening

100

100

80

80

60

60

40

40

20

20

Frequency

101

0

0 0

20 40 60 80 100 120 140 160 180 Angle

0

20 40 60 80 100 120 140 160 180 Angle

Figure 12. Frequency histogram of the orientation of detrital grains in an image of sediments of Lake Vico (Italy), before (left panel) and after (right panel) the application of an opening. Note that in the right panel the frequency of 0◦ is above 100, and the frequency of 90◦ has increase by an order of magnitude (arrows).

Summary Because image analysis is subject to errors, this chapter advocates for the systematic performance of quality controls of the results. Errors can be reduced to a minimum, but to do so it is necessary to identify their cause. Since an image is the result of a long series of sampling and operations, many factors can introduce error. Each parameter can be tested by slightly varying that parameter while maintaining the other constant and monitoring their impact on the ﬁnal measurement. Preparation (or acquisition) errors are easy to test but require performing some empirical trials. Integration errors (or sampling errors) can be substantially limited if basic rules are respected (Table 6). Analysis errors (or errors due to processing the images) require that the transformation applied to the image is fully understood by the operator. There is a great risk of bias if a processing algorithm is used as Table 6. Minimum pixel size of object of interest in a digital image with respect to the property being measured. Property

Object minimum size

Surface area Aspect ratio Orientation Roughness

3 × 3 pixels 150 pixels 500 pixels 2500 pixels

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a magic black box. Finally, efforts should also be made to try to validate the results with external methods and correctly educate geoscientists in image processing and analysis. Acknowledgments We thank J. Vegas, C. Asikainen, and M. Sturm for providing sample and BSE images from central Spain, Lake El’gygytgyn and Baldeggersee respectively. We thank Frank Keimig for smoothing the English language. Pierre Francus is supported by the University of Massachusetts. References Francus P. 1998. An image analysis technique to measure grain-size variation in thin sections of soft clastic sediments. Sed. Geol. 121: 289–298. Francus P. and Karabanov E. 2000. A computer-assisted thin-section study of lake Baikal sediments a tool for understanding sedimentary processes and deciphering their climatic signal. Int. J. Earth Sci. 89: 260–267. Francus P., Bradley R.S., Abbott M., Keimig F. and Patridge W. 2002. Paleoclimate studies of minerogenic sediments using annually resolved textural parameters. Geophys. Res. Lett. 29: 59–1 to 59–4. Gy P. 1992. Sampling of Heterogeneous and Dynamic Material Systems: Theories of Heterogeneity, Sampling, and Homogenizing. Elsvier, Amsterdam, New York, 653 pp. Lowe D.R. and Guy M. 2000. Slurry-ﬂow deposits in the Britannia Formation (Lower Cretaceous), North Sea: a new perspective on the turbidity current and debris ﬂow problem. Sedimentology 47: 31–70. Medalia A. 1970. Dynamic shape factors of particles. Powder Technol. 4: 117–138. Ojala A. and Francus P. 2002. Comparing X-ray densitometry and image analysis of thin-sections in varved sediments. Boreas 31: 57–64. Petterson G., Odgaard B.V. and Renberg I. 1999. Image analysis as a method to quantify sediment components. J. Paleolim. 22: 443–455. Pirard E. 1991. Quantitative mineralogical analysis of Cobalt and Copper distribution in historical slags from Küre (Turkey), Can. Inst. Min. Metall. Bull. 84: 87–91. Pirard E. and de Colnet L. 2000. Moving from colour to multispectral digital imaging in optical microscopy. Nederlandse Vereniging voor Microscopie, Jaarboek: 88–89. Pirard E. and Bertholet V. 2000. Segmentation of multispectral images in optical metallography. Rev. Metall.-Cah. Inf. Techn. 97: 219–227. Serra J. 1982. Image Analysis and Mathematical Morphology. Academic Press, New York, 610 pp. Sahoo P.K., Soltani S., Wong A.K.C. and ChenY.C. 1988. A survey of thresholding techniques. Comp. Vis. Graph. Image Process. 41: 233–260. Starkey J. and SamantarayA.K. 1991.An evaluation of noise reduction ﬁlters, with particular reference to petrographic images. J. Comp.-Assist. Microsc. 3: 171–188. Tovey N.K. and Krinsley D.H. 1991. Mineralogical mapping of scanning electron-micrographs. Sed. Geol. 75: 109–123. van den Berg E.H., Meesters A., Kenter J.A.M. and Schlager W. 2002. Automated separation of touching grains in digital images of thin sections. Comp. Geosci. 28: 179–190.

Part II: Application of Imaging Techniques on Macro- and Microscopic Samples

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6. DIGITAL SEDIMENT COLOUR ANALYSIS AS A METHOD TO OBTAIN HIGH RESOLUTION CLIMATE PROXY RECORDS

ALEXANDRA J. NEDERBRAGT ([email protected]) JÜRGEN W. THUROW ([email protected])

Department of Earth Sciences University College London Gower Street London WC1E 6BT UK Keywords: Sediment, Colour, Digital image, Still camera, Light correction, Colour calibration, CIE L∗ a∗ b∗ , lamination

Introduction The growing importance of high resolution palaeoclimate studies has increased the need for methods that can generate long, detailed, and continuous time series from sedimentary sequences. One sediment property that is suitable for this purpose is sediment colour, as it reﬂects chemical composition, yet is easy to measure using non-destructive techniques. Quantitative colour measurements are now produced routinely, for example during Ocean Drilling Program (ODP) cruises. The most widely used equipment to collect sediment colour data is a photospectrometer, which can measure reﬂectance in small increments across a range of wavelengths. The spectrum can be conﬁned to the range of visible light (400–700 nm), or may include the near ultra-violet or near infrared parts of the spectrum. The shape of the reﬂectance spectrum can provide detailed information about lithological and chemical composition of the sediment (Mix et al. 1995; Balsam and Deaton 1996, and references therein). In many cases, the spectrum is subsequently integrated into 3 colour co-ordinates, to trace stratigraphic variation in sediment colour (e.g., Chapman and Shackleton (1998), Ortiz et al. (1999), Helmke et al. (2002)). However, the maximum stratigraphic resolution is 1 or 2 mm at most. The photospectrometer is therefore suitable to compile decimetre-scale or larger changes in sediment colour. In contrast, images collected with a digital camera summarise reﬂectance values in the range of visible light into three broad wavelength intervals (red, green and blue channels, RGB). Colour data collected from digital images have been used to trace dm-scale change in sediment composition (e.g., Cortijo et al. (1995)) but a much higher stratigraphic resolution is possible. The actual resolution depends on the camera and its lens, but a resolution of one measurement per 100 µm, or better, can easily be obtained with modern cameras 105 P. Francus (ed.) 2004. Image Analysis, Sediments and Paleoenvironments. Kluwer Academic Publishers, Dordrecht, The Netherlands.

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and computers. This makes digital images a suitable source for colour data from ﬁnely bedded and laminated sediments, as it allows description of variation at the sub-millimetre scale. Such high resolution sediment colour time series have been used successfully to reconstruct palaeoclimatic records from laminated and varved sediments (e.g., Merrill and Beck (1995), Schaaf and Thurow (1998), Rodbell et al. (1999), Nederbragt and Thurow (2001b)). However, the practical techniques required to obtain high-quality colour data from digital images are not very well established. For example, effects of an uneven light distribution are not always corrected for (Cortijo et al. 1995). Schaaf and Thurow (1994) discuss how time series can be extracted from grey scale images. The application of those techniques to colour time series is explored by Nederbragt et al. (2000). The aim of this chapter is to describe the practical steps needed to extract colour data from digital images of sediment core surfaces, in such a way that the data adequately represent sediment colour variation at all scales, from laminae to decimetre/metre scale colour banding. The focus is on techniques to ﬁlter out artefacts due to uneven illumination. The data processing described in this chapter can be performed “manually” using image analysis software in combination with a spreadsheet. However, for large data sets it is more efﬁcient to design macros or programs to automate part of the processing. Image data collection Camera set up The basic set up needed to collect sediment surface images consists of a standard photographic stand with two daylight lamps and a digital camera. The various aspects of image collection in general, i.e., sample geometry, image registration, and lighting considerations, are discussed in more detail by Lamoureux and Bollmann (this volume). Apart from standard photographic techniques, the essential requirement for sediment imagery is that physical conditions are kept as constant as possible while scanning a set of cores. Small, uncontrolled changes in the amount of light will be incorporated in the images as artefacts that are difﬁcult to ﬁlter out afterwards. Such distortions may be barely (or not) visible to the human eye, but can be large relative to the often subtle variations in sediment colour. Examples include not only variable sunlight in a room with open windows, but also the presence of reﬂective objects near the sediment core. Sediment cores are often wrapped in foil or cling ﬁlm. The foil can reﬂect light onto the sediment surface, if it is not removed before imaging. During ODP Leg 167, a red-coloured block was included at the end of each section, as an aid for automation of the data processing. However, light was reﬂected from the surface of this block, producing a faint but measurable “red sheen” on the sediment surface as far as 10 cm away from the block (Nederbragt et al. 2000). An additional source of error may be introduced when sediment cores are drying out, because the sediment colour will change as the water content decreases (Balsam et al. 1998). It is usually best to scan wet sediment cores as soon as possible after they have been collected, to avoid that changes in water content during storage create irregularities. Balsam et al. (1998) recommend scanning of dried sediments as the best solution to avoid effects of changing water content, but this is not really an option for entire sediment cores. Sometimes it cannot be avoided that conditions have to be changed during a run. For example, the camera may have to be recalibrated, or a light bulb replaced. When this is the

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case, it will be useful to rescan several images, to create a duplicate set that can be used to adjust for any offset between results obtained before and after the change in the set-up. Scraping Soft sediment surfaces will have to be scraped, not only to expose the fresh sediment colour, but also to smooth away scratches and other surface irregularities as much as possible. Scratches will produce shadows, or reﬂect light, which will show up in the digital image as darker, or lighter values, which are not representative of the true sediment colour. Most sediment can be scraped most easily with a dough scraper, which has a hand grip that makes it comfortable to hold. Such scrapers can be bought in kitchen equipment shops; sanding down sharp corners helps to avoid making new scratches while scraping. Sediments with high water content may be easier to smooth with an electro-osmotic knife (McMillen et al. 1977). Slabs of lithiﬁed sediments can be polished to remove any saw-marks. Overlap It is advisable to photograph consecutive portions of a sediment core with a substantial overlap with adjoining images. Part of the reason is that the quality of a photograph is best in the central area. Deformation of object shape due to imperfections in the camera lens, parallax effects, and changes in light intensity tend to be worst towards the edges of a photograph. The main reason for the purpose of this chapter is that the overlap can be used to test if the uneven light distribution of the light source was corrected successfully. After correction, sediment colour values in the overlapping area of two images should be (nearly) identical. The amount of overlap may be a compromise based on disk storage space and/or amount of time needed to collect a set of images. We prefer to work with a 40% overlap, i.e., 25 cm of sediment is included in each image, while the core is moved in 20 cm steps, with the result that 5 cm at each end of the image is included in the adjacent images also. An additional advantage of imaging the sediment in such ﬁxed-length intervals is that any remaining light-artefacts will show up as a regular pattern with a constant wavelength (i.e., the size of the photographs). Scale It is standard practise to include a centimetre scale in photographs of sediment cores. Wooden trays, which have a ruler ﬁxed along one side, are fairly common. However, if the ruler and the surface of the core are not exactly at the same level, parallax effects will occur towards the edges of the image. This may be a hindrance when the images are used to log laminae-scale features, because the stratigraphic position cannot be determined to millimetre accurately. One method to ﬁnd the exact point at which two adjoining images overlap is to stick a pin into the sediment near the edge of the core liner (Schaaf and Thurow 1994). Another possibility is to drape a cloth tape measure on top of the sediment along one edge of the core surface. A relatively dark cloth tape can also double as a tool for light correction, if necessary.

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Colour calibration tools Accurate colour calibration requires (expensive) specialist tools. The colour registered by the camera depends on the hardware as well as the colour temperature of the light source and the setting of the camera (speed, aperture). The cumulative effect can be determined by imaging objects with known colour values, ideally as often as possible during a scanning session. The ideal set comprises a set of ceramic tiles with accurately known colour values (see also Nederbragt et al. (this volume)). A cheaper alternative is a Munsell colour chart, as they have been printed to be as close as possible to a set of colours with deﬁned tristimulus values. Standard photographic colour separation guides can be used to check for changes in light intensity during a scanning session. However, they cannot be used for calibration, as their colour values are not known in detail. It may be useful to cut down a large colour card into small pieces, and paste those onto a small card that can be placed alongside the sediment in all images. Another photographic item that can be useful for light correction is a neutral grey card, which is imaged to measure the distribution of light intensity across the ﬁeld of view. Such grey cards (and colour separation guides) can be bought in the better photography shops; the standard photographic card is an 18% grey matte card. Extracting colour data Line scan data Colour time series are best extracted “manually” from a set of images on the screen, to be able to select a stratigraphic line (or bar) that is representative for the sediment colour variation. In many cases, however, the original images will be too dark or have too little contrast to reveal all relevant features. Enhancing of contrast and brightness may be required to allow visual inspection of an image, yet it has to be done in such a way that the original colour information can be reconstructed. One solution is to enhance a copy of the original image, select the best area for a line scan in the enhanced copy, and then extract the colour data from the same region in the original image.Alternatively, contrast and brightness can be increased in a controlled way (Nederbragt et al., this volume), applying the inverse transformation to the colour values after they have been extracted from the enhanced image. The choice of the width of the stratigraphic line (or bar) along which colour data are collected is partly a matter of preference and can be varied depending on the type of sediments or the quality of the camera that was used. Collecting colour data along a wide strip in tilted sediments will result in averaging of data from different stratigraphic levels and may lead to unwanted smoothing across laminae boundaries. For that reason, Schaaf and Thurow (1994) preferred to scan images along a vertical line of only one pixel. On the other hand, cameras usually produce a certain amount of scatter in registered colour values even for objects that are homogeneously coloured. Collecting data from a wider bar has the advantage that it reduces camera noise, because random scatter is averaged in the horizontal direction. Nederbragt and Thurow (2001a) scanned bars of 11 to 17 pixels wide as a compromise between smoothing of camera noise and smearing of information across tilted laminae.

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Interpolation Even with the best scraped sediment surface, there will be some areas that are not representative of the true sediment colour (scratches, disturbed intervals, etc.). Such intervals are part of the real sediment thickness, but they should be skipped when collecting the line scans, or the colour data in these intervals should be set to missing values. Taking individual line scans above and below such problem areas and pasting the individual segments together can be time-consuming. A more convenient solution might be to mark the problem areas in the image with a colour that does not occur anywhere in the actual sediment (pure white, for example), take a line scan through the image as a whole, and use a ﬁnd-and-replace function to locate and remove those colour values afterwards. Voids in a core can be handled in a similar way. Ultimately, voids will be subtracted from the record, to reconstruct the true stratigraphic thickness. However, this should be done after the light correction has been performed, which is based on position within the image. Light correction Still camera The essential step to obtain useful sediment colour data from a set of images that are collected with a still camera is the application of a correction for uneven light distribution within the images. Even with the best quality photographic lamps, the distribution of light across the area that is imaged is not completely uniform. However, the deviation from an even distribution will be the same in all images in a given set, if lamps and camera are kept in the same position throughout a scanning session, and if the sediment core is also kept as far as possible in the same position. In that case, the light distribution will be a function of the position within each image. A best ﬁt light correction function can therefore be estimated using the pixel position within the image as the independent variable. Light correction is the ﬁrst step to perform after the line scan data have been collected, and is done on the RGB values before they are transformed into another colour co-ordinate system. In theory, the deviation from a uniform light distribution can be measured from an image of a neutral grey card, which is imaged under the same conditions as the sediment. In practise, the light distribution curve found this way can rarely be used directly to correct the sediment colour values. The problem is that wet sediments are more reﬂective than a matte card, and effectively produce a much steeper deviation from a uniform light distribution (Fig. 1). We therefore prefer to estimate an average correction curve from all images in a set. The following light correction is applied along the stratigraphic axis of the image only. However, the effects of uneven light distribution will be present in all directions within the image. Ideally, line scans should therefore be collected from the same position laterally in all images, to avoid changes in light intensity perpendicular to the stratigraphic axis. In practise, this is usually not feasible, because line scans may have to be taken elsewhere, to avoid scanning across irregularities in the sediment. Light correction in the horizontal direction could be done in the same way as described below for the vertical (stratigraphic) direction, but is in practise rarely necessary. The difference in registered light intensity in a lateral direction along the core surface will usually be small, if the width of the core is

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Figure 1. Variation in lightness measured in an image due to uneven light distribution, as a function of reﬂectivity and colour intensity of the imaged object; high values represent light colours. A) L∗ values from colour digital images, with line scans through the sediment in an image of a sediment core and a reﬂective metal ruler alongside that core, and values through a matte grey card that was imaged under identical conditions (after Nederbragt et al. (2000)). The amount of light received by the camera from a reﬂective object varies with the angle between light source, object, and camera. The sediment, which is wet and therefore slightly reﬂective, results in a light distribution curve that is intermediate between that of the virtually non-reﬂective grey card and the highly reﬂective ruler. B) Measured lightness in grey-scale images of a matte dark grey and a matte light grey card, imaged with the camera set-up described by Schaaf and Thurow (1994). Loss of measured light towards the edges of the image is proportional to the lightness of the object in the centre of the image. As a result, the difference, in number of units, between edge and centre is much larger in the light-grey card than in the dark-grey card. However, the light distribution curve is shape-invariant. Note that the two curves in B are plotted on different scales to facilitate visual comparison of the shape.

narrow relative to the size of the total image. In images like those presented in Figure 2, there is normally no noticeable change in colour values from left to right across the core surface. However, uneven light distribution in a horizontal direction may become a problem when sediments are further enlarged and the core surface ﬁlls nearly the entire image. With such images it is advisable to test beforehand how strong the change in light intensity is laterally, and to restrict the position of line scans to a narrow area along the centre of the core surface. Average light curve and standard deviation A polynomial regression curve is calculated for each image individually, with colour value on the Y -axis, and pixel position on the X-axis. When working with colour images, a regression curve is calculated for each of the three colour co-ordinates separately. The

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Figure 2. Example of a sediment surface image with line scan data, illustrating how raw data are modiﬁed during light correction. A) Enhanced copy of a grey scale image of varved sediment at ODP Site 1034 in Saanich Inlet, British Columbia (data after Nederbragt and Thurow (2001a)). The sediment consists of alternating dark, clay rich winter laminae and light, diatom rich spring/summer laminae. The image was collected with the camera system described by Schaaf and Thurow (1994). White line indicates position of line scan data. B) Raw line scan data. Grey scale data are plotted as collected by the camera on a scale of 0 (black) to 255 (white). Dashed portions represent dark values across voids, which were discarded from the data before further processing. Dark grey line represents curve used to correct the light distribution; it is a 7th degree polynomial ﬁt through grey values in this image and ∼230 other similar images. C) Black line represents line scan data after subtraction of the correction curve in B. Vertical grey lines are drawn for reference. Note that dark-light ﬂuctuations within the varves are stronger in the centre of the image than close to the edges (i.e., more values outside the grey lines). D) Black line represents a moving standard deviation calculated for the line scan data in C. Grey line represents a 7th degree polynomial ﬁtted to the moving standard deviation curve for this image and all other images in the data set. The polynomial curve conﬁrms that the decrease in standard deviation towards the edges in this particular image is a persistent feature which is related to the uneven light distribution. E) Black line represents ﬁnal line scan data, after correction for variation in standard deviation; grey lines as in C. Note increase in amplitude of dark-light ﬂuctuations near the edges of the image compared to the data in C.

order of the regression should be high enough to be able to describe an irregular shape (7th to 9th degree polynomial). Only those images are used that are representative of the average sediment colour. Thin intervals with extreme values (e.g., thin event beds with a different colour) can be set to missing values, without inﬂuencing the ﬁnal average light curve unduly. However, an image should be excluded entirely, if a large part of that image is not

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representative (thicker event beds, or when the sediment does not extend all the way across the image, i.e., top or bottom of a core). A ﬁrst method to obtain the ﬁnal correction curve is to calculate an average for all data points in all individual regression curves. Alternatively, as a second method, the average of all regression coefﬁcients can be taken, to reconstruct a correction curve from the average polynomial equation. The second method is equivalent to estimating a regression curve for all images simultaneously, under the condition that all images cover the entire range along the x-axis. It is computationally easier than the ﬁrst method, but works only if the sediment does indeed extend across the entire image in each and every image. If not, a single non-representative image can dramatically alter the shape of the ﬁnal average curve. Once the ﬁnal regression curve has been obtained, the value in the centre of the curve (i.e., the reference point, which was directly under the camera) is subtracted from the curve, to give a ﬁnal set of correction values which are then subtracted from all the actual data ﬁles (Fig. 2C). For data obtained from laminated sediments, further correction is usually needed for changes in the standard deviation within the images. With the camera set-up used for the image in Figure 2, loss of light intensity towards the edges of the image also results in loss of contrast. As a result, the colour difference between light and dark laminae is smaller than in the centre of the image. The difference appears only small (Fig. 2), but it is actually large enough to show up as a distinct pattern during subsequent analysis of the colour data. A correction for this change in standard deviation is applied after the correction for average light intensity. For each line scan, a running standard deviation and a running mean are calculated, using at least 30 nearest neighbours around each data point. An average standard deviation curve is then estimated from all running standard deviation curves in the same way as described above for the light correction curve (Fig. 2). For correction, the calculated running mean for each individual image and the best ﬁt standard deviation curve are used. Each data point is ﬁrst transformed into a z-score, zi , using the running mean for that pixel (meani ), and the corresponding value in the best ﬁt standard deviation curve (si ): zi = (xi − meani )/si . After that, the inverse operation is applied to obtain the ﬁnal corrected colour value, substituting the standard deviation for a reference point in the curve (sref ) instead of si : xi = zi · sref + meani (the reference point is normally the centre of the curve). Grey card light correction With small data sets, the procedure described above may not yield an average curve that is representative for the true light distribution, especially if there are distinct ﬂuctuations in sediment colour within the data. The colour data in each individual image are a combination of uneven light and true variation in colour. The light distribution part is the same in all images, while the true sediment colour variation varies from image to image. The average light curve method works for large data sets, because stratigraphic changes in sediment colour are usually averaged out, yielding an average curve that describes the light distribution only. With small data sets, the probability is much higher that some true change in sediment colour is somehow incorporated into the average curve. The light distribution measured from a neutral grey card can be used to correct the mean (but not the standard deviation) when an average light curve correction does not produce good results. An additional requirement is that the overlap between images is substantial (see image data collection earlier in this chapter). The correction is based on the observation,

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Figure 3. Example of light correction using values measured in a neutral grey card. A. Line scans through two overlapping images of a sediment section (ODP Section 1098C-3H-2, Palmer Deep, western Antarctic Peninsula; image collected with the camera system described by Schaaf and Thurow (1994)) and line scan through a grey card, i.e., the plain grey ﬁeld in a slightly shiny grey-scale photographic reference card (dashed lines). Grey scale data are plotted as collected by the camera on a scale of 0 (black) to 255 (white). Note that the shape of the grey card appears to match well with that of the image between 36 and 64 cm (Image I, black line), but is steeper than that of the other image (image II, grey line). B) Line scan data after subtraction of grey card curve without adjustment. C) Grey card curve was multiplied by 0.83 before it was subtracted from the line scan data; note improved match of data between 62 and 63 cm. D) Correlation coefﬁcients between four pairs of images for a series of factors by which the grey card curve was multiplied before it was subtracted from the data. The maximum correlation is found for a factor of 0.83, which was applied to the data in C.

that the measured light distribution curve is steeper when the imaged object is lighter or more reﬂective, but that the shape of the curve is invariable (Fig. 1). The curve observed in the grey card is steepened (or ﬂattened) to the point where, when subtracted from the sediment data, the correlation is maximised in all pairs of overlapping intervals (Fig. 3).

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The optimum curve can be found “manually” by setting up a spreadsheet to perform the calculations interactively: ﬁrst, calculate a regression curve through the data extracted from the grey card, to obtain a smooth curve. Load as many of the colour line scans as possible into a single spreadsheet, and set it up to display the correlation coefﬁcients for all the overlapping segments. Then multiply the smoothed grey card light curve by different values and subtract it from the image data. Keep track of how the correlation coefﬁcients are changing, to ﬁnd the multiplication factor that yields the highest average correlation coefﬁcient.

Line scan camera Uneven light distribution is inherent to imagery using a still camera, because the light source has to illuminate a large area. Line scan cameras bypass this light distribution problem, in theory. Whether the camera and light source are moved along the object (e.g., ﬂat bed scanners) or the object is moved under a ﬁxed line scan camera, each line of the image is scanned in the same position relative to the light source. In practise, the amount of light received by the camera will still vary when the distance between light source and object varies. Light correction may therefore still be needed. Figures 4 and 5 illustrate how colour values ﬂuctuate in images of split cores, which were collected with a line scan camera, because of variation in the height of the core halves. Another example could be a set of sediment slabs scanned with a ﬂatbed scanner, when the slabs are not perfectly ﬂat.

Figure 4. Variation in colour intensity of a yellow cloth centimetre tape draped on the sediment surface of a set of sections, which were scanned with a Geotek colour line scan camera. Dark tick-marks on the tape were discarded. The green channel of the RGB co-ordinates was used because the red and blue channels were oversaturated in several images. The grey line indicates average of tape measure in ∼110 sections. Black line represents values for a single core, which was split asymmetrically; the “half” scanned was signiﬁcantly thinner than other cores. The darker values for the tape in this section are the result of the increased distance between the ﬁxed light source and the core surface. The irregular shape of both curves is due to wear of the tape, the dark spikes in the individual section represent mud stains.

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Figure 5. Lightness (L∗ ) data for 2 holes cored at ODP Site 1002 in the Cariaco Basin; plotted are average values per cm interval. Images were collected with a Geotek line scan camera. The age of the sediments ranges from ∼50 kyr BP at 20 m to the Recent; the light interval between 4.2 to 4.7 m represents the Younger Dryas. Data were extracted from the set of images discussed in Figure 4 before and after light correction. A) Data translated into L∗ a∗ b∗ as collected, without correction; note offset between the two holes of up to 5 units in L∗ in several intervals. B) Corrected data showing virtually identical colour variation; grey line represent data for Hole 1002D, black line for Hole 1002E. The difference in the green channel between the tape in each section and the average (see Fig. 4) was subtracted from all three RGB channels in the sediment line scan before translation into L∗ a∗ b∗ . For further discussion, see text.

Images for ODP Site 1002 were collected with a Geotek camera system, i.e., a system consisting of a ﬁxed line scan camera and ﬁxed light source, and a motor that pushes the split core along a rack under the camera. Since not all cores are split exactly down the middle, the distance between the sediment surface and the light source (circa 7 cm) varies as the height of the core surface changes. A cloth tape, which was draped on the core surface to keep track of stratigraphic thickness, had to double as a light correction tool (Fig. 4). Without correction for light variability, parallel holes at the same location show noticeable differences in measured colour values in several intervals. At the time, we did not expect that light correction would be required, so the cloth tape was not kept as clean as it should have been. Line scans were collected through the tape measure in all images, discarding dark values across tick marks, and taking the median per centimetre interval of remaining light values. Assuming that variation in height of the cores is gradual, the average curve, as well as the individual tapes were smoothed to remove small-scale irregularities and then interpolated to obtain a continuous curve. The difference between the average curve and

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the tape measure in a given image was then subtracted from the measured sediment colour values. The corrected sediment colour trends show an improved correlation between the two parallel holes (Fig. 5). Change in conditions during an imaging session A change in external conditions during an imaging session will usually result in an abrupt change in measured colour values between images collected before and after the change in conditions. The best way to deal with the data, is to do a light correction for each of the sets separately. The different colour time series can be brought to the same scale most easily, if several images were re-scanned under the new conditions. After light correction, calculate mean and standard deviation for all data points in all line scans in the duplicated images, once for the subset collected before the change (set1 ) and once for the subset collected afterwards (set2 ), giving mean1 and s1 , and mean2 and s2 . To bring the two sets to the same scale, all line scans in one of the sets (e.g., set2 ) are ﬁrst standardised: z2i = (xi −mean2 )/s2 . The inverse operation is then performed, substituting the mean and standard deviation of the other set: xI = z2i · s1 + mean1 . Testing the result If the light correction is successful, the colour time series should (normally) not contain any pattern that has the same wavelength as the size of the images. The best way to test if this is the case, is to string results from all images together, including the overlap, and calculate a power spectrum. Results are suspect if increased power is found at a wavelength that is equal to the length of the image. It is not impossible that the record contains a real colour ﬂuctuation with the same length as that of the images, but usually the problem is the result of inadequate light correction. It sometimes helps to redo the light correction, dividing the images into two or more subsets; or using a different set of images to calculate the average light correction curves. RGB to L∗ a∗ b∗ conversion and colour calibration At some point in the procedure, the RGB values produced by the camera should be translated into another colour co-ordinate system that is suitable for presentation of palaeoenvironmental colour data. The RGB system is designed for television and monitors, and is not really suited to depict colour variation in numerical values. The L∗ a∗ b∗ system, deﬁned by the Commission Internationale de l’Éclairage (CIE L∗ a∗ b∗ ) is appearing as the standard colour co-ordinate system for sediment colour studies. It has the advantage that the variables are easy to interpret in colours as registered by the human eye, as the system is designed to linearise the perceptibility of colour differences (Berns 2000). The equations to transform the RGB values collected by the camera into L∗ a∗ b∗ co-ordinates are presented in Nederbragt et al. (this volume). The translation is done via an intermediate step, translation of RGB into XY Z tristimulus values; L∗ a∗ b∗ values are a non-linear transform of XY Z. The calculations are simpler if only light-dark variation is of interest. Grey scale is deﬁned

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as the Y -value (Luminance) of the XY Z tristimulus co-ordinates, but L∗ (Lightness) can be used as well. Relative colour values are obtained by translating the measured RGB values into L∗ a∗ b∗ using a default transformation. Such relative data will be sufﬁcient for many applications, in which the objective is to study the pattern of change in colour. However, it may be desirable to obtain calibrated colour values, to allow comparison between different sediment records collected over a longer period of time, and (or) to correlate sediment colour with geochemical data. Calibrated colour values can be obtained if four colour chips with known colour values are imaged regularly (Nederbragt et al., this volume). Ideally, those colour chips are included in each image, to allow calibration of each image individually. This has the additional advantage that any remaining variation related to changes in light conditions are ﬁltered out at the same time. If this is not feasible, colour cards should still be imaged as often as possible, to estimate the best average transformation, which is then applied to the data set as a whole. The four-colour-chips approach produces good quality results if the images are in linear RGB, or if a correction for non-linear R G B was successful (Nederbragt et al., this volume). Using four colour chips for calibration, Nederbragt et al. (2000) could correct for drift in registered colour values by a camera that was used continuously for two months during ODP Leg 167. However, this approach can cause problems if the RGB of the images is not completely linear. The result is that either very dark or very light colours run out of gamut (i.e., the transformation from RGB to XY Z assigns non-existing colour values). If such is the case, the original 3 by 3 matrix transformation is more suitable, because it forces the calculated XY Z values into their appropriate range. A further discussion of non-linear calibration is provided by Ortiz and O’Connell (this volume). Mosaicking Once the colour data have been corrected for uneven light distribution, the individual line scans have to be strung together into a stratigraphic sequence. The overlap between adjacent images will be discarded. The match point can be found manually, by determining the exact pixel position of some recognisable point in both of the images. However, this can be tedious, especially if there are parallax effects with the ruler, or when laminae are slightly tilted and the line scans in two images are off-set along the horizontal axis. A method to help ﬁnd the best match is to calculate a cross correlation function (Davis 1986) between two overlapping segments, and ﬁnd the point at which the correlation is maximised. Examples and comparison with other methods ODP Site 1011, north-eastern Paciﬁc, off California Good quality and accurate sediment colour data can be obtained from digital images with the light correction procedures describe above. An example from non-laminated sediments illustrates that minute ﬂuctuations in colour can be documented successfully (Fig. 6, data from Nederbragt et al. (2000)). During ODP Leg 167, a video camera system was used as a test to collect sediment colour data. Figure 6 shows L∗ and a∗ values collected with this

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Figure 6. L∗ and a∗ values in two parallel holes at ODP Site 1011 (off California); plotted are average values across 5 cm intervals. Note close similarities between the two holes in low amplitude ﬂuctuations in a∗ (∼2 units), illustrating that digital images can provide good quality, reproducible data for metre-scale colour ﬂuctuations. For further discussion, see text.

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system for Upper Pliocene sediments at one of the sites drilled during this cruise. Site 1011 shows distinct meter-scale Milankovitch cycles in L∗ . Variation in a∗ is weak, but can be closely matched between two holes that were drilled at the same locality. Nederbragt et al. (2000) estimated from these and similar data, that the precision of colour records collected from digital images is better than 0.5 to 0.8 unit (1 standard deviation) for each of the three colour variables. The same example also illustrates how translation of the colour data into the CIE L∗ a∗ b∗ colour space facilitates interpretation of the data. As in most sediment records, colour variation at Site 1011 is dominated by distinct changes in lightness, while variation in actual colour (hue) is subtle (Fig. 6). Yet L∗ and a∗ show trends that are (partly) distinct, reﬂecting differential changes in two components of the sediment, total organic carbon (TOC) and carbonate content. Carbonate (light) and TOC (dark) have opposing effects on lightness. At ODP Site 1011, carbonate content and TOC content are negatively correlated, i.e., dark sediments are enriched in TOC, light sediments are enriched in carbonate (Fig. 6). Changes in a∗ (red) correlate with TOC, but not with carbonate content (Nederbragt et al. 2000). The correlation with TOC content is presumably related to small amounts of (weathered) pyrite, which are associated with organic carbon. Thus when colour is used as a proxy for chemical composition at this particular site, a∗ would offer the possibility to distinguish between the contribution of carbonate and TOC to the L∗ signal. Although large scale colour ﬂuctuations can be registered using digital images, it is more convenient to use a photospectrometer to collect colour data from bioturbated sediments. When a resolution of one sample per cm is adequate to describe colour ﬂuctuations, a photospectrometer has the advantage of providing data across the full visible spectrum, while the processing of digital images is more labour intensive. However, the higher stratigraphic resolution of digital images is a deﬁnite advantage in cm-scale bedded and laminated sediments. ODP Site 1098, Palmer Deep, Western Antarctic Peninsula The section at ODP Site 1098 in the Palmer Deep is a ∼50 m thick sequence of intermittently laminated Holocene to Last Glacial sediments. Photospectrometer data were collected during the cruise as part of the shipboard routine. The data in Figure 7 were collected at 1 cm intervals (Barker et al. 1999); spot size is not speciﬁed, but is typically 1 mm or slightly less for the type of photospectrometer that was used. Digital images were collected on-shore after the cruise (Nederbragt and Thurow 2001b). Laminations at Site 1098 vary in thickness from <1 mm to >1 cm. They consist of an alternation between dark sediments, which are enriched in diatoms and organic carbon, and light, clay rich sediments. In a sediment like this, digital image derived colour data not only allow for description of colour variation within the laminae couplets, but also are easier to correlate with other data collected at this site. The spectrometer data undersample the high frequency ﬂuctuations in composition, i.e., it is a matter of statistical chance whether a measurement is taken in a light or a dark lamina. As a result, the data show substantial scatter, and are difﬁcult to correlate with Gamma Ray Attenuation (GRAPE) density data, which represent integration over a ∼0.5 cm (or wider) stratigraphic interval (Fig. 7). A correlation between GRAPE density and sediment colour is expected as bulk sediment density is low in diatom and

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Figure 7. L∗ values extracted from digital images of intermittently laminated sediments in ODP Core 1098A-2H (Palmer Deep, western Antarctic Peninsula; data from Nederbragt and Thurow (2001b)) compared to shipboard GRAPE density data and phospectrometric colour data (Barker et al. 1999). Image data are integrated into 1 average value per centimetre; photospectrometer data are collected at 1 cm spacing with a spot size of ∼1 mm; GRAPE density data represent integration over 0.5 cm. For discussion of data, see text.

TOC rich intervals, which are darker. Results obtained with the photospectrometer could be improved by decreasing the sample spacing, but in this case digital images are more convenient. Integration of digital image derived colour data across one centimetre intervals yields a smoother curve, that shows better correlation with the density data (Fig. 7).

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D

Figure 8. Comparison of X-radiograph and digital image of a varved sediment interval at ODP Site 893 (Section 893B-4H-2, 8–15.5 cm, Santa Barbara Basin, off California). A) Grey-scale data through X-ray image, dark values represent higher sediment density. B) X-radiograph, arrow at top points to position of line scan data in A; vertical white bar denotes interval with clear laminae that are indistinct in the digital image. C) Digital image of the same interval, arrow at top points to position line scan data presented in D. Vertical white bar denotes ﬁnely laminated interval that appears homogeneous in X-radiograph. Image is grey-scale translation of colour original acquired with the still camera system described by Merrill and Beck (1995). D) Grey-scale data through digital image.

ODP Site 893, Santa Barbara Basin, off California The resolution that can be obtained from digital images of sediment surfaces is roughly similar to that of X-radiographs. The maximum resolution of X-radiographs of laminated sediments depends on various factors, including whether the laminae are tilted or not. Similarly, the resolution that is feasible with digital images of sediment surfaces is also partly dependent on the type of sediment. The images discussed in this chapter have a resolution that vary between 80 and 120 colour measurements per centimetre of sediment. At such a resolution, millimetre-scale laminae, like those in Figure 8, can be captured easily in an image of the sediment surface. If laminae are thinner, then it depends on the quality of the sediment surface whether they can be photographed successfully or not. For example, very thin laminae may be difﬁcult to see in silty sediments, because of small irregularities in the sediment surface, which cannot be smoothed away with scraping.

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The information provided by photographic and X-ray images can be substantially different. A comparison of an X-radiograph and a sediment surface image of one interval from ODP Site 893 in the Santa Barbara Basin shows that annual laminations (varves) that are distinctly visible in one record appear absent in the other, and vice versa (Fig. 8). The annual sedimentation cycle in the modern basin shows an alternation between increased terrigenous ﬂuxes (clay and silt) in winter, and increased marine productivity (diatoms and organic matter) during the upwelling season in spring and summer; carbonate ﬂuxes are fairly stable throughout the year (Thunell et al. 1995). The X-radiographs register differences in sediment density, that is, they are especially sensitive to changes in concentrations of diatoms and organic matter, and to changes in porosity. In contrast, sediment colour is highly sensitive to changes in TOC content, but the effect of diatom content appears to be small and usually obscured by other components. For example, diatom rich sediments recovered further north of the Santa Barbara Basin during ODP Leg 167 are dark, because diatoms are concentrated in intervals with high TOC content (Nederbragt et al. 2000), while the diatom rich spring/summer layers in the varves in the Santa Barbara Basin as well as in Saanich Inlet appear light (Figs. 2 and 8). On the other hand, changes in the proportion of carbonate, silt, and clay relative to each other strongly affect the visible colour of the sediment (Balsam and Deaton 1996). Yet these components have similar speciﬁc densities, and such ﬂuctuations may be difﬁcult to see in X-ray images. These two opposing effects are most likely responsible for the difference between the two images in Figure 8. Distinct laminations in the X-ray record, which are weakly developed in sediment colour, probably correspond to high porosity layers of diatom resting spores or diatom mats, while distinct laminations in sediment colour, which are invisible in the X-radiograph, result from changes in carbonate and clay content. Summary This chapter discusses procedures to obtain sediment colour time series from digital images of split core surfaces. This method is ideally suited to obtain sub-mm-scale colour records from laminated sediments. The most essential part of data acquisition to obtain good quality images, is that sediment surfaces are scraped carefully to remove any surface irregularities. After acquisition, line scans have to be collected through all images along the stratigraphic axis. The line scan data are subsequently corrected for uneven light distribution of the light source. Various methods for light correction are described. Examples are presented to illustrate application of the techniques especially to laminated sediments, and to compare the results with those obtained from photospectrometer data and X-radiographs. Acknowledgments Thanks are due to P. Francus, M. Green, J. Helmke, andA. Prokoph for helpful suggestions to improve the manuscript. Part of the illustrations in this paper are based on material collected by the Ocean Drilling Project, which is sponsored by the U.S. National Science Foundation and participating countries under management of Joint Oceanographic Institutions, Inc. We are grateful to U. Röhl for allowing us to use the Geotek camera scanner of the University of Bremen, and to J. Beck, W. Hale, P. Rumford, and A. Wülbers for their help during visits

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to the College Station and Bremen ODP core repositories. The methods described in this paper have been developed as part of research that was supported by various grants from the Natural Environmental Research Council.

References Balsam W.L. and Deaton B.C. 1996. Determining the composition of late Quaternary marine sediments from NUV, VIS, and NIR diffuse reﬂectance spectra. Mar. Geol. 134: 31–55. Balsam W.L., Deaton B.C. and Damuth J.E. 1998. The effects of water content on diffuse reﬂectance spectrophotometry studies of deep-sea sediment cores. Mar. Geol. 149: 177–189. Barker P.F., Camerlenghi A., Acton G.D. et al. 1999. Proceedings of the Ocean Drilling Program, Initial Reports, 178. Ocean Drilling Program, College Station, Tx, [CD-ROM]. Berns R.S. 2000. Billmeyer and Saltzman Principles of Color Technology. Wiley, New York, 247 pp. Chapman M.R. and Shackleton N.J. 1998. What level of resolution is attainable in a deep-sea core? Results of a spectrophotometer study. Paleoceanography 13: 311–315. Cortijo E., Yiou P., Labeyrie L. and Cremer M. 1995. Sedimentary record of rapid climatic variability in the North Atlantic Ocean during the last glacial cycle. Paleoceanography 10: 911–926. Davis J.C. 1986. Statistics and Data Analysis in Geology. John Wiley & Sons, New York, 646 pp. Helmke J.P., Schulz M. and Bauch H.A. 2002. Sediment-color record from the Northeast Atlantic reveals patterns of millennial-scale climate variability during the past 500,000 years. Quat. Res. 57: 49–57. McMillen K.J., Warme J.E. and Hemmen E.H. 1977. Electro-osmotic knife for slicing large box cores. J. Sed. Petrol. 47: 864–867. Merrill R.B. and Beck J.W. 1995. The ODP color digital imaging system: color logs of Quaternary sediments from the Santa Barbara Basin, Site 893. In: Kennett J.P., Baldauf J.G. and Lyle M. (eds), Proceedings of the Ocean Drilling Program, Scientiﬁc Results, 146. Ocean Drilling Program, College Station, Tx, pp. 45–59. Mix A.C., Harris S.E. and Janecek T.R. 1995. Estimating lithology from noninclusive reﬂectance spectra: Leg 138. In: Pisias N.G., Mayer L.A., Janecek T.R., Palmer-Julson A. and Van Andel T.H. (eds), Proceedings of the Ocean Drilling Program, Scientiﬁc Results, 138. Ocean Drilling Program, College Station, Tx, pp. 413–427. Nederbragt A.J. and Thurow J. 2001a. A 6000 year varve record of Holocene climate in Saanich Inlet, British Columbia, from digital sediment colour analysis of ODP Leg 169S cores. Mar. Geol. 174: 95–110. Nederbragt A.J. and Thurow J. 2001b. Sediment colour variation and annual accumulation rates in laminated Holocene sediments (ODP Site 1098, Palmer Deep). In: Barker P.F., Camerlenghi A., Acton G.D. and Ramsay A.T.S. (eds), Proceedings of the Ocean Drilling Program, Scientiﬁc Results, 178. Ocean Drilling Program, College Station, Tx, pp. 1–20 (online). Nederbragt A.J., Thurow J. and Merrill R. 2000. Data Report: Color records from the California Margin (ODP Leg 167): Proxy indicators for sediment composition and climatic change. In: Lyle M., Koizumi I., Richter C. and Moore C. Jr. (eds), Proceedings of the Ocean Drilling Program, Scientiﬁc Results, 167. Ocean Drilling Program, College Station, Tx, pp. 319–324. Ortiz J., Mix A.C., Harris S. and O’Connell S. 1999. Diffuse spectral reﬂectance as a proxy for percent carbonate content in North Atlantic sediments. Paleoceanography 14: 171–186. Rodbell D.T., Seltzer G.O., Abbott M.B., Enﬁeld D.B. and Newman J.H. 1999. An approximately 15,000-year record of El Niño-driven alluviation in southwestern Ecuador. Science 283: 516–520. Schaaf M. and Thurow J. 1994. A fast and easy method to derive highest-resolution time-series data sets from drillcores and rock samples. Sed. Geol. 94: 1–10.

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Schaaf M. and Thurow J. 1998. Two 30 000 year high-resolution greyvalue time series from the Santa Barbara Basin and the Guaymas Basin. In: Cramp A., MacLeod C.J., Lee S.V. and Jones E.J.W. (eds), Geological Evolution of Ocean Basins: Results from the Ocean Drilling Program. Geological Society, Special Publications 131, London, pp. 101–110. Thunell R.C., Tappa E. and Anderson D.M. 1995. Sediment ﬂuxes and varve formation in Santa Barbara Basin, offshore California. Geology 23: 1083–1086.

7. TOWARD A NON-LINEAR GRAYSCALE CALIBRATION METHOD FOR LEGACY PHOTOGRAPHIC COLLECTIONS

JOSEPH D. ORTIZ ([email protected])

Department of Geology Kent State University Lincoln and Summit Streets Kent, OH 44224 USA SUZANNE O’CONNELL ([email protected])

Department of Earth and Environmental Sciences Wesleyan University Middletown, CT 08457 USA Keywords: Grayscale image analysis, Non-invasive sampling, Deep Sea Drilling Program, Ocean Drilling Program, JOIDES Resolution, ODP Leg 100, ODP Leg 162, Sediment core photography, Marine stratigraphy

Introduction While a picture may say a thousand words, scientists and engineers often need to extract precise, quantitative information regarding physical processes from photographic evidence. Image analysis can, for example, be used as part of a quality control process in an industrial application, to monitor earth systems from space using satellite data, or to reconstruct changes in past climate from photographs of deep-sea sediments. How well questions related to each of these applications can be answered depends on a variety of factors, some of which can be easily controlled, others of which impose inherent tradeoffs (for example the relationship between depth of ﬁeld and focal length). Taken as a whole, these variables along with the hardware and software employed for capture, manipulation, and storage of the image compose the “total system response” or “lifecycle” of the image. Extraction of depth series of grayscale values from photographs of deep-sea sediments provides a means of characterizing the stratigraphy of marine sequences in ﬁne detail. Relating these grayscale proxy records to speciﬁc sediment components can, however, be somewhat difﬁcult. This difﬁculty can arise from several factors. Perhaps the most inherent of these difﬁculties is the fact that conversion of a colorful scene to monochromatic grayscale results in distortions of the original information in the scene. Consider for example, that different shades of color can have the same grayscale value leading to 125 P. Francus (ed.) 2004. Image Analysis, Sediments and Paleoenvironments. Kluwer Academic Publishers, Dordrecht, The Netherlands.

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misidentiﬁcation. A second concern is that differential wetness of the split core surface can result in variable amounts of specular reﬂectance from the core surface and thus contribute to variable glare within an image. The method thus works best in environments that are relatively monochromatic such as a binary mixing between terrigenous clay and marine carbonate. Because sediment brightness is often controlled by sediment carbonate content, grayscale values are often interpreted in terms of sediment carbonate content. Attempts to relate the two variables quantitatively often prove to be difﬁcult. One source of difﬁculty that must be addressed with this method is the need to intercalibrate grayscale values from photographs of cores in which lighting conditions and geometry may have differed. We explore a revised means of intercalibrating grayscale images that considers the nonlinearity inherent in the total photographic system response. Comparison of corrected grayscale values with measurements of sedimentary carbonate content by linear correlation indicates that the corrected grayscale values can be used to predict carbonate content with an error of less than 10%. This test provides an objective means of evaluating the quality of the proposed grayscale calibration method. This chapter focuses on one aspect of how grayscale analysis is employed within the paleoclimate community to convert conventional ﬁlm-based photographic evidence of freshly split core surfaces into proxy records useful for reconstructing stratigraphic relationships between cores, and semi-quantitative compositional analysis of marine sediments. This method is attractive because recent interest in high frequency climate variability has generated the need for very high-resolution climate records. For example, Bond et al. (1992) used grayscale analysis to evaluate the level of climate variability that occurred during Marine Oxygen Isotope Stage Five, the last interglacial. Hagelberg et al. (1994) compared long time series of climate variability (one of which was a proxy carbonate record derived from sediment grayscale) at high sedimentation rate sites to evaluate whether harmonics of the primary Milankovitch tones could give rise to climate cyclicity in the sub-Milankovitch part of the climate spectrum. Grayscale data from the Cariaco basin has been an invaluable aid to stratigraphic correlation both between cores from the basin and for direct comparison at the annual level with oxygen isotopic records from the GISP2 Greenland ice cores (Hughen et al. 1996; Behl and Hughen 1997). At the outcrop scale, grayscale analysis has proven useful for comparison with magnetic susceptibility records from eolian loess sequences (Porter 2000), as well as extraction of cyclicity from ancient sediments (Warren et al. 1998). Grayscale analysis methods have even been applied to photographs of physical stratigraphic models to relate the physical properties of formations within the experimental basin to their seismic response (Herrick et al. 2000). Grayscale analysis of deep-sea sediment core photographs is attractive for several reasons. There is a very extensive data set of available core photos (Fig. 1). The method is also non-invasive and thus leaves material untouched for further analysis. Data gathering can be rapid, although post processing of the extracted data can be time-intensive. Standard practice within both the Deep Sea Drilling Program (DSDP) and the Ocean Drilling Program (ODP) was to photograph all archived cores. Details on the DSDP/ODP photographic methods can be found below in the metadata section. Given the 97,056 m of DSDP and 210,640 m of ODP cores that have been collected through leg 205, this provides an extensive data set for potential analysis (see for example http://www-odp.tamu.edu/glomar.html and http://www-odp.tamu.edu/resolutn.html).

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Figure 1. A typical analog photograph of a ten meter long Ocean Drilling Program Core, in this case Core 1H from Hole 625C recovered during Leg 100. The units on the photographed ruler are in centimeters.

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Figure 2. Uncorrected grayscale values extracted from a scanned version of the ODP photograph of Hole 625C Core 1H recovered during Leg 100. Increasing values correspond to darker sediments. The grayscale convention employed is with white equal to zero.

What is grayscale analysis? Grayscale analysis within the paleoclimate community provides a means of quantifying differences in optical density of black and white photographs of marine cores, lithologic outcrops, or similar data sets (Fig. 2). The method can be employed with analog media that has been digitally captured or with digitally generated images. The optical density is generally expressed as grayscale values on an 8-bit scale ranging from 0 to 255 in which either endpoint may represent black or white depending on the convention employed by the particular hardware and software in use. Depth series extracted from the photograph can be related to lithologic variation and in well-calibrated data, to quantitative compositional changes within the core. Depth series derived in this way may also be transformed into the time domain, given age data and the development of a depth-age transformation (for example, Prokopf and Patterson (this volume)). We shall see that the potential to extract more quantitative data from ODP core photos is greater than for DSDP photos due better lighting control and the inclusion of a grayscale photographic standard in each image. It should be pointed out that the calibration approaches discussed below are post hoc corrections designed for use with legacy photographic prints. Better results could be obtained by direct scanning of ﬁlm negatives, but this is not feasible, as ODP does not provide direct access to ﬁlm negatives, but rather fulﬁlls requests for core images with photographic prints. Direct application of these methods with modern still or video digital cameras is not advisable as the response of CCD detectors is linear. The need for careful calibration to a consistent grayscale standard still applies however (e.g., Nederbragt and Thurow (this volume)).

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The digital lifecycle Before we consider approaches to the calibration of grayscale images it is important to keep in mind that the quality of the information that can be extracted from the image depends not only on the calibration and the quality of the photograph itself, but on the entire system response or lifecycle of the image. While this information may seem intuitive to experienced users, it is worth discussing for those who may be new to these methods. The system response includes: the input device and capture conditions, the acquisition software employed, viewing and analysis components, and the output media. Each step in this process can introduce potential bias, which will limit the quality of the lithologic information that can be extracted from the image and therefore its potential paleoclimatic signiﬁcance. Likewise, metadata should be preserved at key stages of the system response to ensure the greatest image ﬁdelity. For example, acquisition metadata should include measurements of lighting conditions, and the exposure settings used when the photograph was taken. Analysis metadata should include any information regarding how an analog image was captured to digital form, and notes regarding which software and ﬁlters or manipulation were applied during post processing. Archiving metadata should retain information related to version control, ﬁle formats, and whether any compression was applied to the image. We shall see that each of these components can introduce bias into the measurement process. When, generating a photographic image, it is important to keep in mind that the acquisition process is imperfect. Information is lost and bias is introduced. For a perfect recording media, there would be a one-to-one response between the luminance factor of the scene, and the optical density of the recording media. For black and white photographic image analysis, the most fundamental form of bias is the representation of a colorful world as a grayscale response. In practice, real-world photographic slides, ﬁlm, and print media provide an s-shaped, or sigmoidal response (Giorgianni and Madden 1998). The sensitivity to the scene luminance response is lost beyond thresholds near the brightest and darkest extremes within the scene (Fig. 3). Likewise, the slope of the luminance to optical density response is rarely unity. This leads to changes in the contrast of the image relative to the original scene. These problems are accentuated by the fact that no photographic output media is capable of reproducing the full range of colors (gamut) seen in the real world. The choice of output media thus can inﬂuence the viewer’s perception of the scene. Scanning a negative or photographic print can compound errors of the type described above. For example, improper gamma correction could introduce bias during the scanning process. Finally once a photographic image has been digitally captured, there is an inherent tradeoff between image resolution and storage requirements. Images should always be scanned at a resolution greater than that required for the intended application. Moreover, a digital master or archive version of the image should be saved for each captured image. This archive image can be used to recover data should the working version of the image be corrupted. The ﬁle size and thus storage requirements of the working image can be reduced through compression, but this advantage comes at the cost of the loss of high frequency information within the image. There are two classes of compression routines currently available: lossy compression, which degrades image quality, and lossless compression, which can reduce image size without the loss of information.

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-2.00

-1.50 -1.00 Log scene luminance

-0.50

0.00

Figure 3. The theoretical relationship between scene luminance and visual (optical) density of a black and white photograph is not linear. The straight line represents a one-to-one system response. The s-shaped or sigmoidal curve represents the typical response for analog media such as 35 mm ﬁlm (after Giorgianni and Madden (1998)).

The industry standard joint photographic expert group (JPG) format is a lossy compression format that achieves high compression ratios by the truncation of high frequency information within the image following a two-dimensional Fast Fourier Transform of the input data. Information lost in this way cannot be recovered, and multiple compression cycles will result in ever-greater image degradation. Compression methods such as LZW compression are lossless and operate by encoding repetitive components within the ﬁle with less storage-intensive strings. This approach is best suited to compression of text ﬁles, rather than images. In addition, lossless methods are not capable of reaching the high compression ratios (with acceptable visual image quality) seen in lossy methods. Each of the considerations described above can result in grayscale values that may be biased relative to the original scene, by altering the threshold response and contrast of the scene in the case of the input and output issues, or by smoothing gradients within the image in the case of compression. For these reasons, metadata regarding the capture characteristics must be recorded, and archive digital images should never be compressed. Researchers must determine empirically whether information lost in working copies of lossy compressed images are acceptable in their particular application. For example, compression may be appropriate for development of a low resolution image suitable for qualitative viewing, but not quantitative data extraction. In case of doubt, it is best to err on the side of caution and save images in formats that lack native compression such as the tagged image ﬁle format (TIFF), rather than formats such as JPG that include native compression.

NON-LINEAR GRAYSCALE CALIBRATION METHOD

131

Approaches to grayscale calibration If we seek to generate a long, quantitative depth series of grayscale values extracted from a sequential series of core photos, we quickly realize that there is both intra- and interphotographic variation in the quality of the lighting affecting the scene. This variance can, for example, arise from variation in the performance of the light source or from glare bouncing off the wet surface of the core and the photographic setup. For example, space limitation aboard the JOIDES Resolution during the development of the Ocean Drilling Program resulted in the re-conﬁguration of the core photography station during remodeling of the core lab on several occasions. The net result of these changes was to place irregularly shaped walls close to the photographic station with the potential to bounce light from the photographic ﬂash back into the scene in complex ways (see metadata section). To minimize these effects, the ﬂoors, walls, and ceiling of the ODP core photographic area are painted ﬂat photographic black. Despite this, some intra- and inter-photographic variation within the ODP core photographs is evident. The standard procedure for correcting lighting bias within these photographs is referred to as the background subtraction method (Bond et al. 1992). This method is applied by determining the grayscale values of the white ruler (actually the surface of the core table) adjacent to the sediment core. Due to variations in lighting as described above, the grayscale value of the ruler differs from place to place within the image. To correct the image for this grayscale variation, a smooth polynomial function is ﬁt to the variations in the grayscale value of the white ruler. When the grayscale value of the ruler adjacent to a sediment surface is subtracted from the grayscale value of the sediment, the result is a simple, one point, correction which assumes that the tonal value of the ruler is constant. This constant correction factor assumes that all shades of gray are equally biased by the locally variable lighting conditions. Given what we know of the typical relationship between scene luminance and optical density in silver-halide based ﬁlm photography, it seems unlikely that the correction factor would follow such a simple functionality (see Fig. 3 for example). In fact, one expects the grayscale bias in analog photography to vary as a function of the scene luminance and to exhibit response thresholds near the light and dark limits (Giorgianni and Madden 1998). Fortunately, we can test the simple assumption that the grayscale bias is independent of the observed grayscale response. This can be done using information recorded in each ODP core photograph (but not the DSDP photos). As part of the standard photographic process, ODP includes a Kodak Q-13 grayscale zone card as a component of the scene. The Kodak Q-13 card includes a twenty-zone, grayscale standard with values that range from white to black, spanning the full grayscale range (Table 1). Unfortunately during the DSDP a single zone, Kodak 18% middle gray card was generally employed rather than the multi-zoned Kodak Q-13 card. Correction of the DSDP data using the methods developed below is thus not possible. Using the multi-zoned grayscale calibration card, it is possible to compare the observed grayscale values for the zones on the card with their nominal or expected values (see metadata section below). This effectively provides a type of calibrated gamma correction by mapping the dynamic range captured in the photographic image back into the standardized grayscale range. In situations where the intra- and inter-photo lighting varies, as is the case with the shipboard ODP photography, this approach is likely superior to a traditional

132

ORTIZ AND O’CONNEL Table 1. Grayscale zones and nominal values from the Kodak Q-13 grayscale zone card. Grayscale zone

Nominal Grayscale value

1

0.0

2

13.4

3

26.8

4

40.3

5

53.7

6

67.1

7

80.5

8

93.9

9

107.4

10

120.8

11

134.2

12

147.6

13

161.1

14

174.5

15

187.9

16

201.3

17

214.7

18

228.2

19

241.6

20

255.0

gamma correction that is not referenced to a known standard, such as the nominal values of the Kodak Q-13 grayscale zone card. As an example, consider data extracted from the Kodak Q-13 grayscale zone card for Core 4 of Hole 625C recovered during ODP Leg 100 (Fig. 4). If we plot the observed grayscale values against their nominal or expected values (Fig. 4) and compare them with a theoretical one-to-one grayscale system response curve, several interesting observations can be drawn. If the basic assumption behind the background correction method were to apply, we would expect to see a grayscale response that is linear, but offset from the idealized response by a constant slope. Use of a linear gamma correction would be sufﬁcient to correct such data, provided that the proper slope was know to translate the observed values of the Q-13 grayscale zone card back to their nominal values. In contrast, the overall shape of the observed grayscale response is sigmoidal as predicted in Figure 3. Observed grayscale values between 0 and ∼40 slightly underestimate the nominal grayscale value for the grayscale card. For nominal grayscale values between ∼45 and 175, the observed grayscale values overestimate the nominal values. Above nominal grayscale values of ∼175, there is little or no sensitivity in the observed grayscale values. If we calculate residuals by subtracting the nominal grayscale values from the observed ones, we can see the nonlinearity in the bias response quite clearly. A maximal bias on the order of ﬁfty grayscale units occurs in the mid-tones near the grayscale value of 125

NON-LINEAR GRAYSCALE CALIBRATION METHOD

133

250 Observed Grayscale 225

Nominal Grayscale

Observed grayscale value

200 175 150 125 100 75 50 25 0 250

225

200

175

150

125

100

75

50

25

0

Nominal grayscale value

Figure 4. The relationship between nominal grayscale values and observed grayscale values extracted from Hole 625C Core 1H recovered during Leg 100 is non-linear. Data is plotted with grayscale values substituted for optical density. The dashed line represents a one-to-one system response for comparison. The grayscale convention employed is with white equal to zero.

(Fig. 5). Because grayscale values in the image plateau near 175, nominal grayscale values above this level cannot be differentiated. This compression of the nominal grayscale range or dynamic means a reduction of resolution and thus lost information (Fig. 6). To correct for the grayscale bias, we plot the residual values against the untransformed, observed grayscale values. Plotting the data in this way is useful for two reasons. First, it is strikingly clear that observed residuals for grayscale values greater than ∼175 hold no useful information: they plot nearly orthogonal to the observed grayscale axis. For values between 0 and 175, it is possible to ﬁt the data with an empirical polynomial function, so that the bias in the grayscale values can be removed, and the observed grayscale values can be mapped into the standardized, nominal grayscale space. The result of this mapping is demonstrated by comparison of the raw and corrected down core grayscale depth series (Fig. 7). In the section that follows, we apply the nonlinear correction after ﬁrst using the background correction method of Bond et al. (1992). This corrects for within-photo lighting variability, and also ensures that the grayscale values are mapped back to an absolute standard. The bias described above results from differential sensitivity of the image reproduction system to the observed luminance of the scene and from the representation of real world colors as shades of gray. In the section that follows, we test the empirical approach we have developed, which builds upon the background correction method to begin the development of a non-linear grayscale correction process for use with analog ﬁlm.

134

ORTIZ AND O’CONNEL 50 40 30

Observed - nominal grayscale

20 10 0 -10 -20 -30 -40 Residual grayscale

-50

Lost information

-60 -70 250

225

200

175

150 125 100 nominal grayscale value

75

50

25

0

Figure 5. Residual grayscale values plotted against nominal grayscale values of the Kodak Q-13 grayscale card. The residuals are deﬁned as observed values minus nominal values of the Kodak Q-13 grayscale card using data extracted from Hole 625C Core 1H recovered during Leg 100. Notice that the mid-tones exhibit the greatest bias. Grayscale values above 175 (open circles) represent information lost from the image due to lack of sensitivity (see text and Fig. 6 for details). The grayscale convention employed is with white equal to zero.

Evaluating the nonlinear correction method Our approach is to make use of a combined background subtraction and nonlinear grayscale bias correction, using the Kodak Q-13 grayscale zone card included in each ODP photograph as an internal calibration standard. The rationale for this is that lighting varies both within the scene and between scenes. The background correction method is applied as outlined in Bond et al. (1992). Following this correction, any remaining bias is removed by calibration of the image back to the nominal grayscale values recorded on the Kodak Q-13 grayscale zone card. To test the quality of the method, we compare the corrected grayscale values with measurements of calcium carbonate content of the sediment from the corresponding depth in core. The objective of this test is to determine whether the corrected grayscale values correspond to the observed carbonate content which controls sediment brightness in the North Atlantic sediments used for this study (Bond et al. 1992; Ortiz et al. 1999). Our rationale with this test is that if photographic bias dominates the grayscale variability, there should be a poor correlation between sediment carbonate content, and the grayscale values extracted from the digitized photographs. Likewise, the correction approach applied should improve the relationship between measured sediment carbonate content, and corrected grayscale values. The data set consisted of 53 core photographs from ODP 162, Sites 980, 983, 984 and 45 carbonate measurements. Using the core photos from ODP Leg 162, one observes a very

NON-LINEAR GRAYSCALE CALIBRATION METHOD

135

50 40 30

Observed - nominal grayscale

20 10 0 -10 -20 -30 -40 Residual grayscale -50 Lost information -60

Poly. (Residual grayscale)

-70 250

225

200

175

150

125

100

75

50

25

0

Observed grayscale value

Figure 6. Residual grayscale values plotted against observed grayscale values based on data extracted from Hole 625C Core 1H recovered during Leg 100. Values above 175 plot orthogonal to the observed grayscale axis indicating a loss of information from the image. The dashed line represents a polynomial ﬁt that can be used to remove image bias by mapping the observed grayscale values back into the nominal grayscale space. The grayscale convention employed is with white equal to zero.

interesting response similar to that which we observed for the data from Leg 100 (Fig. 8). If the grayscale bias were independent of the nominal grayscale value, the assumption in the background correction method, then the bias should plot as a horizontal line with a constant offset relative to the true grayscale value for each of the twenty zones in the grayscale standard. Interestingly, the bias exhibits a non-linear, parabolic functionality in which the extreme light and dark tones are only slightly biased, whereas the mid-tones exhibit a much greater degree of bias (Fig. 8). The magnitude of the bias depends on the mean grayscale value of the scene, violating the assumption of constant bias. This indicates that signiﬁcant grayscale bias remains within the scene after images have been background corrected. We thus compared the background corrected grayscale values with the nominal values for the standard grayscale card and calculated residuals as in Figure 6. The residuals provide the non-linear grayscale correction function that can be used to map the background corrected grayscale values back onto the standardized grayscale. Ultimately however, the quality of the grayscale correction method is determined by how well the extracted grayscale values relate to some objectively measured lithologic quantity. For this comparison we compared the corrected grayscale values against geochemical

136

ORTIZ AND O’CONNEL

40 Uncorrected grayscale

50

Corrected grayscale

60 70

Grayscale value (white =0)

80 90 100 110 120 130 140 150 160 170 180 0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950 1000

Depth below coretop (cm)

Figure 7. A downcore comparison of the corrected and uncorrected grayscale values from Hole 625C Core 1H recovered during Leg 100 indicates how the nonlinear correction inﬂuences the data. The grayscale convention employed is with white equal to zero.

measurements of sediment carbonate content from Ortiz et al. (1999). Carbonate content was estimated by coulometry and results are presented as weight percent carbonate. For each carbonate sample, we identiﬁed corrected grayscale values from the corresponding depth in core and averaged the grayscale data from the corresponding centimeter for comparison with the carbonate data that was collected from one-centimeter depth intervals. The 45 pairs of grayscale and carbonate values were then compared by linear correlation to determine the degree of correlation between the two data series, the variance explained, and the standard deviation of the relationship. Several types of error likely contribute to the standard deviation of the regression. These include: small weighing and analysis errors in the coulometric data, errors inherent in the empirical grayscale calibration technique, colocation errors arising from depth mismatches between the carbonate and grayscale data, and sediment heterogeneity errors arising from the comparison of surface grayscale values with volumetric carbonate values. The last two errors are likely the largest sources of error in the method. Despite these errors, the results demonstrate a strikingly linear relationship throughout the observed range of grayscale and carbonate content, and the observed errors progressively decrease with each additional correction that is applied (Fig. 9). Table 2 summarizes the statistics of the linear correlation analysis between uncorrected, background corrected,

NON-LINEAR GRAYSCALE CALIBRATION METHOD

137

90 980A-7

983A-5

80

984A-2

Observed - nominal grayscale

984A-4 70

984A-6

60

984C-6

984A-7

50

40

30

20

10

0

-10 250

225

200

175

150

125

100

75

50

25

0

Nominal grayscale value

Figure 8. The magnitude of the nonlinear correction varies as a function of sediment brightness and photographic exposure as demonstrated by data from North Atlantic sediments in cores from ODP Holes 980A, 983A, 984A, and 984C. The grayscale convention employed is with white equal to zero. The residuals are determined relative to the nominal values of the Kodak Q-13 grayscale card.

Table 2. Comparison of linear correlation analysis statistics for various grayscale corrections applied to data extracted from ODP Leg 162 core photographs based on n = 45 pairs. Grayscale correction method

Linear correlation

Standard deviation

None

0.76

11.1

Background correction

0.77

10.9

Background correction followed by nonlinear correction

0.82

9.7

and non-linear corrected grayscale values and sediment carbonate content. The non-linear correction following background correction accounts for 82% of the variance in the data set with a standard deviation of 9.7% (Table 2). In contrast, linear correlation of the uncorrected grayscale values with the carbonate data explains only 76% of the variance in the data set with a standard deviation of 11.1%. These results are encouraging and suggest that the correction methods employed provide a potentially promising means of extracting grayscale values that can be quantitatively related to sedimentary composition at least in situation where sediment are essentially monochromatic.

138

ORTIZ AND O’CONNEL 180

Hole 980A 160

Hole 983A

Hole 984B

Corrected grayscale (white=0)

140

120

100

80

60

40

20

0 0

10

20

30

40

50

60

70

80

90

Measured carbonate (%)

Figure 9. Simple linear regression of carbonate measurements against the corrected grayscale values indicates that 82% of their variance is shared, and that corrected grayscale values can be used to predict carbonate with errors of 9.7% in cores from ODP Holes 980A, 983A and 984B. The grayscale convention employed is with white equal to zero.

Summary Grayscale image analysis provides a useful means of extracting both stratigraphic depth series and quantitative data useful for compositional analysis of sedimentary cores and lithologic sections. For quantitative application of the method, the user should always consider the context of the complete imaging system (acquisition, processing, storage, output) from which the data arose. Our results demonstrate that bias of mid-tone grayscale values is more sensitive than bias of highlights or shadows. When corrections are applied to the grayscale values that take this nonlinearity into account, the resulting grayscale values compare favorably with sediment carbonate content, a strong inﬂuence on sediment brightness in the sediments that were studied. Future implementation of grayscale image analysis will beneﬁt from comparative measurement of sample and grayscale standards to account for this source of bias. Acknowledgments The methods described in this paper were developed in collaboration with Mr. Jai Ranganathan, a Wesleyan undergraduate, and summer research assistant to JDO and SEO.

NON-LINEAR GRAYSCALE CALIBRATION METHOD

139

Analysis of the leg 162 data constituted part of Mr. Ranganathan’s Senior Thesis at Wesleyan University. Details of the ODP shipboard photographic environment are kindly provided by Mr. John W. Beck, ODP Photographic Services Supervisor (Personal Communication, 2003). This research used samples and/or data provided by the Ocean Drilling Program (ODP). ODP is sponsored by the U.S. National Science Foundation (NSF) and participating countries under management of Joint Oceanographic Institutions (JOI), Inc. Funding for this research was provided by post-cruise USSSP (TAMRF) research grants to JDO and SEO for work conducted in conjunction with the Ocean Drilling Program. Metadata The black and white images employed here were initially generated by ﬂash photography using a downward viewing, ceiling mounted, 4 × 5 view camera ﬁtted with a 105 mm lens. While a 150 mm lens is generally considered standard with the 4 × 5 format, the limited space available for shipboard photography aboard the JOIDES Resolution necessitates this compromise. Within these space constraints, strobe lighting is placed above the photographic table to provide as even illumination as possible. The strobe power is adjusted to provide day light color balance with an exposure of approximately f/16 @ 1/125 s. These settings produce ample depth of ﬁeld and are sufﬁciently fast to eliminated movement and minimize the inﬂuence of ambient light. As a ﬁnal precaution, the ﬂoor and ceiling of the photographic area have been painted ﬂat photo black to minimize inﬂuence of ambient light on the scene illumination and color balance. Each ODP core is photographed twice, once using 4 × 5 inch T-Max black and white ﬁlm and once with Ektachrome color ﬁlm. This pair of ﬁlms is selected because they have the same ISO speed and therefore do not require any exposure changes when switching between black and white and color photography. To maintain photographic consistency, ODP purchases ﬁlm in large lots to assure the same emulsion number is available on a large quantity of ﬁlm. At the beginning of each leg, samples from the current ﬁlm lot are test shot aboard the ship using an 18% photographic gray card as the standard. The densities of this standard are then read and any necessary ﬁltration is added to the camera. The added ﬁltration will generally remain the same for each ﬁlm lot, although the ﬁlm is tested with each new leg. When ﬁlm with a new emulsion number is placed in service this testing is carefully repeated to check for proper ﬁltration. All of the ﬁlm is processed aboard the ship in a very accurately controlled processing procedure. ODP makes every effort, given the inherent limitation aboard the ship, to produce the most accurate image data possible. Each ODP photographic scene includes lettering denoting the ODP Leg, Site, Hole, Core, Core type, section identiﬁers, metric rulers, the split sediment core sections themselves, and a Kodak Q-13 “Color Separation Guide and Grayscale” (Fig. 1). The grayscale zone card in the Kodak Q-13 card is used as the internal standard employed with the nonlinear correction method developed here. Once images were obtained from ODP, digital image capture was achieved using a Visioneer 6100usb CCD ﬂatbed scanner. A print of the image was scanned at 300 dpi using automated gamma correction. The resulting digital version of the image was stored in the tagged information ﬁle format (TIFF). Image analysis to extract grayscale values was performed on a Powermac G3 computer using the public domain NIH Image program (developed at the U.S. National Institutes of Health and available on the Internet at

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http://rsb.info.nih.gov/nih-image/). The grayscale convention employed is white equal to 0 and black equal to 255. The observed grayscale values of the image were calibrated against the nominal grayscale values of the Kodak Q-13 grayscale zone card photographed as part of the image scene. The Kodak Q-13 grayscale zone card has 20 grayscale zones that vary in optical density from 0.5 to 1.95 in 0.1 optical density steps. The scanning resolution of 300 dpi used here provides approximately 18 pixels for each of the twenty grayscale zones. To remove noise generated during the photographic and scanning process, these values are averaged. In some cases, the single pixel that marks the boundary between two grayscale zones spikes up toward values that exceed the mean value of the next higher grayscale zone by several tens of grayscale units. These pixels, which are likely contaminated by glare from refracting light during the scanning process, were omitted from the average. The use of an automated gamma correction, as opposed to a manual correction, likely contributed to some of the observed error in the grayscale dynamic, however, the approach employed here provides an objective, rather than subjective means of correcting for this. Using the grayscale zone data as a standard, it is possible to compare the observed grayscale value for each zone on the card with its nominal or expected value (Table 1). This effectively provides a type of calibrated gamma correction by mapping the dynamic range captured in the photographic image back into the standardized grayscale range. In situations where the intra- and inter-photo lighting varies, as is the case with the shipboard ODP photography, this approach is likely superior to a traditional gamma correction that is not referenced to a standard such as the nominal grayscale values of the Kodak Q-13 grayscale zone card.

References Behl R.J. and Hughen K.A. 1997. Ultra-high resolution stratigraphic methods for paleoclimate and paleoceanographic studies. AAPG Bulletin, American Association of Petroleum Geologists, Tulsa, OK, 81: 679. Bond G., Broecker W., Lotti R. and McManus J. 1992. Abrupt color changes in isotope stage 5 North Atlantic deep sea cores; Implications for rapid change of climate-driven events. In: Kukla G.J. (ed.), NATO ASI Series I: Global Environmental Change, vol. 3, Springer Verlag, Berlin, pp. 185–205. Giorgianni E.J. and Madden T.E. 1998. Digital Color Management, Encoding Solutions, AddisonWesley, Reading, MA, 576 pp. Hagelberg T.K., Bond G. and DeMenocal P. 1994. Milankovitch band forcing of sub-milankovitch climate variability during the Pleistocene. Paleoceanography 9: 545–558. Herrick D.T., Gouveia W. and Pratson L.F. 2000. Building a lithology-based elastic model from digitized photographs of stratigraphy.Annual Meeting ExpandedAbstracts,AmericanAssociation of Petroleum Geologists and Society of Economic Paleontologists and Mineralogists (AAPG), Tulsa, OK: 67. Hughen K.A., Overpeck J.T., Peterson L.C. and Trumbore S. 1996. Rapid climatic changes in the tropical Atlantic region during the last deglaciation. Nature 380: 51–54. Ortiz J.D., Mix A., Harris S. and O’Connell S. 1999. Diffuse spectral reﬂectance as a proxy for percent carbonate content in North Atlantic sediments. Paleoceanography 14: 171–186. Porter S.C. 2000. High-resolution paleoclimate information from Chinese eolian sediments based on grayscale intensity proﬁles. Quat. Res. 53: 70–77.

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Warren J.D., Denney T. and Savrda C.E. 1998. Matlab algorithm for grayscale analysis of carbonate cyclicity; example application to the Demopolis Chalk (Cretaceous, Alabama). Comp. Geosci. 24: 923–931.

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8. FROM DEPTH SCALE TO TIME SCALE: TRANSFORMING SEDIMENT IMAGE COLOR DATA INTO A HIGH-RESOLUTION TIME SERIES

ANDREAS PROKOPH ([email protected])

SPEEDSTAT 36 Corley Private Ottawa, Ontario K1V 8T7 Canada R. TIMOTHY PATTERSON ([email protected])

Department of Earth Sciences and Ottawa-Carleton Geoscience Centre Herzberg Building, Carleton University Ottawa, Ontario K1S 5B6 Canada Keywords: Image color time-series, Wavelet transform, Lamination, Sedimentation, Time scale, Depth scale, Varves

Introduction Requirements and strategy Line scans of image color from laminated sediments provide an excellent high-resolution tool for the investigation of paleoclimatic and paleodepositional conditions, particularly for Holocene sediments (e.g., Nederbragt and Thurow (2001)). Evidence of orbital and solar activity cycles, oceanic and atmospheric feedbacks in circulation patterns, volcanic activity and plate tectonics, are archived by a variety of means including sedimentary columns, melt layers in ice, tree rings and stalagmite growth-rings (Hays et al. 1976; Berger et al. 1989; Frakes et al. 1992). It is unfortunately difﬁcult to determine absolute ages for events in many high-resolution geological records, because all such measurements (including image colors) are recorded along a longitudinal axis, or as a depth scale, and not as part of a time scale. Absolute dating techniques such as radiocarbon 14 C dating can provide such a time scale, but most available methods require expensive analytical techniques on often rare mineralogical and biotic components in the sediments, and have age uncertainties of ∼ ±2% at the 2δ error scale (e.g., Gradstein and Agterberg (1998)). Consequently, radiogenic time-scales cannot 143 P. Francus (ed.) 2004. Image Analysis, Sediments and Paleoenvironments. Kluwer Academic Publishers, Dordrecht, The Netherlands.

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resolve most high-frequency changes in sedimentation rates or accretion growth. Thus, by using radiogenic dates, a sediment color time-series that is obtained from line scans can only be scaled to an “averaged” sedimentation rate when developed using a radiogenic time-scale. Alternatively, laminations (varves) or sediment beds can be counted. For example, identiﬁcation of sediment color (or gray-scale) contrast in line scans can be obtained from images, or directly from the outcrop. If the time duration of each lamination or bed (e.g., annual) is known, then the lamina/bed thickness provides a measurement of sedimentation rate. Thus, a succession of laminations (or sediment beds) will yield a lamination thickness time series (e.g., Schwarzacher (1993), Varem-Sanders and Campbell (1996)). Because laminae thickness and laminae (sediment) color can be measured, and the duration of the laminae deposition is known, sediment color from image data represents not only one variable measured in depth-scale, but actually characterizes three different variables: sediment color, sedimentation rate (i.e., varve thickness per year), and time scale (Fig. 1). Variability of sedimentation rate and sediment color can be sensitive to different controlling processes. For example, variability in redox conditions inﬂuence sediment color but not the sedimentation rate, while variability in marine productivity may inﬂuence the sediment thickness, but not color. The simultaneous extraction of sedimentation rate and sediment color within a highresolution time scale can be essential to relate ﬂuctuations in the amount of sediment accumulation to synchronous ﬂuctuations in the environment (e.g., climate change). The following requirements have to be met to accurately extract sediment color and sedimentation rate from a sediment color line-scan: 1) occurrence of a well-deﬁned extraterrestrial cyclicity (e.g., annually due to Earth’s rotation around the sun) in the sedimentary succession; 2) sufﬁcient high signal-to-noise ratio of the cyclicity within a sediment image. For example, the signal-to-noise ratio for annual laminations is deﬁned by the ratio of summerto-winter-color contrast to the background color contrast (measured over the thickness of each annual layer); 3) existence of one or more absolute tie-ages (e.g., radiocarbon ages) for the sediment column. Earth’s orbit around the sun is very regular (i.e., 365.25 days) due to the low friction of Earth’s movement with extraterrestrial matter. Thus, the variability in solar irradiance due to variation in the Earth’s orbit can be related to the formation of annual varves in lake and marine sediments, annual tree rings, ice melt layers, or ∼20,000–100,000 year marine bedding rhythms (Milankovitch 1941). Other, non-orbital extraterrestrial cycles such as the ∼11 year sunspot cycle are less useful because of a lack of physical explanation for the narrow bandwidth periodicity in sunspot numbers. Basically, two techniques permit the automated extraction of laminae from the color contrast in line scans: 1) thresholding; a threshold color value is set (e.g., 125 for medium gray), and all transitions across this threshold are counted (e.g., box-counting technique) and divided by two. This method has the disadvantage that noise that crosses the threshold is also counted and “real” low-contrast laminae may not be counted. 2) edge or inﬂection point detection; a value of color contrast (“edge”) between one or more of the following data points is set (e.g., 100), and all “edges” are counted. This

DEPTH SCALE TO TIME SCALE TRANSFORMATION

145

Sediment gray value vs. Depth x(s) 0

Core

0

255

Depth s in cm 1

2

0.5 Varve thickness v(t) in cm

Sediment gray value x(t)

0

0

2 Relative age (t) in years

4

200 100

0 Figure 1. Illustration of different inﬂuences of variability in varve thickness (= annual mean sedimentation rate) and variability in sediment gray value in time on their representation in the sediment gray value in a sediment core. Note, that varve thickness and sediment gray-values are not necessarily linked.

method has been used by DendroScan (Varem-Sanders and Campbell 1996) and has the disadvantage that high-frequency noise or sub-seasonal cycles with high contrast may be also counted as lamina, and low-contrast “real” laminae may not be counted. Aim of study Here, we present a tuning methodology based on the wavelet transform that detects and extracts in four semi-automatic steps the wavelength of laminae (e.g., varve thickness), sediment color, and generates a time scale based on a sediment color line scan taken at equidistant depth-scale (e.g., pixels from sediment images) (Fig. 2). In more mathematical terms, the sediment thickness of the complete sedimentary succession, and radiogenic ages t are determined at their sampling depth s, and the average sedimentation rate ν is calculated by linear regression. For sediment color time series of

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PROKOPH AND PATTERSON

Image processing

Image acquisition Image digitizing/scanning Image editing Line scan extraction Line scan editing Depth series data (Sediment image color) x(s)

Depth-to time scale transform

Entire spectrum wavelet analysis Sedimentary cycle pattern in Depth-scale over entire spectrum

1

Narrow band (detail) wavelet analysis

2

Depth-to-time scale transformation

3

Sediment color in time scale x(t)

4

Sedimentation rate in time scale v(t)

Interpretation Figure 2. Flow chart of image processing and depth-to-time-scale transform. Note that detailed explanation in the text is restricted to data processing methods. For more details on image processing methods see Schaaf and Thurow (1994) and Nederbragt and Thurow (2001).

laminated sediments, we can measure the sediment thickness s for a number n of annual layers, and sedimentation rates νi for each individual varve i is νi = si /ti

(1)

with t = 1 yr. Converted to the time domain, each time interval becomes: ti = si /νi , and each discrete time point (datum) tj in a succession of a number n of laminae

tj = t0 +

j si i=1

νi

(2)

with i = 1, 2, . . . , n, j = 1 to n, and t0 the absolute age at the top of the time series. Line scans from sediment images provide discrete data equidistantly in depth (e.g., gray value of pixel) and not in the time domain. In this way a time series x = f (s) of

DEPTH SCALE TO TIME SCALE TRANSFORMATION

147

gray values x at equidistant depth intervals (pixel size) s with pixel number r is formed. Consequently, the discrete depth interval s is constant and not the time interval t. For this reason, the following methodology is proposed to transform all sedimentary signals into an equidistant time-scale. Before we explain the methodology step by step, we give an introduction to the wavelet analysis techniques used, followed by brief remarks on image processing requirements. The 4-step methodology utilizes line scans obtained from images of laminated sediments, but can also be used for other geological or geophysical (e.g., well-logging) time-series as long as the requirements outlined above are respected. We apply this methodology to a synthetic signal and an example from Holocene marine anoxic sediments with annual lamination (varves). We also show how the method deals with variable sedimentation rates, non-laminated intervals and various types of noise. Wavelet analysis Wavelet analysis emerged as a ﬁltering and data compression method in the 1980’s (e.g., Morlet et al. (1982)). Since then, it has become widely applied in geophysics (e.g., Grossman and Morlet (1984)). Wavelet analysis transforms information from a “depth” or “time” domain into a spectral domain by using various shapes and sizes of short ﬁltering functions, so-called “wavelets”. In time-series analysis, wavelets permit an automatic localization of periodic-cyclic sequences. In contrast to the Fourier transform that uses a single window of constant width, the wavelet transform uses narrow windows at high frequencies, and wide windows at low frequencies (Rioul and Vetterli 1991). The wavelet coefﬁcients W of a time series x(s) are calculated by a simple convolution 1 s−b ds, (3) Wψ (a, b) = √ x(s)ψ a a where ψ is the mother wavelet; the variable a is the scale factor that determines the characteristic frequency or wavelength;√ and b represents the shift of the wavelet over x(s) (Chao and Naito 1995). Alternatively, a can be replaced by a, the so-called L1-norm, which calculates W comparable to the power in spectral analysis (i.e., variance). In this contribution, we have utilized a continuous wavelet transform, with the Morlet wavelet as the mother function (Morlet et al. 1982). The Morlet wavelet is simply a sinusoid with wavelength/period a modulated by a Gaussian function, and has provided robust results in analyses of climate-related records (Prokoph and Barthelmes 1996; Appenzeller et al. 1998; Gedalof and Smith 2001). A parameter l is used to modify wavelet transform bandwidth-resolution either in favour of time or in favour of frequency, and represents the length of the mother wavelet or√ analysis window. The bandwidth resolution for wavelet 2 , and a location resolution b = √al . The parameter transform varies with f = 4π al 2 l = N t = 10 is suggested for all analyses, which give sufﬁciently precise results in resolution of depth and frequency, respectively (Prokoph and Agterberg 2000; Ware and Thomson 2000). Thus, the shifted and scaled Morlet mother wavelet is deﬁned as 1

1

1

1 s−b 2 al )

l (s) = π − 4 (al)− 2 e−i2π a (s−b) e− 2 ( ψa,b

.

(4)

148

PROKOPH AND PATTERSON

The relative bandwidth error is constant in all scales and is ∼ 1/10 = 0.1 (=10%) for l = 10. For example, a varve thickness of 1 cm has an error of ±0.1 cm. The value l = 10 also diminish effects of local artefacts or non-laminated sediment parts in the images. Several possibilities to adjust the width, types and other characteristics of mother wavelets that are similarly useful to perform the depth-to-time transform successfully are presented in Torrence and Compo (1998). Figure 3 illustrates the real part of the complex Morlet wavelet with the parameters used and the relative analysis window size used depending on depth and wavelength.

A

Continuous wavelet transform

Period=Scale (a)

analysis window width

x0

b

xi Time series

xn

B

Morlet wavelet (real part)

Figure 3. Schematic presentation of (A) simpliﬁed analysis windows for continuous wavelet analysis including (B) real part of Morlet wavelet centered at location xi . For explanation of the axis a, b as well as x0 see equation (3) in text.

The wavelet coefﬁcients on the top and bottom of the data set have an “edge effect”, because only a half of the Morlet wavelet lies inside the line-scan data set, and the missing

DEPTH SCALE TO TIME SCALE TRANSFORMATION

149

data in the analysis windows are replaced (“padded”) by zeros. The missing data can be up to 50% of the analysis window. Thus, for relatively long wavelengths (e.g., wavelength a covers more than a half of the whole data series), the edge effect decreases to zero as soon as data points cover the complete analysis window. The boundary of edge effects on the wavelet coefﬁcients forms a wavelength dependent curve, called the “cone of inﬂuence” (Torrence and Compo 1998). Wavelet coefﬁcients for wavelengths (or scales) longer than the borderline of the cone of inﬂuence become less signiﬁcant. However, since the data set used for bandwidth wavelet analysis generally consists of many laminae, in the highfrequency variations, the inﬂuence of edge effect at l = 10 covers not more than 5 laminae both on top and bottom. To transform a measured and hence limited and discrete time-series, the integral in equation (3) has to be modiﬁed by using the trapezoidal rule to evaluate the wavelet transform (Prokoph and Barthelmes 1996). The matrix of wavelet coefﬁcients Wl (a, b) can be coded with the appropriate colors or shades of gray for graphical expression, using a “scalogram”. In our examples, we used shades of gray, with black representing 75–100%, dark gray 50–75%, light gray 25–50%, and white 0–25% of maximum Wl (a, b). Wavelet transform using the Morlet wavelet can be performed with several software packages (e.g., MATLAB® ; Prokoph and Barthelmes (1996), Torrence and Compo (1998)). The wavelet analysis technique used in this article is explained in detail in Prokoph and Barthelmes (1996). The series of wavelength awmax (b) with strongest local wavelet coefﬁcient Wl (a, b) has to be extracted from the wavelet coefﬁcient matrix, because this series of wavelengths determines the lamination thickness at each location. For example, the output-ﬁle can provide the depth-scale (1st column) and the lamination thickness (2nd column). The extraction of awmax (b) can easily be performed with a search algorithm for “maximum” in a spreadsheet. Image processing Sediment color line scan data can be acquired, for example, from photographs of cut or rough sediment surfaces, thin section photographs, Backscattered Electron Microscope (BSEM) photographs, or X-ray imaging. The quality, resolution, costs and color calibration of these imaging techniques varies signiﬁcantly. Figure 4 illustrates how different resolution and image acquisition techniques can enhances/ smooth contrasts in sediment color, and that very-high resolution and high-cost images (i.e., BSEM) are not necessarily optimal for automatic counts of varves. The photographs can already be in digital format, or may be transferred to digital (electronic) format after scanning (Lamoureux and Bollmann, this volume). The most common, and due to low compression, recommended high-quality digital ﬁles are TIFF-ﬁles, but several other bitmap-ﬁle formats are also useful. Several image processing software packages such as NIH-Image (for Macintosh), IMAGEJ (for all platforms), or XVIEW (UNIX) are suitable for extracting and editing sediment color line scans from digital sediment images. Variations in the image background color should be calibrated to equal standard value by using trend lines according to Nederbragt and Thurow (2001). In this way, errors in the sediment color (e.g., slightly different core diameter, or X-ray intensity ﬂuctuations) can be corrected.

150

PROKOPH AND PATTERSON

B

X-ray

A

Thin section

1 mm

1 cm C

Gray-scale value

250

X-ray

200

Thin section

150 100 50

BSEM

0 898.70 D

898.75

100 µm

BSEM

Summer (Diatoms) Summer

898.85 Depth in cm

898.80

Debris flow

Spring (Diatoms) Spring

Winter (debris) Winter

Figure 4. Graphic correlation of digital image output from 898.7–898.89 cm depth of core TUL99B-03, Efﬁngham Inlet, west coast of Vancouver Island (after Patterson et al. (2001)). A) X-ray image (1 cm = 116 pixels, line-scan width: 3 pixels); B) Thin section image (resolution: 1 cm = 1000 pixel, line-scan wide: 40 pixel); C) Line-scan outputs of sediment color (gray value); D) BSEM image (resolution: 1 cm = 12, 500 pixels, line scan wide: 400 pixels), diatoms are represented by bright colors in X-ray and thin section (gray-scale value >200) and debris layers by dark colors (gray-scale values <100). Note that the correlation of the line scans is almost perfectly positive or negative, but varve detection of X-ray images is not suppressed by thin sub-annual debris layers.

Mean gray values are then measured for several pixel line scans that perpendicularly cross the sediment lamination from each image, and are saved as an ASCII ﬁle in two columns (pixel number, gray value). Further editing of all line scans involves correcting depth values from pixel numbers, replacement of extreme gray values, e.g., due to small cracks or concretions, by using adjacent gray values (after Schaaf and Thurow (1994)), and connecting the time-series data of each image to a complete data set for the entire core.

DEPTH SCALE TO TIME SCALE TRANSFORMATION

151

The pixel size has to be calibrated with a depth scale, which is photographed or scanned together with the sediment column (e.g., Nederbragt and Thurow (this volume)). Methodology Determination of the range of lamination (e.g., varve) thickness from the line-scan timeseries is carried out by using the wavelet analysis with program CWTX.F, or other automatic techniques (e.g., Varem-Sanders and Campbell (1996)). By using wavelet analysis over the entire spectrum of wavelength (pixel range from 2 to r), the lamination thickness range is marked by grey or black bands in the wavelet scalogram. It is important that a useful signal-to-noise ratio exists in the raw image; in particular a strong contrast between the summer and winter layers (varves). For very noisy sections (signal-to-noise ratio smaller than 1 to 1) and interbedded sections with completely missing laminae, it is recommended that the range of lamination thickness (measured in distance units such as pixel, mm, cm) determined manually from the images, or from the line scan. Narrow bandwidth wavelet analysis of the sediment color data x(s) is performed in the range of lamination thickness bandwidth determined by the previous step. By narrowing the bandwidth of the range of varve thickness in a section, high-frequency noise (“white noise”), as well as overlying long-term sediment color variability are removed in the wavelet coefﬁcients. The user deﬁnes the number of depth-intervals m for which the varve thickness is extracted before or during the run of the wavelet analysis software used. The number of depth-intervals should be m > S ∗ 2/νmin with νmin deﬁning the minimum varve thickness. The depth interval is s = S/m. Consequently, the absolute depth of each interval k is deﬁned by sk = s0 + s ∗ k, with s0 representing the depth at the top of the time-series. The wavelength with the highest variance at location sk determines the local sedimentation rate (i.e., varve thickness) νk that is extracted by the wavelet analysis software in the second column of output ﬁle. T is sediment color xk for each depth sk at the same s can then be calculated using a simple linear data interpolation algorithm to extract three new time series νk , xk , sk in depth-scale with equidistant s. Here, we use MITTELN.C for UNIX to construct equidistant time series that is downloadable from http://www.geocites.com/speedstat/MITTELN.C. To obtain an absolute rather than relative time-scale, a tie age tp at depth sp has to be provided from an independent source (e.g., radiogenic age, bio- or litho stratigraphic marker age) for calibration. If there is no independent age available, the new time series can still be used for evaluation of environmental processes, but cannot be linked to other records. The absolute datum t of each lamination at depth interval k = 1 . . . n can then be calculated to yield time-scale data tk by tk = tp +

k s i=1

νi

for s ∗ k + s0 > sp

(5.1)

for s ∗ k + s0 < sp .

(5.2)

and tk = tp −

k s i=1

νi

152

PROKOPH AND PATTERSON

These calculations can be done with a simple spreadsheet, for example in MS EXCEL® . By this stage, an absolute depth sk , a sediment color value xk , a varve thickness νk , and an absolute “counted”, but non-equally spaced time tk has been extracted for each depth interval k = 1 . . . m. Finally, the equal-distance data (s = constant) sk , xk , νk , tk is transformed into n equidistant time intervals with t = constant using a simple linear interpolation algorithm (i.e., MITTELN.C) to yield si , xi , νi , ti . Note, that t = 1 year is the highest possible resolution for the varve thickness time series νi . The highest possible time-resolution t for the sediment color x is t = (tn − t0 )/r. This resolution is usually much higher (i.e., by the number of pixel per varve) than the highest possible resolution for sedimentation rate (= varve thickness).

Testing of the method Synthetic signal To illustrate such a combined statistical approach, we introduce here a synthetic signal (Fig. 5) to demonstrate that the methodology is able to resolve the original climate signals and ﬂuctuations of sedimentation rate from a complex sediment color depth-series. This synthetic signal combines following features: 1) A(t) = (2 cos(2πt/20) + 50)∗ (5 cos(2πt) + 5) calculated for t = 1 . . . 500 and t = 0.25 year. This signal simulates sediment color (gray scale) variations in a range from 30 (dark) to 70 (brighter), and maximum amplitude of up to 40, with four pixels covering 1 year intervals. This signal represents low-contrast-laminae stages (e.g., no winter-summer precipitation difference = zero annual amplitude) and high-contrast-laminae stages (e.g., strong seasonal precipitation contrast = annual amplitude of 40 gray values). 2) B(t) = 2 cos(2πt/50) + 50) calculated for t = 1 . . . 500 and t = 0.25 year. This signal may represent a long-term cyclicity in the record (e.g., sunspot cyclicity) (Fig. 5B). 3) C(t) = 10∗ ε calculated for t = 1 . . . 500 and t = 0.25 year. This signal represents white (random) noise ε with amplitude of up to 10 that can arise from random geological processes as well as limitations in the image quality (Fig. 5C). 4) D(t) = A(t) + B(t) + C(t). Thus, the different time-series signals (A), (B), (C) are added over 500 years. The units for A(t), B(t), C(t), and D(t) are gray value units (Fig. 5D). 5) E(t) = 20 cos(2πt/20.25) + 20.5 calculated for t = 1 . . . 500 and t = 0.25 year. This signal represents a 20.25 year-cosinusoidal variation on sedimentation rate ν(t) with amplitude of 20.5 to 60.5 (average: 40.5), with unit for E(t) in mm/year (Fig. 5E). 6) The ﬁnal sediment color signals x(s) is related to a depth-scale by time-scale to depth-scale transform s(t) = s(t − 1) + E(t)∗ t, s(0) = 0, t = 1 . . . 2000 and t = 0.25 year. The transformed synthetic signal time series is 20318 mm long (Fig. 6A1, A2) with an amplitude range x(s) of 85 to 130 units (i.e., gray values). By simple linear interpolation the time series x(s) is stretched to 20000 data points in equidistant depth and provides an assumed image resolution of s = ∼ 1 pixel/mm.

DEPTH SCALE TO TIME SCALE TRANSFORMATION

gray value units

A1

D

E

1 year

60 40 20

Modulation of annual cycle amplitude 20 years

gray value units

gray value units

C

mm/ year

B

80

70 50 30

gray value units gray value units

A2

153

Long-term climate cyclicity

50 years 52 50 48

Random noise 10 6 2

140

Sum (A+B+C)

120 100 80

20.25 years

76

Annual sedimentation rate

56 36 16

0

100

200

300

400

500

Age in years before present Figure 5. Synthetic time-series for signals over 500 years embedded in sediment image color line-scan. Vertical scale: Sediment gray-value. For details on construction of the signals A1, A2, B, C, E, see text. Note that (A2) is a zoom into (A1).

154

PROKOPH AND PATTERSON Table 1. CWT-output of narrow-band analysis of synthetic signal. Raw (k)

Depth (mm)

Wmax(b) varve thickness

Age (years) T0 = 0

1.00 1

11.16

58.48

0.17

2

21.32

58.48

0.35

3

31.47

58.48

0.52

4

41.63

58.48

0.69

k=5

s5

ν5

T5

k

sk

νk

Tk

k = 1995

s1995

ν1995

T1995

1996

20276.37

62.87

491.25

1997

20286.53

62.87

491.41

1998

20296.68

62.87

491.57

1999

20306.84

62.87

491.73

m = k = 2000

20317.00

62.87

491.89

The depth-scale to time-scale transform of the synthetic signals The wavelet analysis of the depth series x(s) show wavelet coefﬁcients with >25% of maximum variance in shades of gray (Fig. 6B, C). In the overview analysis (Fig. 6B), a very strong ∼800 mm cycle band, a highly ﬂuctuating ∼20 to 60 mm, and weaker ∼400 mm and ∼2000 mm bands emerge. From the synthetic signal (Fig. 5E) with an average sedimentation rate of ∼40 mm/year, we can conclude that these cycles represent ∼20 years, ∼1 year, ∼10 years and ∼50 years. However, it is not possible to separate the components of the ∼20 year cycle that belong to the sedimentation rate and climate cycle ﬂuctuations, respectively. The ∼10 year cycle is not in the model, and thus may represent a bandwidth error effect that is inherited in the analysis methodology. Since this work refers to the analysis of images, we can, generally conclude that the ∼20–60 mm cycle band represents the annual lamination variation. In the detailed wavelet analysis (Fig. 6C), we separate the 5–200 mm band to cover the annual cycle band and give some space to possible unusually thick or thin laminae (“outliers”). There are no outliers in the synthetic signal, but they are common in sedimentary time-series. The wavelength of the strongest local signal aWmax(s) for each depth interval b (column 3) (Table 1), which represents the sedimentation rate νk is extracted in a numerical output ﬁle of the wavelet analysis. Then, according to equations (5.1) and (5.2), the time scale is calculated as a function of depth (column 4, Table 1). Here, we use a tie-age tp = 0 years BP at 0.0 mm. The ﬁrst step of the transform shows that the recovered time scale ranges from 0–491.8 yr. BP., that is 1.8% shorter than the original time scale. Now, mean gray-value data x for the intervals k = s are calculated, and xk is attached as column 5 to the time scale. Then, the time scale T , sedimentation rate ν, and signal (sediment color) x are transformed from equidistant depth intervals k to equal time intervals

DEPTH SCALE TO TIME SCALE TRANSFORMATION

A1

Gray value units

130 110 90 4000

A2 Gray value units

155

4200

4400

4600

4800

5000

130 110 90 70 0

5000

10000 Depth in mm

15000

20000

4 Wavelength in mm

B

Annual cycles

50 100

20 year cycles 50 year cycles

500 1000 2000 5000 20000

Wavelength in mm

C

5 10 20 50 100 200 0

5000

10000 Depth in mm

15000

20000

Figure 6. Time-series analysis of synthetic signals of periodic signals and noise (Fig. 5E) modulated by annual sedimentation rate (Fig. 5F). A1: Zoom into 1000 mm interval of synthetic signals transformed from time to depth scale; A2: complete 20000 m of synthetic time-series (e.g., sediment color line scan from image); B: Scalogram of the wavelet analysis over the complete spectrum of the synthetic signals using Morlet wavelet with 10 oscillations; stripped line marks “cone of inﬂuence’ of edge effects; C: Scalogram of the narrow bandwidth wavelet analysis of synthetic time-series in depth scale in the bandwidth of 5–200 mm covering the variability in annual sedimentation rate (e.g., varve thickness). Vertical axis: logarithmic scaled wavelengths (periods). The signal variances are represented by the darkness of the gray value (white = <25% of maximum variance, light gray <50% of maximum variance, dark gray, 75% of maximum variance, black = >75% of maximum amplitude) in the scalogram. Note that the sedimentary cycles have ﬂuctuating intensity and wavelengths.

156

PROKOPH AND PATTERSON Table 2. Recovered synthetic signals in time scale Ti . Raw (i)

Time (yr. BP) Ti

Varve thickness ν(t)

1

0.13

58.48

Image color x(t) 116.94

2

0.38

58.48

114.68

3

0.63

58.48

121.11

4

0.88

58.48

116.76

i=5

T5

ν5

x5

i=5

Ti

νi

xi

i = 1962

T1962

ν1962

x1962

1963

490.63

58.48

108.98

1964

490.88

58.80

108.20

1965

491.13

62.47

106.00

1966

491.38

62.87

106.83

n = i = 1967

491.63

62.87

110.13

i with a simple linear interpolation algorithm (Table 2). The recovered time series x(t) and ν(t) are the results of this transform, which, ideally, should be exact replicas of the synthetic signals (Figs. 5D and E), respectively. Discussion of the result of the transform Visual comparison of the recovered time series with original synthetic signals (Fig. 7B, C, E) show that the amplitude, mean, and phase at t = 0 are very similar. Differences are; (i) the 1.8% shorter recovered time-series and the slightly shorter ∼20 year cycle lengths in x(t) and ν(t) which are directly connected with the time-scale, (ii) the recovered sedimentation rate cycles, which are less sinusoidal but rather binary, and (iii) the occurrence of an outlier in the sedimentation rate (∼80 mm/year at ∼300 yr. BP) (Fig. 7E). Wavelet analysis (Fig. 7A, D) show very sharp 20–year cycle bands both in climate signal (i.e., image color) and sedimentation rate, respectively. In particular the ∼10 year interference signal (Fig. 6B) is absent, and the annual cycle band narrows to ∼0.9–1.1 years (Fig. 7A). Spectral analyses of the original and recovered synthetic signals (Fig. 8) show that the cycle bandwidths are virtually identical. In particular, the widened annual 37–62 mm spectrum and the artiﬁcial ∼400 mm (10 year) cycle, that occurred in the depth scale, is narrowed by the time-series recovery. Spectral analysis separated two variance peaks for the annual cycle in the original synthetic data (Fig. 8B). The annual cycle band in the recovered data also ranges from ∼0.95–1.05 years but with more, smaller peaks (Fig. 8E). In summary, the depth-to-time scale transform methodology proposed is able to: 1) Extract (recover) sedimentation rate and sediment color time-series correctly in amplitude and phase from a single sediment color depth series (image data), if the sedimentation rate ﬂuctuates in well-deﬁned bandwidths (e.g., restricted range of laminae thickness).

DEPTH SCALE TO TIME SCALE TRANSFORMATION

157

C

1 2 5 10 20 50 100 200 500 130

Sediment Image Color Bright

110 90

Dark

130 Gray value units

B

Gray value units

Wavelength in years

A

Wavelength in years

D

E

110 90 0.5 1 2 5 10 20 50 100 200 500

mm/year

80

Sedimentation rate v(t)

Recovered data Original data

60 40 20

0

50

100

150 200 250 300 350 Age in years before present

400

450

500

Figure 7. Wavelet analysis of recovered synthetic signals in time-scale; A: Scalogram of the recovered image color in time-scale. Note the narrow variability of the annual cycle, and occurrence of 20 year and weak 50 year cyclicity, as well as low inﬂuence of edge effects. For explanation of gray scale bar on top see Figure 6C; B: Overlay of recovered and original synthetic signals in time scale. Note the slight phase shift between the two series due to a shortened recovered time-series (492 instead of 500 years); C: 40-year zoom into original and recovered synthetic sediment image color signals. Note that the original variability between low contrast and high contrast “varves” is preserved in the recovered synthetic signals; D: Scalogram of the recovered sedimentation rate in time-scale. Note the narrow variability of 20-year cyclicity. For explanation of gray scale variations see Figure 6C; E: Overlay of synthetic recovered and original sedimentation rate signals. Note the artiﬁcial spike up to ∼80 mm at 300 year BP, and slight artiﬁcial variability in amplitude.

PROKOPH AND PATTERSON

0.83

0.91

1.00

1.11

1.25

1.42

1.66

1.99

2.49

3.31

4.95

500

0

9.80

4000

Period in years

80000

20 yr.

x(t)

40000

1.05 yr. 0.96 yr. 0.83

0.91

1.00

1.11

1.25

1.42

1.66

1.99

2.49

500

3.31

50 yr.

0

4.95

Spectral Power

v(t)

20.25 yr.

8000

9.80

B

12000

Period in years ~800 mm (20 years)

22.5

25.4

29.0

33.8

40.6

50.7

x(t)-recovered

0.89

0.98

1.09

1.23

1.40

1.63

1.96

2.45

3.26

4.87

0

80000

0.95-1.05 yr.

20 yr.

40000

100000000

10000

1

0.89

0.98

1.09

1.23

1.40

1.63

1.96

0

2.45

50 yr. 492

Spectral Power

67.5

v(t)-recovered 6250

3.26

E

Period in mm

20.25 yr.

492

Spectral Power

12500

4.87

D

62-37 mm (1 year)

101.1

0

x(s)

~400 mm (10 years)

201.1

40000 ~2000 mm (50 years) 20316

Spectral Power

80000

9.64

C

9.64

A

Spectral Power

158

Period in years Figure 8. Spectral analysis (periodograms) of synthetic signals (see Figs. 5, 6); A: from synthetic sedimentation rate in time-scale (Fig. 5E); B: from synthetic sediment image color in time-scale; note the double peak for annual signal; C: from synthetic time-series in depth scale generated from sedimentation rate modulated periodic signals and noise (Fig. 6A); note artiﬁcial ∼400 mm cycle (∼10 years) and broad band of annual cycle (37–62 mm). Black bars indicate ranges of signiﬁcant period bands; D: from recovered synthetic sedimentation rate signals in time-scale; note the sharpness and same variance of the 20 year peak as in original synthetic data (Fig. 5A); E: from recovered synthetic sediment image color signals in time-scale, note the similarity in the variance of the 20 year and 50 year peak as in original data, as well as the broad, and wide band of low-variance annual cyclicity. Bold line: linear scaled periodogram; ﬁne line: logarithmic scaled periodogram.

DEPTH SCALE TO TIME SCALE TRANSFORMATION

159

2) Compare quantitatively both sedimentation rate and sediment color, because the recovered time series are related to exactly the same time scale. 3) Separate cycles in sedimentation rate and sediment color at the correct (original) amplitude, without interference signals even if their wavelengths are identical. Extract correct sedimentation rates and sediment colors even when there is a low contrast between laminae and the background signal. As a drawback, bandwidth errors, edge effects and other analytical uncertainties can provide (1) ∼2% errors in bandwidth that can result in shortened or lengthened time-scales, and (2) artiﬁcial outlier values in sedimentation rate. In addition, laminae that are less than two pixels wide, completely missing time intervals, or intervals that are related to non-deposition or erosion will not be represented in the timescale. However, the location of missing laminae can often be detected by wavelet analysis over the entire spectrum, because of the occurrence of abruptly shifting gray and black bands in the scalograms (Prokoph and Agterberg 2000). Example: Marine Laminated sediments from the west coast of Vancouver Island, NE Paciﬁc Geological and technical background An ∼11 m sediment core was collected in 1999 from Efﬁngham Inlet, SW Vancouver Island, British Columbia to investigate the climate and oceanographic variability in the NE Paciﬁc over the last ∼5000 years. The laminae consist of dark, mineral-rich layers (winter layers) and diatom-rich spring-summer layers. X-ray images of 20 cm-slabs of the sediment core were taken and digitized in a resolution of 116 pixel/cm. The example documents the analysis and depth to time scale transform of a 37 cm long section (873–910 cm depth) that is composed of annual lamination in various thickness, contrast and gray levels (Fig. 9E). The top of the section is estimated to have been deposited at ∼3800 yr. BP. Three pixel wide line-scans were extracted from the X-ray images using program IMAGEJ after background calibration (e.g., Nederbragt and Thurow (2001)). Time-scale construction The wavelet analysis over the complete wavelength-spectrum reveals a strong cycle band in the range of ∼0.15–0.4 cm (Fig. 9A) that is overlaid by relatively weak ∼0.8 cm, ∼1.2 cm, and ∼2.5 cm cycles at the top. Extraction of the three most intense wavelengths aWmax(b) (Fig. 9C) shows that the ∼0.15–0.4 cm cycle band can be traced through the section. Visual comparison also indicates that this wavelength band reﬂects the mean annual sedimentation rate or varve thickness. (2) Narrow-band wavelet analysis (Fig. 9B) in the annual bandwidth for k = 1000 intervals (i.e., s = (960–873 cm)/1000 = 0.037 cm), shows that the varves are thickest at ∼883–897 m depth. (3) Using these cycle lengths as proxies of sedimentation rate νk , the time-scale is calculated according to eq. (5) (Table 3). The age at the top t0 is approximately 3800 years before present (Patterson et al. 2001). The transform extracts 137 annual laminae providing

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Relative Power of wavelength

0

A Wavelength in cm

0.1 0.2

~1year

0.5 1 2 5 10 20 30 0.1

Wavelength in cm

B

0.2

C

0.6

Wavelength in cm

0.3 0.4 0.5

Major wavelength (= varve thickness)

0.4 0.2 0

Sediment image color line scan

200

Gray value units

D

100%

100

E

0

873 Top

878

883

888

893

898

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908 cm Bottom

Figure 9. Wavelet analysis of sediment color (in gray scale) data from two X-ray images from a representative section 873–910 cm depth of core TUL99B03. The time-series of the two core-slabs has been connected at 893 cm depth; A: Wavelet analysis over complete spectrum, the excellent preservation of the annual cycle of ﬂuctuating thickness (∼0.15–0.4 cm); B: Narrow band wavelet analysis of 0.15–0.5 cm bandwidth; C: Major wavelength (strongest local wavelet coefﬁcients) at each location; D: Digitized sediment color line-scan (∼4,000 data points), the gray-values range from 0 (black) to 255 (white); E: X-ray image with digitized line-scan (horizontal gray line).

an age range of the complete interval of 3800–3937 years before present. In the next step, mean sediment gray value data x(s) are calculated using MITTELN.C for the depth intervals s = 0.037 cm of the wavelet analysis output forming xk . (4) The time intervals tk are then transformed to i = 685 equal time-intervals t = 0.2 years using MITTELN.C. Then, νk and xk are transformed for the same time intervals to νi and xi using MITTELN.C, respectively. Consequently, the data sets of sedimentation

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Table 3. Wavelet transform output of narrow-band analysis of X-ray data. Raw (k)

Depth (mm)

Wmax(b) varve thickness

Age (years) T0 = 3800

873.00 1

873.04

0.19

3800.20

2

873.07

0.19

3800.39

3

873.11

0.19

3800.59

4

873.15

0.19

3800.79

k=5

s5

v5

T5

k

sk

vk

Tk

s995

v995

T995

909.85

0.50

3936.72

k = 995 996 997

909.89

0.50

3936.79

998

909.93

0.50

3936.86

999

909.96

0.50

3936.94

m = k = 1000

910.00

0.50

3937.01

rate (varve thickness) and sediment gray values are transformed into time scale of equal time interval t = 0.2, forming the time-series ν(t) and x(t) respectively (Fig. 10B, D). The horizontal alignment of high wavelet coefﬁcients in the sediment color time-series in the annual cycle band (black and dark-gray bands in Fig. 10A) indicates that the timeintervals are indeed well equalized, compared to the depth-series (Fig. 9). Palaoenvironmental interpretation of time-series The wavelet coefﬁcient >25% maximum variance in varve thickness form a persistent 11 years cyclicity (Fig. 10C) that is not detectable from the depth-series (Fig. 9). The ∼11 year wavelength could be related to ∼11 year sunspot (“Schwabe”) cycle (Friis-Christensen and Lassen 1991). For further ﬁltering and modelling purposes, these two period bands and their amplitudes can be extracted and used as input parameter for periodic data driven models of sediment accumulation. The sediment color variability is dominated by the annual variations. A short-term ∼10 cyclicity appears over ∼40 years (= four cycles) on the top and may indicate a temporary inﬂuence of sunspot activity on mineralogical and biotic composition of the sediment. Summary High-resolution time-scales are important for the precise correlation of spatially distributed geological records, and further development of process-oriented models used to predict climate change and other terrestrial processes. The extraction of digital line-scan data from images of laminated sediments provides a tool for the rapid and non-invasive analysis of sedimentary records, including sediment and ice cores, and tree ring growth patterns.

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Relative Power of wavelength

A

Wavelength in years

0

100%

0.5 1 2 5 10 20 50 100

Sediment image color

B

Bright

Gray value units

200

Wavelength in years

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100

Dark 0 3800 0.5 1

3820

3840

3860

3880

3900

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3840 3860 3880 3900 Age in years before present

3920

2 5 10 20 50 100 Varve thickness

D 0.4

cm

0.3 0.2 0.1 3800

3820

Figure 10. Wavelet analysis of recovered image color and varve thickness data in time-scale from 873–910 cm depth of core TUL99B03; A: Scalogram of sediment image color, note the excellent and narrow band preservation of the annual cycle and ∼10-year cyclicity at the top; B: Recovered sediment image color time series in time scale in 0.2-year resolution; C: Wavelet analysis of varve thickness, note the persistent and narrow band preservation of a ∼11-year cyclicity (dotted line); D: Recovered varve thickness time series (0.2-year time scale).

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The four-step semi-automatic methodology is based on wavelet and other transform to transform digital line-scan image data from obtained laminated sedimentary successions, from a depth-scale into a time-scale using narrow-band wavelet analysis with Morlet wavelet as the “mother” function, and additional linear transforms and interpolation algorithms. Using the same method high-resolution time-series of lamination (i.e., varve) thickness and sediment color are extracted, providing useful information on paleoenvironmental ﬂuctuations during the sedimentation. With this methodology, it is possible to (1) extract temporal variability in sedimentation rate and climate proxy signals (e.g., image color, mineral composition) even if the wavelengths of the signals overlay each other, (2) extract a high-resolution time scale, and (3) extract original temporal variability in periodicity, abrupt changes and phase shift with ∼2% accuracy error. Furthermore, it is possible to connect samples (e.g., geochemical, paleontological) taken from the sedimentary section precisely to the constructed time-scale. The extraction of high-resolution time-scales using variations in image colors from laminated sediments is only dependent on: - the presence of a well-deﬁned extraterrestrial periodic cyclicity (e.g., annual rotation of the Earth around the sun) in the entire sedimentary succession to be analyzed, - continuity of this signal in the digitised sediment image or succession of images, - a requirement for at least 4 data points (pixel) covering the thinnest lamina, and - the requirement of one or more tie-ages (e.g., radiocarbon dating) to ﬁt the relative counts into an absolute time-scale. Acknowledgments This research was supported by a Natural Sciences and Engineering Research Council of Canada strategic project grant to RTP. We thank E. Verrecchia, P. Francus, and two anonymous reviewers for their suggestions and careful evaluation of the manuscript. References Appenzeller C., Stocker T.F. and Anklin M. 1998. North Atlantic oscillation dynamics recorded in Greenland ice cores. Science 282: 446–449. Berger A., Loutre M.F. and Dehant V. 1989. Inﬂuence of the changing lunar orbit on the astronomical frequencies of pre-Quaternary insolation patterns. Paleoceanography 4: 555–564. Chao B.F. and Naito I. 1995. Wavelet analysis provides a new tool for studying Earth’s rotation. EOS 76: 164–165. Frakes L.A., Francis J.E. and Syktus J.I. 1992. Climate Modes of the Phanerozoic: the History of the Earth’s Climate Over the Past 600 Million Years. Cambridge University Press, Cambridge, U.K., 274 pp. Friis-Christensen E. and Lassen K. 1991. Length of the solar cycle: An indicator of solar activity closely associated with climate. Science 254: 698–700. Gedalof Z. and Smith D.J. 2001. Interdecadal climate variability and regime-scale shifts in Paciﬁc North America. Geophys. Res. Lett. 28: 1515–1518. Gradstein F.M. and Agterberg F.P. 1998. Uncertainty in stratigraphic correlation. In: Gradstein F.M., Sandvik K.O. and Milton N.J. (eds), Sequence Stratigraphy: Concepts and Applications. Elsevier, Amsterdam, pp. 9–29.

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Grossman A. and Morlet J. 1984. Decomposition of Hardy functions into square integrable wavelets of constant shape. SIAM J. Math. Anal. 15: 732–736. Hays S.D., Imbrie J. and Shackleton N.J. 1976. Variations in the Earth’s orbit: Pacemaker of the ice ages. Science 194: 1121–1132. Milankovitch M. 1941. Kanon der Erdbestrahlung und seine Anwendung auf das Eiszeitproblem. Serbian Academy of Science, Belgrade 133, 633 pp. Misiti M., Misiti Y., Oppenheim G. and Poggi J.-M. 1996. Matlab Wavelet Toolbox User’s Guide. The Mathworks, Inc. Mass. Morlet J., Arehs G., Fourgeau I. and Giard D. 1982. Wave propagation and sampling theory. Geophysics 47: 203. Nederbragt A.J. and Thurow J. 2001. A 6,000 year varve record of Holocene sediments in Saanich Inlet, British Columbia, from digital sediment colour analysis of ODP Leg 169S cores. Mar. Geol. 174: 95–110. Patterson R.T., Prokoph A., Dallimore A., Thomson R.E., Ware D.M. and Wright C. 2001. Impact of abrupt Holocene climate changes and solar cyclicity on ﬁsh population dynamics in the NE Paciﬁc. GSA annual meeting, Boston, USA, Paper No. 65–0. Prokoph A. and Barthelmes F. 1996. Detection of nonstationarities in geological time series: Wavelet transform of chaotic and cyclic sequences. Comp. Geosci. 22: 1097–1108. Prokoph A. and Agterberg F.P. 2000. Wavelet-Analysis of Well-Logging Data from Oil Source Rock, Egret Member, Offshore Eastern Canada. AAPG Bulletin 84: 1617–1632. Rioul O. and Vetterli M. 1991. Wavelets and Signal Processing. IEEE Special Magazine: 14–38. Torrence C. and Compo G.P. 1998. A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc. 79: 61–78. Schaaf M. and Thurow J. 1994. A fast and easy method to derive highest-resolution time-series datasets from drillcores and rock samples. Sed. Geol. 94: 1–10. Schwarzacher W. 1993. Cyclostratigraphy and Milankovitch Theory. Developments in Sedimentology 52. Elsevier, Amsterdam, Netherlands, 225 pp. Varem-Sanders T.M.L. and Campbell I.D. 1996. Dendroscan: a Tree-Ring Width and Density Measurement System. Special Report 10, Canadian Forest Service Centre. UBC Press, Vancouver, Canada, 131 pp. Ware D.M. and Thomson R.E. 2000. Interannual to Multidecadal Timescale Climate Variations in the Northeast Paciﬁc. J. Climate 13: 3209–3220.

9. X-RAY RADIOGRAPHS OF SEDIMENT CORES: A GUIDE TO ANALYZING DIAMICTON

SARAH M. PRINCIPATO ([email protected])

Institute of Arctic and Alpine Research and Department of Geological Sciences University of Colorado Campus Box 450 Boulder, CO 80309-0450 USA Currently at Department of Environmental Studies Box 2455, 300 N. Washington St Gettysburg College Gettysburg, PA 17325 USA Keywords: X-ray radiographs, Diamicton, Glacial marine sediments, Till, Image analysis, Ice-rafted debris, Iceland

Introduction An important issue in glacial and marine geology is developing a method that allows discrimination between the processes of deposition of diamicton units, especially distinguishing subglacial till from glacial marine sediments. It is important to discriminate between these sediments because they lead to different interpretations of glacial history, but this distinction is difﬁcult to make (c.f., Vorren et al. (1983), Domack and Lawson (1985), Dowdeswell et al. (1994), Licht et al. (1999)). Standard grain size analysis of sediments in marine and lake cores commonly include the <2 mm fraction of the sample, so only percentages of sand, silt, and clay are reported. A problem with this approach arises when one is trying to characterize sediments containing abundant clasts larger than 2 mm, such as unstratiﬁed diamicton units associated with glacial sedimentary systems. In such cases, the standard measurements of the matrix may not represent the true grain size spectra of the sample (Andrews and Principato 2002). The purpose of this paper is to describe a technique for analyzing the >2 mm size fraction using image analysis of X-ray radiographs (shortened to radiographs throughout text) of sediment cores. Radiographs were ﬁrst used in geological studies to examine paleontological specimens and later applied to studies of sedimentary rocks and sediments (Hamblin 1962; Calvert 165 P. Francus (ed.) 2004. Image Analysis, Sediments and Paleoenvironments. Kluwer Academic Publishers, Dordrecht, The Netherlands.

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and Veveers 1962; Bouma 1964). Although radiographs are now commonly used in marine core studies to count ice-rafted debris (IRD) (Grobe 1987; Andrews et al. 1997), to deﬁne lithofacies and decide on sampling intervals (Jennings and Weiner 1996), detailed, computerized image analysis of radiographs of diamicton units is lacking, with the exception of a study by Licht et al. (1999) on sediments from the Ross Sea. By simply counting the number of IRD with depth, information regarding the size, shape, and orientation of the clasts is lost. For example, a large clast and a small clast will both count as one pebble of IRD, but the mode of deposition of these two clasts could be different. Finding one large clast versus ﬁnding several small clasts would appear as a drop in IRD during the interval when the large clast was deposited, but since the large clast covers entire interval, there is a sampling bias. Therefore, taking into account other characteristics of IRD, such as size, shape, and orientation, provides more insight into the depositional environment of the sediments. The advantage of using radiographs of sediment cores is that it provides a quick, relatively inexpensive data set, with minimal sediment intrusion, for describing sediment cores that can then be quantiﬁed using image analysis. Detailed procedures of digital image analysis based on gray scales have been described for laminated sediments (see Migeon et al. (1999) and Loﬁ and Weber (2001)), but a systematic technique has not been fully developed for poorly sorted, coarse grained sediments. This paper describes a semi-automated, image analysis technique (Fig. 1) that characterizes clasts >2 mm based on grain size, inclination, length, shape, area, and that also counts the pebbles with depth automatically (Fig. 2). This is followed by a speciﬁc case study that demonstrates the use of the image analysis technique on diamicton units from North Atlantic continental margins including the Iceland shelf (MD99-2256, Upper and Lower Diamictons, and B997-323pc1), Greenland shelf (91-K14), and Cumberland Sound (Basal undifferentiated diamicton, BUD) (Fig. 3). Image acquisition It is possible for the researcher to face two very different practical situations before starting the acquisition of radiographs for an image analysis study. The ﬁrst one is the study of newly acquired sediment cores. In this case, the researcher has full control on the acquisition of radiographs. The second is the study of radiographs that have been previously acquired by other researchers with other goals, and the sediment cores are no longer available for X-raying. This section outlines how to proceed in both situations. Acquiring new radiographs When a partially digital system is used, there are two steps in image acquisition, and both steps inﬂuence the quality and accuracy of the ﬁnal image analysis, 1) acquiring the radiograph of the sediment core, and 2) importing the radiograph into digital format. Comparison of images obtained at each step of the process with the original sediment and/or the original radiograph are necessary in order to evaluate biases introduced, such as distortion of scale and intensity. Image acquisition can be time consuming and costly, depending on the resolution required for the study. Hardware and software requirements increase, as the need for details increases. For example, preparation and analysis of

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Sediment core

X-ray radiograph NIH Image (open .tif) Scan image, save as .tif

Adjust LUT (brightness/ contrast)

Rank filter (median to reduce noise)

Analyzechoose options

Make binary

Density sliceadjust LUT again

Zoom in; erase adjacent pixels

Analyze particles (compute min. particle size)

Print and save analyzed image Show resultsprint and save

Set scale Open results in spreadsheet program and complete statistical analyses Figure 1. Flow chart for image analysis of radiographs.

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M

P

X m A

Figure 2. The properties of clasts that can be measured on a radiograph. M = length of major axis; m = length of minor axis (dotted line); P = length/perimeter; area is calculated by sum of pixels enclosed within P ; A = angle from horizontal; X = x, y center (i.e., pebble counts with depth). 75ºN

Greenland

GREENLAND 68ºN

Nansen Fjord

500

Kangerlussua

land in Is Baff

Baffin Bay

300

200

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60ºN

66ºN

St 500

Labrador

q Trough

on ds Hu

BUD

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500

DE

NM

AR

K

R ST

AI

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T

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B997-323

0 20 00 1

100

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ICELAND

1500

Labrador Sea

MD99-2256

64ºN 45ºN

100

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60ºW

45ºW

30ºW

500

-30ºW

-28ºW

-26ºW

-24ºW

-22ºW

-20ºW

-18ºW

Figure 3. Location of diamicton units used in the case study.

ﬁne-grained varved sediments are more time consuming and require images of higher resolution than the analysis of diamicton units. Ideally, acquisition of radiographs is completed before invasive sedimentological sampling and analyses begin. The production of a radiograph is based on the differential absorption of X-rays in a core due to variations in density, thickness, and composition (including grain size and mineralogy) of the sediment (Baker and Friedman 1969; Patchen 1968). The power, exposure time, current strength, ﬁlm type, and slab thickness is recorded so that consistency between radiographs is maintained or lack of consistency is recorded (Patchen 1968). There is a complex relationship between voltage, current, and exposure

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time, so experimentation with the X-ray machine is usually required to get a radiograph of good quality (Hamblin 1962). In order to identify features with the same amount of certainty for all radiographs, consistent radiograph quality should be maintained throughout the image analysis study. Varying acquisition conditions can indeed inﬂuence the number of clasts counted. Standard materials should be X-rayed along with the sediment core sections in order to compare continuous radiographs from one core or to compare radiographs between cores. First, materials of known and contrasting densities, such as basalt, andesite, rhyolite, and pumice, are placed on each radiograph in order to provide a gray scale calibration that can be compared with these materials of known density. Second, the depth scale is marked on the core sections with lead nails and lead numbers while it is being X-rayed (Bouma 1964). This helps maintain consistent depth measurements throughout the analysis and record distortion in the depth scale. Due to X-ray scattering, the resulting image may vary in intensity from the top to the bottom of the image. Compensation for this is made by adding a calibrated gray scale on the side of the original sediment, before it is X-rayed, as previously discussed. It is preferable to X-ray sediment slabs of uniform thickness to avoid the problems of superposition of clasts and other features (Hamblin 1962; Grobe 1987). A technique for making slab radiographs is described by Bouma (1964). The slab of sediment can be placed on either plastic or plexiglas since both of these materials are isotropic to X-rays (Bouma 1964). Image analysis of slab radiographs is comprehensively described by Ojala (this volume). Slab radiographs are not a feasible solution for coarse-grained sediments with abundant clasts >1 cm, as the thin slab would exclude many clasts and would not provide an accurate representation of the original sediment. It is also physically difﬁcult to cut through large clasts, so making slab radiographs of diamicton units is not always possible. Although the problems of overlapping and adjacent clasts remain when X-raying entire core or half core sections, they are faster and easier to X-ray than sediment slabs, which require time consuming preparation. Split and whole core radiographs of cores containing diamicton units provide a larger and more representative sample than a slabbed sample because large clasts are more likely to be included. When X-raying a cylindrical core or core half, the sediment is not of uniform thickness, and thus the X-rays penetrate more completely through the sides of the core sections than the thicker center (Baker and Friedman 1969; Patchen 1968). It is possible to compensate for a variation in sediment thickness by using an aluminum ﬁlter that adjusts the penetration of radiographs (Baker and Friedman 1969). It is also possible to digitally remove this artifact by taking an X-ray of a homogeneous core tube and using it as background that can be digitally subtracted (Nederbragt et al., this volume). Digital formatting (scanning) Once good quality radiographs are acquired and the radiograph image provides a realistic representation of the original sediment, the next step is to convert the radiograph into digital format for computerized analysis. The radiograph itself, a negative, may be used for analysis or a positive print of the radiograph can be made (Bouma 1964). For radiograph negatives or prints, ideally one should use a ﬂatbed scanner with transparency capability, such as the Epson Expression 1680 SE color ﬂatbed scanner (de Keyser 1999). This type of scanner is more expensive than the average desktop scanner, so it is sometimes beyond the

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limit of the budget of a project. However, if extensive, detailed, and completely automated radiograph image analysis is desired, using this type of scanner is critical. It is preferable to use a ﬂatbed scanner over a digital camera, as additional distortion and light source become issues when photographing the radiographs. Sometimes it is possible to directly capture a primary digital radiograph image using a CCD camera or digital radiograph system (Duncan et al. 1998; Migeon et al. 1999), but for pre-existing radiographs, it is necessary to scan either prints of radiographs or the radiograph negatives. Ideally, one should use similar scanning resolution, brightness, and contrast for all radiographs, but if alterations are made, such as changes in brightness/contrast, enlargements or reductions of the image size and ﬁle type, then these data should be recorded. The original depth scale should be left on the image throughout the analysis to evaluate the amount of distortion in length and shape attained in the radiograph image and scanning procedures. After scanning, pixels are converted to a physical scale (i.e., cm or mm) (Nederbragt et al., this volume). Scans of 400 dpi have adequate resolution to distinguish pebbles from noise and are of manageable ﬁle size (typically 10 MB). Image resolution depends on the goal of the study and the level of detail required to identify features. For example, in the case study described in this chapter, a 2 mm clast is represented by 10 pixels. Alternative to direct radiograph scans The alternative approach reduces bias from radiographs of varying qualities and of different ages, and it is necessary when the researcher is using radiographs previously acquired by other researchers with other goals. It is suggested that all radiographs be closely examined on a light table before image processing begins. The gray scale of the computerized image will represent relative radiograph density, and the NIH program will only recognize differences in gray scale or pixel intensity. The human eye is sometimes needed to discern stray marks from pebbles and to identify operational errors (Bouma 1964). It is also important to evaluate whether the direct scan captured the majority of clasts >2 mm (Fig. 4). If these problems of stray marks, operational errors, and missing clasts are overwhelming, then an alternate, simple technique is to trace the visible pebbles onto clear mylar or transparency paper ﬁrst and then scan the tracings of pebbles (Fig. 4). A pen with a tip of constant width should be used so that the thickness of the pen does not inﬂuence the apparent size of the clast. Then, the scanning procedure outlined in the previous section is performed. This alternative technique is simple and inexpensive, but it is very subjective because it involves decisions of an operator. Image processing There are several steps in the image processing procedure, and they are similar for both direct scans of radiographs and scans of tracings. The procedure was completed on a G-4 Macintosh computer with 256 MB of RAM using the public domain NIH Image program (Rasband (1996); developed at the U.S. National Institutes of Health and available on the Internet at http://rsb.info.nih.gov/nih-image/), but it is also possible to complete this analysis on a PC/IBM type computer. For more details regarding speciﬁc commands and tools used in the program, refer to the online manual (http://rsb.info.nih.gov/nih-

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100 cm

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110 cm

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C

D

Figure 4. The image analysis procedure from acquisition of the radiograph to ﬁnal analysis. A) The original radiograph; B) A ﬁltered binary image created from directly scanning the radiograph; C) Tracings of the clast in the radiograph when examined on a light table; D) Final analysis of clasts completed in NIH Image software. It is evident from b and c that over 50% of the clasts are lost with the direct scanning technique in this study, making the tracing step important for these radiographs. This is due to the quality of the radiograph and the capability of the ﬂatbed scanner.

image/manual/contents.html). The scanned images were saved in tagged image ﬁle format (tiff) in order to be opened with the NIH Image software. For more details regarding memory requirements and other procedures speciﬁc to the NIH Image software, refer to the Metadata section. Brightness The brightness and contrast of the image was intuitively adjusted. This step is subjective, as brightness depends on monitor settings, scan of the image, brightness of the original radiograph, and one’s vision, but an attempt to retain a constant level of clast brightness between radiographs should be made. If gray scale standards of known densities (see Acquiring Radiographs section) are used on each radiograph this subjectivity is reduced. The image must be bright enough to deﬁne the outline of clasts and not so bright that the background remains indistinguishable from the clasts. Segmentation Clasts of a speciﬁc density range of pixels are highlighted in this step. See metadata and Nederbragt et al. (this volume) for details.A careful comparison with the original radiograph is useful to check the segmentation.

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Make binary The image of the radiograph is transformed into a binary image. The dense pixel clusters, which represent clasts, will be black and the remaining matrix will be white. Only the black pixels will be analyzed. Filters Sometimes the resulting binary image contains stray marks and requires cleaning. This is done using a ﬁlter that reduces the noise (Fig. 5). This is a very critical step, and in order to compare within and between core radiographs, the same ﬁlter should be applied to each image. One or two iterations of a median ﬁlter are usually necessary. The median ﬁlter replaces each value of a pixel with the median value of a 3 × 3 pixel area around it, which results in a reduction of noise (Rasband 1996). In addition to the stray marks and noise, another problem that remains is that some clasts may be in contact with each other. Although some complex algorithms, such as watershed segmentation (Nederbragt et al., this volume), exist to separate adjacent touching clasts, we favor a simpler technique that is to use the eraser tool to delete a minimal number of pixels. Deleting pixels manually alters the original image, so extra caution should be taken with this step. In order to minimize the number of pixels deleted and reduce alterations of the image, zoom in on the adjacent clasts so that each click of the eraser equals one pixel. Remove as few pixels as possible to make the clasts separate entities. It is important to repeatedly compare the altered image with the original radiograph to make sure that the image being analyzed provides a good representation of the original radiograph. It is possible to calculate an error term for removing pixels from adjacent clasts, and the small percentage of area that each clast loses. (For example, if the scale is set to 4.8 pixels = 1 mm, then removing one pixels causes a loss of approximately 0.21 mm in length or 0.0441 mm2 in area). Image measurement Measurement options In order for the computerized image to physically represent the radiograph from which it was derived, a spatial calibration must be applied to the image (see metadata for NIH speciﬁcs). Analyze particles The goal of analyzing the non-matrix of diamictons is to count clasts >2 mm using the image analysis. The abundance of clasts <2 mm are counted using standard sedimentological procedures, such as using a Malvern or Sedigraph (Syvitski 1991). Simple ratios of pixels to mm can be used to compute the minimum particle size that represent the non-matrix fraction. In our case study, we only counted objects >10 pixels, i.e., >2 mm. Therefore, the minimum particle size for this resolution is 10 pixels. It is better to have a high resolution scan of the original image in order to reduce the number of pixels that are lost when erasing

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B997-323pc1, ca. 100-120cm section of x-ray

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100 cm

110 cm

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120 cm

120 cm B

Figure 5. A) Unﬁltered binary image and B) median ﬁlter applied to binary image. The ﬁlter provides a cleaner image with less stray marks and noise. One pixel equals approximately 0.2 mm.

pixels to separate clasts. A print out of the analysis should be compared with the original radiograph and sediment core (see metadata for more details). Measurements At least four properties of clasts are measured using image analysis: grain-size, inclination, shape, and perimeter. Grain-size is commonly measured in terms of the long axis of clasts (Boggs 1995). This is used in laser diffraction measurements and traditional sieving measurements of sediment. In this study, the clasts are represented by a cluster of black pixels, and the long axis is measured. The NIH image program deﬁnes a major axis of the best

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ﬁtting ellipse encompassing each clast, and this is used as the long axis of the clast, which deﬁnes the grain-size. The inclination of clasts is measured by the angle between the major axis and a line parallel to the x-axis of the image. These angle measurements are used to infer fabric of the sediment (see case study described below). The NIH program measures angles between 0–180 degrees. However, for fabric measurements, since absolute direction cannot be inferred from a sediment core (due to possible rotation during the coring procedure), this study transforms the angle data to measurements between 0–90 degrees. This is done by subtracting 180 from measurements greater than 90 degrees. It is more important to determine how close to vertical and how close to horizontal the clasts are than to determine whether they dip to the right (0 degrees) or to the left (180 degrees). This gives a more accurate measurement of the degree of shearing, i.e., fabric, that the sediment has undergone (Hrouda 1982). Shape and perimeter are the two ﬁnal parameters used in the image analysis case study. The shape value is deﬁned by Francus and Karabanov (2000) as four times the area of the clast divided by pi times the square of the length of the major axis. In this study, the perimeter is the length of a line drawn around the outside of the clast. Caution should be exercised when interpreting measurements of image analysis, especially for interpreting the orientation and perimeter measurements. There is an extreme lack of robustness in these two measurements for small clasts, although size measurements of small clasts are still valid. In order to avoid some of these problems, datasets could be limited to particles >50 pixels. In this study, analyzing only clasts >50 pixels would result in the elimination of more than 75% of the dataset. Therefore, the small clasts (as small as 10 pixels) are still included, but they are interpreted with caution. Also, orientation measurements are only interpreted as fabric for elongate clasts, i.e., when the ratio between the major axis to minor axis is 1.7 or greater (Domack 1982). This ratio does not rely on clast size, and it must be consistent for large and small clasts in order for the fabric measurements to be valid. Advantages of using image analysis There are at least seven advantageous, general aspects of X-raying and image analysis of radiographs that make it useful in many sediment core studies, in addition to the analyses of diamicton units. Speciﬁc results are illustrated through a case study of diamictons from marine cores and discussed in the following section. Radiographs are relatively inexpensive, quick, and require minimal sample preparation (Bouma 1964). However, the rapidity of sample preparation and X-raying depends on the sample size and resolution of the study. Once the image acquisition and processing is complete, a computerized analysis procedure provides quantitative data relatively rapidly and inexpensively. In the past, radiographs have been described qualitatively and used to decide on sampling intervals (for example, Jennings and Weiner (1996)), but image analysis adds quantitative data to the qualitative descriptions with minimal disturbance or sampling the sediment. Also, the core does not necessarily even have to be split. Another advantage is that it measures the x-y center of clasts, which makes it possible to count the number of clasts with depth, i.e., NIH Image automates IRD counts (Fig. 6). A sixth advantage is that an estimation of grain size can be made using the length of the major axis measurement. This is far less tedious than wet or dry sieving coarse sediment

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samples. Other parameters that can be calculated from radiographs include inclination or dip of clasts, shape of clasts (Francus and Karabanov 2000; Pirard, this volume), perimeter, length of the minor axis, and ratios of these parameters. It is also possible to get a quasi 3-D image of sediment cores from radiographs by taking the radiograph at 0 and 90 degrees, and stereography is possible if radiographs overlap (Hamblin 1962). The seventh advantage of this image analysis technique is that data is stored in digital format, and it is available for re-evaluation and future work. IRD Counts for B997-323pc1 Lithofacies 14C date

Depth (cm)

(reservoir corrected)

0

Counts for Entire Core number of clasts

0 0

1 13040+190 >25900

100

3

0

100

10

20

60 65

40

2

50

Counts for 60-128 cm number of clasts

70

80

76

120

Depth (cm) 88

160

82

94 200

200

100

240

106

280

112

More

120 126

Figure 6. Core B997-323pc1, North Iceland Shelf, a) Lithofacies: 1 = sandy mud, 2 = silty clay with scattered pebbles, and 3 = stiff diamicton; b) IRD counts for entire core using image analysis; c) IRD counts for the transition between units 2 and 3 using image analysis. These automated IRD counts correspond well to the lithofacies changes. The transition from unit 2 to 3 at approximately 85 cm shows an increase in IRD.

Drawbacks to image analysis Most of the problems associated with the image analysis of radiographs stem from the fact that a 2-D interpretation of a 3-D object is made, and some of the measurements are only estimates of the properties of clasts and represent apparent measurements. For example, the inclination of a clast represents only the apparent inclination of the clast. Clast size interpreted from the length of major axes sometimes provides only a minimum estimation, as the maximum length of the major axis is likely oblique to the cut of the core and not parallel to it, causing an underestimation in grain size. One possible solution to this is to

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take X-rays of cores at various orientations, at least at 0 and 90 degrees (Hamblin 1962). A second solution to this 2-D problem is to use computer assisted tomography (CAT) scans and not rely on radiographs (Kantzas 1995), but the cost of this procedure is at least an order of magnitude more expensive than simple X-ray radiography. The procedure described in this paper is also limited by the resolution of the scanner, quality of the original radiographs, and computer processing capabilities. The subjectivity in the selection of the threshold level can be reduced by incorporating calibration material (Nederbragt et al., this volume). This is not routinely done, and adding gray scale calibration standards to pre-existing radiographs is not possible. If the cores have been intensely sampled and nothing remains to re-X-ray, but radiographs are available, then one should use the tracing method. Example: case study of ﬁve diamicton units from North Atlantic continental margins Study sites and purpose Diamicton is poorly sorted, unstratiﬁed sediment, containing a wide grain size distribution form clay size particles up to pebbles and boulders (Flint et al. 1960a; 1960b). Conventional grain size analyses usually describe the matrix and ignore larger clasts (Andrews and Principato 2002). This is because sample size prevents statistically representative larger than gravel-size percentages in piston cores. Radiographs provide information for quickly estimating the non-matrix grain size distribution in a sediment core, but they also contain this sampling size bias. Diamicton units observed in marine cores from ice-proximal or former ice-proximal environments are usually interpreted as either glacial till, glacial marine sediment, sediment gravity ﬂows, or some combination of these processes, but a distinction between these options is frequently difﬁcult (Vorren et al. 1983; Domack and Lawson 1985; Dowdeswell et al. 1994; Licht et al. 1999). Despite the wide range of depositional environments for diamictons, the resulting sediments commonly look similar and interpreting them is difﬁcult (Domack and Lawson 1985). The purpose of this case study is to examine radiographs of ﬁve diamicton units from marine cores from the North Atlantic continental margins (Fig. 3) and determine if image analysis of the coarse fraction can help distinguish differences in depositional environment. Two of the diamicton units, basal undifferentiated diamicton (BUD) from Cumberland Sound, SE Bafﬁn Island and core 91-K14 (K14) from Kangerlussuaq, East Greenland have been studied in detail (Jennings 1989; Jennings 1993; Jennings and Weiner 1996; Smith and Andrews 2000). Based on at least ﬁve properties, including foraminiferal assemblage work, sedimentology, and clay mineralogy, the depositional environments of these two units are generally considered to be known without detailed image analysis of radiographs. K14 and BUD are interpreted as glacial marine sediment and subglacial till, respectively. The sediments in the two units are considered “end members” in the image analysis, as subglacial terrestrial and marine environments should result in contrasting sedimentary signatures (O’Cofaigh and Evans 2001). Till is deﬁned as unconsolidated sediments deposited by glacial ice (Goldthwait 1971), and glacial marine sediment includes sediments released from glacier ice or an ice shelf into the marine environment through a water column (Andrews and Matsch 1983; Powell 1984; Dowdeswell and Scourse 1990). The depositional environment of the other three diamicton units, from the north and southwest Iceland shelf, contained in cores B997-323pc1 and MD99-2256 (Upper and Lower diamicton units), are

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either till, glacial marine sediment, or reworked glacial marine sediment, but this is not clearly known (Principato 2001). These three units are referred to as “unknowns” in terms of depositional environment. The goal of the image analysis is to describe the radiographs of the “unknown units” and compare and contrast them with the well known “end member” examples. Materials and methods The case study involves comparing radiographs of different ages (at least 10 years difference) that were taken at the Institute of Arctic and Alpine Research (INSTAAR), Woods Hole Institute of Oceanography (WHOI), or the Bedford Institute of Oceanography (BIO), so the radiographs are of varying quality and consistency. The initial purpose for taking these radiographs was to describe the cores and to decide on sampling intervals (Jennings and Weiner 1996). The speciﬁcs of the radiograph procedures were not always completely documented. B997-323pc1 and K14 were X-rayed at INSTAAR with a HP Faxitron radiograph system, at a power of 110 kV, current of 2.4–2.8 milliamps, and an exposure time varying from 1 min, 45 sec to 2 min, 30 sec. Using this design, the radiograph machine took a snap shot, and the core was moved with approximately 5 cm overlap for each successive radiograph. Lead contactpak Kodak Industrex M Film was used. Radiographs of MD992256 were taken at WHOI using a moving radiograph system, Philips Industrial X-ray machine. Split core sections were placed directly on radiograph ﬁlm, and the X-ray source passed over the core approximately 4 times with a speed of approximately 45 mm/min and power of 130 kV. The radiographs of BUD were taken on split core halves at the Bedford Institute of Oceanography, and positives of the radiographs were made (Jennings 1989; Jennings 1993). As discussed above, it is not ideal to do automated comparisons between radiographs taken at different institutions that vary in quality, especially if the X-ray speciﬁcs are not known. To avoid image analysis biases of scanning caused by variations in gray scale and radiograph quality, the tracing technique described above was used. Most of the cores were intensely sampled after the original radiographs were taken, so re-X-raying these cores is not possible. The water content also would have changed, which would affect the density of the sediment (Easterbrook 1964; 1982; Vorren et al. 1983), and the resulting radiograph. Results Common properties used for describing sediments are grain size, fabric, shape, and roundness (Boggs 1995). Proxies for these parameters derived from the image analyses include length of major axis, angle from horizontal (inclination), perimeter, and area (Table 1). Grain size data is estimated using the length of major axes of clasts, and histograms show the grain size distributions for each core (Table 1 and Fig. 7). The grain size data are positively skewed, so statistical analyses were completed on the log transform of the length of major axes. Box plots show that there is signiﬁcant overlap between K14 and BUD (Fig. 8) and indicate that in these two examples glacial marine sediment cannot be distinguished from till based on image analyses of grain size alone. One-way analyses of variances of the length of major axes data (log transformed) show that these diamicton

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Table 1. Statistical results of the image analysis.

mean

Core

Major Axis (mm)

Log of Major Axis

Tilt

Perimeter (mm)

Shape

Area (mm2 )

B997-323pc1

34.54

6.84

0.79

42.38

19.95

0.65

median

5.80

0.76

39.62

16.60

0.64

16.00

standard deviation

4.43

0.19

25.76

13.49

0.14

138.36 42.08

mean

8.49

0.89

50.40

25.63

0.66

median

7.70

0.89

54.91

22.50

0.67

27.00

standard deviation

3.49

0.17

30.75

10.73

0.15

38.61 47.35

mean

K14

8.92

0.93

57.44

27.13

0.63

median

7.75

0.89

41.53

24.00

0.61

33.00

standard deviation

3.17

0.15

24.06

11.30

0.15

43.55 54.26

mean

BUD

8.14

0.83

22.82

24.08

0.69

median

6.20

0.79

20.31

17.70

0.69

20.00

standard deviation

6.39

0.24

18.1

18.61

0.15

125.72 64.76

mean

Upper 2256

9.20

0.91

39.68

27.03

0.68

median

Lower 2256

7.80

0.89

37.42

22.80

0.68

31.00

standard deviation

6.11

0.20

29.39

18.58

0.13

178.58

units are not all the same (95% conﬁdence). Individual comparisons, made using the Scheffe Test (Hamilton 1998) show that B997-323pc1 can be distinguished from most of the other units based on length of major axes except for the upper diamicton in MD99-2256 (95% conﬁdence). The remaining diamicton units cannot be distinguished from each other at this conﬁdence interval based on length of major axes. It is important to note that the upper and lower diamictons just miss the 95% conﬁdence interval cut-off. If a 90% CI was used, it would be possible to distinguish these units, as the probability value is 0.067. The orientation of clasts, i.e., fabric of sediment, is sometimes a useful parameter in interpreting the depositional environment of sediments and distinguishing basal till from glacial marine sediments (e.g., Domack (1983), Domack and Lawson (1985)). In the image analysis, fabric is interpreted by the angle from horizontal of the clasts including only clasts with a major: minor axis ratio of 1.7 or greater (Domack 1982). Based on the box plots and statistical calculations a large spread and standard deviation in the angle measurements is evident (Fig. 8). For the end members, BUD has a much narrower range than K14, and the median angle for BUD is higher than for K14 indicating that BUD has undergone shearing from ﬂowing ice. With the exception of a couple of outliers, the Upper Diamict in MD992256 does not overlap with BUD leading to the interpretation that it has a different fabric than the till end member. The Upper Diamict in MD99-2256 also has a lower median angle than the Lower Diamict in -2256. This means that the upper diamicton has a sedimentary

X-RAY RADIOGRAPHS OF SEDIMENT CORES …

179

BUD

K14

number of clasts

number of clasts

30

20

10

10 0

2

4

8 16 size (mm)

32

0 2

64

4

300 200 100 0 2

4

8 16 size (mm)

32

64

Upper Diamict, MD99-2256

number of clasts

number of clasts

B997-323pc1

8 16 size (mm)

32

64

50 40 30 20 10 0 2

4

8 16 size (mm)

32

64

MD99-2256, lower diamict

number of clasts

80

60 40 0 2

4

8 16 size (mm)

32

64

Figure 7. Histograms of grain size of clasts from each of the diamicton units. All of the diamicton units have a peak between the 4–8 mm diameter size, and it is difﬁcult to distinguish them based solely on this property.

fabric (long axes are horizontal), and the lower diamicton has a sheared fabric (long axes have high (>45◦ ) inclination) (Hrouda 1982). The shape and perimeter yield nondiagnostic results for differentiating the diamicton units. As shown in box plots, with the exception of BUD, which has a large spread, the rest of the diamicton units are indistinguishable from each other based on these parameters (Fig. 8). This may be a result of including small particles (see Measurements section for comments on robustness). Length measurements contain several outliers, and the diamicton units are statistically indistinguishable at the 95% conﬁdence interval. Using the x-y center measurements, a proxy for IRD is derived for each core (Fig. 6). This is useful for generating automated IRD counts, but since clasts >2 mm are common in diamicton units interpreted

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PRINCIPATO Box Plots of Image Analysis Data log of major axes, all cores 2.0

90.0

1.2

45.0

0.4

angle from horizontal, all core

0 B997323pc1

K14

BUD

Upper

B997323pc1

MD99-2256

K14

BUD

Upper

Lower

MD99-2256

length (mm)

220

shape

1.01

1

Lower

106

0.65

8

0.28 B997323pc1

K14

BUD

Upper

Lower

B997323pc1

K14

MD99-2256

BUD

Upper

Lower

MD99-2256

glacial marine sediment glacial till

Figure 8. Box plots for diamicton units. a) Grain size looks similar for BUD and K14, with the exception of a greater degree of skewness in BUD. B997-323pc1 contains the most outliers, but otherwise it has a similar inter-quartile range and median to the upper diamict of MD99-2256. b) Angle from horizontal data shows wide ranges of angles and no preferred dip orientation. c) Shape parameter looks similar for most of the diamicton units, with the exception of BUD, which has the largest spread. d) The length/perimeter box plots show lots of outliers and no speciﬁc trends.

as till and glacial marine sediment, these counts are not used to discriminate between the units. Discussion The results of the case study show that there are at least 4 properties of sediments that can be estimated from radiographs that are not included with standard grain-size analyses. This procedure adds description and semi-quantitative information about each diamicton unit, including automated >2 mm clast counts. Statistical results show that it is difﬁcult

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181

to discriminate between the diamicton units with image analyses alone. Based on the length of major axes and tilt of clasts, K14 and BUD, the two “end members”, are not statistically distinguishable (95% conﬁdence), but the box plots illustrate differences in the median and spread for inclination data, length of major axes, and shape (Fig. 8). It is difﬁcult to match the “unknowns” with either of the “end members”, but the lack of overlap between BUD and the Upper Diamict in MD99-2256 suggests that this latter unit is not a glacial till. The difﬁculties in discriminating the diamicton units are not a failure of the image analysis techniques, but rather they are a reﬂection of the complicated depositional processes that created these units. It also shows that local factors may exert a stronger control over the deposition of diamicton units than regional factors. For example, based on angle data, MD99-2256 upper and lower diamicton units had properties similar to glacial marine sediment and till respectively, but these two units did not exactly match glacial marine sediment in K14 and till in BUD. This shows that it is easier to distinguish between different diamicton units in one core than it is to correlate diamicton units from different geographic areas. It is likely that till deposited in Cumberland sound is quite dissimilar to till deposited on the Iceland shelf, as bedrock lithology and subglacial recycling processes differ. The deposition of diamicton units are the result of complicated processes, and more work needs to be done in order to understand the depositional environment of diamicton units on the Iceland shelf. It is best to use a multifaceted approach to describe and interpret diamicton units (Principato 2001). In the case of BUD, foraminifera and clay mineralogy analyses are most useful in interpreting its origin (Jennings 1993), but in the case of K14, sedimentological parameters, such as carbon content and magnetic susceptibility, and foraminifera are diagnostic (Jennings and Weiner 1996; Smith and Andrews 2000). Thus, when trying to understand the origin of diamicton units, it is important to combine several factors, and image analysis provides a fast and easy way to describe the >2 mm fraction in diamicton units.

Future direction The tracing technique described in the case study is valid when using radiographs of various ages, and when the core has been extensively sampled and cannot be re-X-rayed using new digital techniques. For future studies, direct digital acquisition of radiograph images is preferable, and a technique for this has recently been developed (see Migeon et al. (1999), Loﬁ and Weber (2001)). Using direct digital images would eliminate some of the shortcomings of the image acquisition procedure described in this study, and it would reduce the subjectivity of the processing steps, such as adjusting brightness and making the segmentation. Digital corrections of radiographs should help reduce problems associated with variations of X-ray penetration due to the shape of the core tube. It is also possible to acquire 3-D radiograph images using CAT scans (Kantzas 1995) instead of X-raying the core at several orientations. Digital acquisition of 3-D, CAT radiograph images is the path to the future of image analysis of radiographs, as it eliminates the 2-D problem of traditional radiographs. However, the expense of this 3-D procedure is probably not justiﬁable for most studies.

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Summary This study develops an image analysis technique for describing and semi-quantitatively analyzing diamicton units. Properties such as grain size of clasts >2 mm, angle from horizontal (inclination), perimeter of clasts, shape, and area are used for proxies of sedimentologic properties and fabric of the sediments. Automated clast counts are described using this procedure. It is ideal for studies incorporating radiographs of varying quality and consistency. Advantages of this technique are that it is relatively rapid, low cost, and non-destructive. Drawbacks include subjectivity in grayscale adjustments and problems associated with interpreting a 2-D image from a 3-D object. The future of radiograph analysis is to use 3-D radiograph images using CAT scans, although this may not be economically justiﬁable. The case study of sediments from the Iceland shelf, Greenland, and Cumberland Sound illustrates at least four of the parameters that can be quantiﬁed from radiographs, such as grain size, fabric, shape, and area. The study also shows that diamicton units are complex and local factors exert a large control over the resulting sedimentary deposit. Acknowledgments This research is supported by National Science Foundation grants OPP-0004233 and OCE9809001. Helpful discussion and comments on an early version of the manuscript by Drs. John T. Andrews, Anne E. Jennings, and Damian B. O’Grady are appreciated. Dr. Gudrun Helgadottir, chief scientist of the Bjarni Saemundsson B9-97 cruise, and the IMAGES V program Marion Dufresne cruise and the crews on each are thanked for obtaining cores used in this study. Ellen Roosen and Parker Hackett are acknowledged for helping prepare radiographs at Woods Hole Institute of Oceanography. Dr. Pierre Francus is thanked for organizing the image analysis workshop and for his tips on using the NIH Image program. Thank you to Drs. Eugene Domack and Antti Ojala for helpful reviews. Metadata: additional steps for analyzing radiographs, speciﬁc to the NIH Image software Image processing Memory requirements The memory requirements for NIH Image are at least 4 MB of RAM, but more than 32 MB is suggested. The amount of memory used by the NIH Image software is adjustable. The size of the ﬁle capable of being analyzed is limited by the undo buffer and size of the clipboard. Adjust the size of the buffers so that they are greater than the image size. On Macintosh computers it is also necessary to allocate more memory to NIH Image to avoid functional errors. It is necessary to quit and restart NIH Image before any memory changes are effective. Brightness Once memory requirements are met, open the image and adjust the brightness of the image using the color Look Up Table (LUT) tool. This step is subjective, as brightness depends on

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monitor settings, scan of the image, brightness of the original radiograph, and one’s vision, but an attempt to retain a constant level of clast brightness between radiographs should be made. It is difﬁcult to obtain the same level of brightness and contrast on radiographs of different qualities, but if gray scale standards are used on each radiograph this problem is reduced. The image must be bright enough to deﬁne the outline of clasts and not so bright that the background remains indistinguishable from the clasts. Density slice (segmentation) A density slice of the image should be made to highlight clasts of a speciﬁc density, after the brightness of the image is satisfactory. The LUT tool is used to highlight (in red) objects of a speciﬁc density range of pixels. It is important to adjust the LUT such that most clasts are included, while background “noise” (i.e., non-clast marks of brightness) is excluded. Caution should be exercised with this step because only objects highlighted with the density slice will be analyzed. Make binary Once an acceptable density slice is achieved, convert the image into binary format. This is done using the “make binary” command, and pixels highlighted in red by the density slice, will now have a value of black (255). Image measurement Measurement options In order for the computerized image to physically represent the radiograph from which it was derived, the image needs to be calibrated for distance. It is simple to set the scale in NIH Image using the depth markers on the radiograph. In order to determine the scale, use the “select tool” in NIH Image to measure the number of pixels between two depth markers. Enter the scale in the “set scale” box, under the analyze menu. Adding a physical scale makes metric size measurements possible. NIH Image software provides at least 10 measurement options, including area of clast, x-y center, perimeter, length, major axis, minor axis, angle from horizontal, major axis to minor axis ratio (Fig. 2). Other options that should be selected when measuring clasts are “include interior holes” and “headings”. Including interior holes is especially important if tracings are being analyzed so that the entire clast is measured and not just the rim around it. Analyze particles When the processing is complete, the analyzed image should be printed and saved. The printout should be checked with the original radiograph to assess the quality of the results. An advantage to using the NIH program is that all analyzed particles are labeled with a number, so it is possible to identify errors and stray marks, such as depth and scale markers, and delete them from the spreadsheet before making statistical analyses. In addition to deletions, if a large number of clasts from the original radiograph were not identiﬁed in the image analysis, then one should start over with a better scanner, higher scanning resolution, adjust the brightness and contrast again, or use the tracing technique (Fig. 4).

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Hrouda F. 1982. Magnetic anisotropy of rocks and its application in geology and geophysics. Geophysical Surveys 5: 37–82. Jennings A.E. 1989. Late Quaternary history of Cumberland Sound, Bafﬁn Island, Arctic Canada. Ph.D. thesis, University of Colorado, Boulder, 319 pp. Jennings A.E. 1993. The Quaternary history of Cumberland Sound. Southeastern Bafﬁn Island: The Marine evidence. Geographie Phys. Quatern. 47: 21–42. Jennings A.E. and Weiner N. 1996. Environmental change in eastern Greenland during the last 1300 years: evidence from foraminifera and lithofacies in Nansen Fjord. 68 ◦ N. Holocene 6: 179–191. Kantzas A. 1995. Recent advances in the characterization of porous media using computer assisted tomography of X-rays. Canadian Well Logging Society 20: 99–111. Licht K.J., Dunbar N.W., Andrews J.T. and Jennings A.E. 1999. Distinguishing subglacial till and glacial marine diamictions in the western Ross Sea. Antarctica: Implications for a last glacial maximum grounding line. Geol. Soc. Am. Bull. 111: 91–103. Loﬁ J. and Weber O. 2001. SCOPIX-digital processing of X-ray images for the enhancement of sedimentary structures in undisturbed core slabs. Geo-mar. Lett. 20: 182–186. Migeon S., Weber O., Faugeres J.C. and Saint-Paul J. 1999. SCOPIX: A new X-ray imaging system for core analysis. Geo-mar. Lett. 18: 251–255. O’Cofaigh C.O. and Evans D.J.A. 2001. Deforming bed conditions associated with a major ice stream of the last British ice sheet. Geology 29: 795–798. Patchen D.C. 1968. The technique of X-ray radiography; some applications to geology. Proc. West Virginia Acad. Sci. 40: 247–254. Powell R.D. 1984. Glacimarine processes and inductive lithofacies modeling of ice shelf and tidewater glacier sediments based on Quaternary examples. Mar. Geol. 57: 1–52. Principato S.M. 2001. A multifaceted approach to understanding the depositional environment of diamicton units from the Iceland Shelf. Geol. Soc. of Am. Abstracts with Programs. 33, 6: A–315. Rasband W. 1996. NIH Image v. 1.60 manual, 102 pp. Software available to download on the website of the National Institute of Health, http://rsb.info.nih.gov/nih-image/. Smith L.M. and Andrews J.T. 2000. Sediment characteristics in iceberg dominated fjords. Kangerlussuaq region. East Greenland. Sed. Geol. 130: 11–25. Syvitski J.P.M. 1991. Principles, methods, and applications of particle size analysis. Cambridge University Press, London, 368 pp. Vorren T.O., Hald M., Edvardsen M. and Lind H.O.W. 1983. Glacigenic sediments and sedimentary environments on continental shelves; general principles with a case study from the Norwegian shelf. In: Ehlers J. (ed.), Glacial Deposits in North-West Europe. A.A. Balkema, Rotterdam, pp. 61–73.

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10. APPLICATION OF X-RAY RADIOGRAPHY AND DENSITOMETRY IN VARVE ANALYSIS

ANTTI E. K. OJALA ([email protected])

Geological Survey of Finland P.O. Box 96 FIN-02150, Espoo Finland Keywords: Lake sediments, Varves, X-ray radiography, X-ray densitometry, Digital image analysis, Line-scan, Lake Nautajärvi, Finland

Introduction The physical properties of soft sediment records in lakes and sea basins often provide valuable and sensitive proxies for the investigation of long- and short-term environmental ﬂuctuations (e.g., Segerström et al. (1984), Harrison and Digerfeldt (1993), Zolitschka (1998), Brauer et al. (1999)). Depending on the local settings and characteristic sediment features such as composition, texture and ﬁne-scale structure, these records potentially reﬂect the effects of external forcing on sedimentation. For this reason, it is important to develop a variety of methods that can routinely and repeatably be applied to sediment sequences. Once developed, tested and calibrated these methods would allow us to identify and study natural ﬂuctuations and therefore gain understanding of past environmental conditions. X-ray radiography is a rapid and non-destructive method for observing sediment composition and sedimentary structures with variable annual to centennial resolution (Calvert and Veevers 1962; Axelsson 1983). It has been widely applied in studies of soft sediment structures after Hamblin (1962) introduced the method in the examination of the minor structures of sandstones and siltstones (e.g., Calvert and Veevers (1962), Edmondson and Allison (1970), Axelsson and Händel (1972), Digerfeldt et al. (1975), Karlén (1976), Koivisto and Saarnisto (1978), Axelsson (1983), Bodbacka (1985), Britt et al. (1992), Algeo et al. (1994), Tiljander et al. (2002), Ojala and Francus (2002)). Based on Hamblin’s (1962) experience, Calvert and Veevert (1962) studied the minor structures of unconsolidated marine sediments from the Gulf of California, USA, among other localities. Edmondson and Allison (1970) made X-ray radiographs of laminated sediments from Lake Washington, USA, whereas Digerfeldt et al. (1975) applied the method in documenting predominately clayed varves from Lake Järlasjön, Sweden. Later, Karlén (1976) also applied X-radiography to laminated sediments from a lake fed by a mountain glacier in Northern Sweden. Koivisto and Saarnisto (1978) applied X-ray radiography to the study of thinly laminated sediments from Lake 187 P. Francus (ed.) 2004. Image Analysis, Sediments and Paleoenvironments. Kluwer Academic Publishers, Dordrecht, The Netherlands.

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Valkiajärvi, Finland, and Bodbacka (1985) investigated the rate of sediment accumulation in Lake Mälaren, eastern Sweden. In a review of varved lake sediments, Saarnisto (1986) even recommended the systematic use of the method in the study of laminated sediment sequences, emphasizing advantages in recording and documenting the number, thickness and structure of varves. In more recent studies, the X-ray radiography technique has provided very ﬁne-scale resolution, through the use of more systematic sediment preparation (e.g., sediment embedding with epoxy resin) and application of various digital image analysis techniques (e.g., Mehl and Merkt (1992), Algeo et al. (1994), von Rad et al. (1999), Saarinen and Petterson (2001), Tiljander et al. (2002), Ojala and Francus (2002)). The enhanced sample preparation, coupled with systematic use of digital image analysis of X-ray radiographs can provide a routine method for digitally documenting clastic-organic varve records (Ojala et al. 2000) with a high temporal resolution (Ojala and Saarinen 2002; Tiljander et al. 2002). Based on these investigations, easy storage of the varve chronology is facilitated and a valuable proxy record of environmental change — the quantitative components of varves — can be investigated more objectively, rapidly and with a seasonal-scale resolution. Using examples from Lake Nautajärvi, located in central Finland (Ojala and Francus 2002), this paper summarizes the method of X-ray densitometry and its robustness and biases, with emphasis on digital image analysis and automated counting and measuring of varved sequences. The clastic-organic type varves that have accumulated and been preserved in Lake Nautajärvi consist of two layers. A light layer of mineral material is transported into the basin during the spring ﬂoods, and a dark layer of organic material that is mainly a consequence of biological production within the lake. It accumulates during summer, autumn and winter (Renberg 1982; Ojala 2001). Methods It is often necessary to carefully identify the key elements of the research — the speciﬁc analytical data we want to extract and a convenient resolution we need to use — before an optimized analysis method is selected. This usually includes questions such as how rapid, how inexpensive, how repeatable and how reliable a research method can be applied. There is no simple answer to these questions and it needs to be decided in each case individually. However, it is possible to achieve similar results using different physical methods or variations in one principle method. As an example, in the digital image analysis of a 10-cm-long section of Lake Korttajärvi clastic-organic varves, Tiljander et al. (2002) found that relative gray-scale variations corresponded very well between surface images of scanned and polished epoxy-impregnated block and digitized X-ray radiographs. X-ray radiography is based on the penetration of X-rays emitted from an X-ray source through an object and their registration on photographic ﬁlm or by a digital X-ray imaging system (e.g., SCOPIX, Migeon et al. (1999)) placed behind the object (Fig. 1) (Bouma 1969). Depending on the thickness and composition of the object, the material absorbs a proportion of the emitted X-rays and allows the rest to transmit through. As a result, the density-based heterogeneities in the object will appear as contrast differences (dark and pale) on the X-ray ﬁlm (or a CCD camera, Migeon et al. (1999)). Therefore, Xray radiography is a particularly valuable method in sedimentology, when the material accumulated over time has considerable spatial variability in density. Moreover, depending

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189

Figure 1. A simpliﬁed set-up for passing X-ray beams through a varved sediment sample. The principal adjustments for X-ray radiography are crucial to make the beam pass perpendicularly through the varves. Modiﬁed from Algeo et al. (1994).

on the apparatus settings and sample size, both quantitative and qualitative information can be gained with annual to centennial resolution (e.g., Axelsson (1983), Mehl and Merkt (1992), Tiljander et al. (2002)). Acquisition of digital X-ray radiographs of clastic-organic varves The acquisition of comparable high-quality gray-scale images of ﬁnely varved sections is usually the most critical and time-consuming phase in digital image analysis. Owing to the simple 2-fold varve structure and considerable density difference between mineral-rich spring lamina and organic lamina deposited during the summer, autumn and winter, Xray radiography is an important and useful tool in documenting thin (<1 mm) varves of the clastic-organic type (Ojala et al. 2000). In practice, dense mineral-rich layers have a greater ability to absorb X-rays than organic layers, therefore showing a lighter shadow in the X-ray ﬁlm. The apparatus for varved sediment radiography in this study comprised typical X-ray equipment, a Philips constant potential MG102L, with a standard focal distance of 100 cm and a focal spot size of 0.4 × 0.4 mm. Depending on the nature, thickness and composition of the material under investigation, the exposure time of 1 to 3 minutes and the tube voltage values of 20 to 40 kV have been found suitable for the ﬁne focus of 6 mA (Tiljander et al. 2002). The values of 2 minutes and 30 kV that were applied in this study were deﬁned for this particular material and equipment and for the AGFA Structurix D7/DW X-ray ﬁlm type, and are therefore only suggestive. When X-ray equipment is conﬁgured for new material, it is recommended that multiple test samples are run with different adjustments in order to achieve the best possible resulting X-ray radiographs. On a general level, there are some principal technical adjustments to the set up of the X-ray equipment that should to be taken into account to improve the resolution and quality of the images (e.g., Axelsson (1983), Mehl and Merkt (1992), Algeo et al. (1994)).

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Figure 2. Outline of the steps in line-scan based X-ray densitometry.

A smaller local spot size results in X-ray images of greater detail. The distance between the X-ray source and the object should be as long as possible because of the conical nature of the X-ray beam. A longer distance results in a less divergent path of the beam through the sample and therefore also a more realistic shadow. In addition, the object should be placed as directly beneath the X-ray source as possible because the angle of exposure varies outwards. Therefore, a considerable loss of resolution might occur at the ends of the object if the beam does pass through varves perpendicularly. Moreover, a longer object-to-receptor distance will increase the magniﬁcation of the shadow and also the distortion of the image, but will decrease the sharpness of the shadow (Fig. 1). To overcome some of the difﬁculties, fresh and frozen sediment cores of Lake Nautajärvi were subsampled with aluminum trays and embedded using a modiﬁed method of wateracetone-epoxy exchange (Lamoureux 1994), described comprehensively by Tiljander et al. (2002). Embedded sediment samples and thin-sections made of them are often used as a source for ﬁne-scale images of sedimentary properties (e.g., Mehl and Merkt (1992), Zolitschka (1996), Tiljander et al. (2002)). Here, these overlapped and 11 × 1 × 1.5 cm impregnated blocks were then sliced to uniform thickness (2 mm) for X-ray radiography (Fig. 2). On a practical level, ca. 10 samples were X-rayed at the same time, and a calibration sample made of glass was used in order to produce comparable gray-scale images (Fig. 3).

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191

Figure 3. X-ray images of clastic-organic varves from Lake Nautajärvi representing the period from ca. AD 200 to 600 BC. Radiographs are taken from epoxy-embedded slabs of uniform 2-mm thickness. A calibration sample made of glass is seen in the right-hand corner.

X-ray ﬁlms were then processed using a standard combination of developer-ﬁxer liquids, which provides another opportunity to adjust the lightness and contrast of the ﬁnal Xray radiographs. Recent developments in digital X-ray imaging systems, i.e., SCOPIX (Migeon et al. 1999; Loﬁ and Weber 2001), offer additional advantages as they acquire high-resolution radiographs of sediment cores directly after X-rays pass through the sample and are captured by a CDD camera. Gray-scale images were subsequently digitized with a ﬂatbed scanner (Agfa DuoScanTM ) equipped with a transparent adapter, and using an optical resolution of 1000 dpi. Digitized images were stored as bitmap computer images (TIF) containing 256 shades of gray. As mentioned, the optimized resolution should be considered on a case-by-case basis depending on the amount and quality of speciﬁed analytical data that needs to be extracted from the images. Here, an optical resolution of 1000 dpi was used in the Lake Nautajärvi case study due to several factors. It was considered detailed enough for the study of seasonal variation because one varve of 0.67 mm thickness, which has been the average varve thickness in the Lake Nautajärvi sequence for almost the past 10 000 years (Ojala and Saarinen 2002), is then represented by 26 gray-scale data points (pixels). In addition, 1000 dpi was the best optical resolution of the ﬂatbed scanner, and the ﬁle size of the 1000 dpi resolution images was not beyond the capacity of the computer. Processing and calibration of gray-scale images The key issues in processing X-ray radiographs prior to digital image analysis are to improve the quality of the gray-scale images and to produce images that are comparable between different ﬁlms. As discussed by other authors, e.g., Saarinen and Petterson (2001),

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contrast and brightness adjustments are the most common type of image enhancements in sedimentological studies, but it is also possible to use various ﬁlters to decrease the noise present in images (e.g., Cooper (1997), Russ (1999)). Although caution is required not to decrease the amount of information the images potentially provide, speciﬁed ﬁlters can be very convenient tools in targeting digital image analysis to observe speciﬁc details of sedimentological features at high-resolution (e.g., Francus (1998)). In the Lake Nautajärvi study, 8 X-ray radiographs (each containing 10 images) covering the last approximately 10 000 years were calibrated to enhance comparison among images throughout the entire 6.6-metre-long sediment sequence. This was done by manually adjusting the brightness and contrast of the ﬁlms according to the glass calibration steps (Fig. 3) using Paint Shop Pro© Software. The procedure resulted in up to ±2% ﬂuctuations in relative densities between ﬁnal radiographs, which were considered satisfactory for this particular study. In addition, gray values of 0 were removed from the images for computing reasons, and then each of the 11-cm-long images was separated into an individual ﬁle for the digital image analysis. Digital image analysis The purpose of digital image analysis is to convert a visual image into a numerical format that allows investigators to obtain quantiﬁed and qualiﬁed information. For this procedure, we use computer-based image analysis programs to classify the different components of the computer bitmap images in order to study their spatial occurrence. When applied to sedimentology and to varve studies in particular, the principal aim is to discriminate the physical properties of these sequences such as the location and structure of varves and their seasonal components. Recent developments in digital image analysis have provided great potential to record varve structures with a high temporal resolution (e.g., Zolitschka (1996), Petterson et al. (1999), Ojala and Francus (2002), Saarinen and Petterson (2001), Tiljander et al. (2002)). These studies have demonstrated how the systematic use of digital image analysis techniques, for example in X-ray densitometry of clastic-organic varves (Tiljander et al. 2002), could provide a routine method for digitally recording long and continuous sections of varved sediments with a seasonal resolution. In addition, having the varve data in digital form allows easy storage of the results and instant statistical data treatment. Linescan image analysis and automated varve counting Single or multiple linescan analysis is perhaps the most common and simplest technique to investigate and record the number of varves, varve thickness variations and changes in within-varve components (e.g., Petterson et al. (1999), Tiljander et al. (2002)). A line plot is a standard tool in many of the commercial image analysis programs as well as in those available as public freeware, such as the NIH Image program developed at the U.S. National Institutes of Health (available on the Internet at http://rbs.info.nih.gov/nih-image/). A line plot creates a relative density proﬁle plot based on the current line selection. Many image analysis programs also allow the operator to perform multiple line selection or even a rectangular selection for densitometric measurements. In principle, a narrow window or

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193

a single line selection often yields more detailed and sharper results and contain more inherent variability in gray values that may not be real. A wider window, on the other hand, smoothes results considerably when averaged into a single density proﬁle (Zolitschka 1996). In the Lake Nautajärvi case study, the DendroScan image analysis program (VaremSanders and Campbell 1996) originally developed for tree-ring analysis was primarily applied to record and to analyze the varves. In principle, this software assembles all the gray values (pixels) along a manually deﬁned path (a line of black pixels = gray value 0) that is drawn perpendicular to the varve structure in the image. The program then identiﬁes boundaries based on major inﬂection points between the maximum and minimum grayscale values of the translated density signal, and also produces a linear array of density (Fig. 4). At this point these values are only relative X-ray densities, because they have not been calibrated against any real densities. Owing to the sharp boundary between ﬁne-grain organic matter laid down during the winter ice cover time and the onset of a more dense mineral-rich spring layer representing the beginning of a new “varve year”, DendroScan is a very useful tool in deﬁning boundaries of clastic-organic varves from the X-ray radiographs. A DendroScan output ﬁle (Fig. 4) consists of basic information on the number and location of varves (including varve thickness), and also of densities that, in this case, reﬂect the internal structure of varves (Tiljander et al. 2002). Some suggestions of how these relative X-ray density values can be calibrated against real data will be provided below. The possibility of using digital image analysis as an automated varve counting and recording system is often discussed among sedimentologists working with annually laminated sediments (e.g., Zolitschka (1996), Lotter and Lemcke (1999)). However, as shown in the example images from Lake Nautajärvi (Figs. 5 and 6, Table 1), not even the best quality varves can provide completely accurate results, as they have been accumulated in a naturally variable environment and always contain irregularities (Renberg 2000). Hence, these computerized techniques always require operator assistance, and applications such as line-scan image analysis can only be considered as semi-automated analytical methods. Here in the Lake Nautajärvi case study, stereomicroscopic examination of the fresh sediment surface and polished surface of the embedded sediment subsamples was performed concurrently with the study of original X-ray radiographs to verify the number and location of varves deﬁned by the DendroScan. Ultimately, the locations of the varve boundaries are therefore based on the subjective decisions of the operator. Examples from Lake Nautajärvi clastic-organic varves Studies of high-resolution archives that reﬂect seasonal variation, such as varved lake sediments, are fundamental for paleoenvironmental reconstructions. For example, physical characteristics of clastic-organic varves (with a varve thickness of 0.5 to 1.5 mm) that are deposited and preserved in many Finnish and Swedish lakes (Renberg 1982; Petterson et al. 1993; Ojala et al. 2000), such as Lake Nautajärvi, potentially reﬂect ﬂuctuations in environmental change. The rate of annual mineral matter inﬂux into Lake Nautajärvi depends on the magnitude of spring catchment’s runoff, the supply of ﬁne-grain mineral material from the catchment and the tendency of the catchment to erode. The record therefore reﬂects changes in local conditions, such as forest ﬁres and anthropogenic activities within the lake drainage area, as well as more regional climate ﬂuctuations. Winter and spring temperature and precipitation (snow/water) have an effect on the spring discharge of

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Figure 4. Demonstration run of the DendroScan program (Varem-Sanders and Campbell 1996) when applied to X-ray radiographs of clastic-organic varves. In the upper image, the original X-ray radiograph has been cut onto DendroScan output ﬁle afterwards. The lower image shows a program output ﬁle.

ANALYSIS OF X-RAY IMAGES OF VARVES

195

Figure 5. Two X-ray radiographs from 206 to 252 BC and 2592 to 2646 BC of Lake Nautajärvi sediment show that the visually striking components, mineral-rich and organic laminae, are far from perfect throughout the sequence for studies of automated line-scan image analysis. Therefore, it is also necessary to estimate the error in the varve chronology.

water, therefore contributing to the annual inﬂux of detrital matter into the lake. In addition, the annual accumulation of organic matter seems to be related to the summer characteristics of climate, namely the length and strength of the growing season (Ojala 2001). The line-scan based digital X-ray densitometry methodology provides several advantages in collecting physical characteristics of varved sections. The method facilitates easy storage of varve chronology and physical property measurements, allowing routine replication of the analyses on a varve-by-varve basis, and the re-evaluation and the cross-validation of the replicated analyses (Ojala 2001). For example, the 9900-year-long varve chronology of the Lake Nautajärvi sequence is based on replicated, digitally recorded varve analyses (Ojala and Saarinen 2002). This study illustrates that a good amount of operator time and patience needs to be put into the characterization and documentation of varved sequences and a varve-based chronology, including error estimates. Only then can we achieve results comparable to other records and characterize the quality of varve chronology (Lotter and Lemcke 1999; Ojala 2001). Cumulative varve chronology errors in the Lake Nautajärvi

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Figure 6. Each of the four routinely replicated DendroScan varve analyses (transects 1, 2, 3 and 4 represented by white lines on X-ray image) of the Nautajärvi section dated from 225 BC to 49 BC identiﬁes the dominant structures and composition of the varves. Curves on the left-hand side represent the average values of varve thickness (A), mean relative X-ray density (B) and minerogenic sum (C), with maximum and minimum ﬂuctuation shaded with gray (Ojala 2001).

ANALYSIS OF X-RAY IMAGES OF VARVES

197

Table 1. Pearson’s correlation coefﬁcients (r) of varve thickness, mean relative X-ray density and minerogenic sum (LS) for four individual varve analyses (transects 1, 2, 3 and 4) of a 10-cm-long section from Lake Nautajärvi dated to the period 225 BC to 49 BC (see also Fig. 6) (Ojala 2001). Varve thickness

transect 1

transect 2

transect 3

transect 4

transect 1

1

transect 2

0.775***

1

transect 3

0.5251**

0.5607**

1

transect 4

0.7384***

0.8153***

0.4725**

1

Minerogenic sum (LS)

transect 1

transect 2

transect 3

transect 4

transect 1

1

transect 2

0.9005***

1

transect 3

0.8516***

0.9021***

1

transect 4

0.9013***

0.9373***

0.8677***

1

Mean relative X-ray density

transect 1

transect 2

transect 3

transect 4

transect 1

1

transect 2

0.9368***

1

transect 3

0.9301***

0.9376***

1

transect 4

0.9297***

0.9613***

0.9504***

1

∗∗∗ p < 0.001, ∗∗ p < 0.01, N = 32

sequence were estimated to be ca. ±1%, but as seen in Figure 5, varves are not distinct enough for automated line-scan analysis everywhere in the sequence. By applying ﬁnescale digital image analysis it is possible to facilitate a more objective estimation of varve thickness, which then allows us to calculate the absolute accumulation of any substance or organism in the sedimentary basin per unit area and temporal unit (e.g., Renberg (1982), Segerström et al. (1984)). Moreover, quantitative analyses of the components of a varve can be studied and recorded more objectively, rapidly and with very ﬁne-scale resolution. These individual components are often identiﬁed as representing certain seasons or even short-term events within seasons (e.g., spring ﬂood intensity, autumn storm), and therefore solely inform about environmental change. Here, the statistical treatment of the output data from the DendroScan varve analysis (X-ray densitometry) provides calculations on several relative density parameters that reﬂect detrital mineral-rich and autochthonous organic matter content of each varve (Fig. 7, Table 2). Relative mean annual X-ray density (i.e., the average grey-scale value) indicates the general nature of the varves, whereas the minimum and maximum values illustrate the extreme material composition within each year. By deﬁning the area below and above the X-ray density curve and separated by varve boundaries, it is possible to reveal variables that better reﬂect the annual accumulation of different components — in this case mineral (LS) and organic matter (DS) — of varves. Increased values of LS and DS indicate a higher rate of annual mineral and organic matter deposition, respectively. Other statistical parameters such as the standard deviation, median and skewness may also provide characteristic information on varve structure. Table 2 shows the deviation in the annual parameters of a short section

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Figure 7. A line-scan digital image analysis of Lake Nautajärvi clastic-organic varves dated to ca. 100 BC. The density curve provides information on the seasonal accumulation of minerogenic/organic material when separated by varve boundaries and treated statistically (see Table 2). LS = an annual accumulation of mineral matter, DS = an annual accumulation of organic matter.

of the Lake Nautajärvi varves dating back to ca. 100 BC. Despite the very similar thickness between example varves 3 and 8, their composition reﬂects the accumulation of different seasonal components. Varve number 3 is composed of thicker organic lamina, whereas number 8 has higher maximum value and records a greater annual detrital matter yield. Materials and external processes forcing the sedimentation in lakes with clastic-organic varves are discussed in detail by Ojala (2002). Figure 4 illustrates one of the problems in acquiring and adjusting images for digital analysis of the varved sequences from the Lake Nautajärvi sequence. As we wish to use as broad a scale as possible in order to distinguish ﬁner sedimentological details (for example using enhanced contrast function that is built-in in the NIH-Image software), caution is required in image processing and calibrating not to exceed the scale applied for multiple images. Here, the values of the light mineral-rich layer (demo year 1974) extend beyond the gray-scale of the analysis. In their study of lakes Kassjön and Nylandsjön, Sweden, Petterson et al. (1993) highlighted that the physical properties of clastic-organic varves are very well preserved after deposition, although natural compaction of the unconsolidated sediments occurs at the top of the sequence. Only with very well deﬁned, conspicuous varves can automated digital image analysis provide entirely objective results (Petterson et al. 1993; Lotter and Lemcke 1999; Ojala 2001). Moreover, and as mentioned above, these computerized techniques of quantitative and qualitative analysis often require operator assistance to provide reliable

ANALYSIS OF X-RAY IMAGES OF VARVES

199

Table 2. The annual relative X-ray density data of the 12 example years from Figure 7.

Year

Thickness (mm)

Average

Median

1

0.79

150.1

161

216

82

3253

2

0.38

91.0

91

127

75

2202

3

0.56

113.6

112

153

73

3111

4

0.48

117.3

109

168

81

5

0.64

103.8

105

142

83

6

0.30

105.5

104

146

68

7

0.66

116.4

110.5

160

81

2942

1765

25.9

670.9

8

0.58

142.6

146

224

77

2586

3279

52.4

2740.6

max

min

DS

LS

stand. dev.

Variance

4652

42.8

1835.4

1365

14.7

214.9

2499

34.2

1167.3

2616

2229

33.2

1099.1

1704

1301

15.2

230.4

1794

1942

32.6

1065.9

9

0.46

103.9

102.5

137

76

2719

1871

21.3

454.6

10

0.43

100.8

95

134

74

2621

1714

21.0

440.9

11

0.46

99.8

92

144

70

2793

1797

24.9

620.5

12

0.69

93.4

90

133

67

2707

1847

21.8

473.6

results. If perfect information is required without any uncertainties, repetitive analyses are needed in order to calculate a mean sequence with conﬁdence limits. Importantly, such a repetition does provide valuable information about the reliability of the analysis method applied, but substantially increases the amount of work involved. However, as an example, a replicated analysis of the 10-cm-long section of X-ray radiograph of Lake Nautajärvi clastic-organic varves (dated 225 BC to 49 BC) (Ojala 2001) clearly indicated that even a single analysis provides relatively accurate information about the dominant structure of varves (Fig. 6, Table 1). All the parameters are highly correlated between transects 1, 2, 3 and 4. As discussed above, the concept of image calibration against actual densities is of great importance. The correspondence between relative X-ray density and dry bulk density (g cm−3 ) variations of the Lake Nautajärvi sequence between the present and 2000 BC is presented in Figure 8. There is a very good correspondence between these variables and only the ﬁnest details differ, mainly because of the very different sampling resolution of these two methods. Even the amplitudes of the records seem to be very comparable. Gray-scale values of 40 and 100 therefore roughly correspond to the dry bulk density values of 0.1 and 0.4 g cm−3 , respectively. Saarinen (personal communication) has successfully calibrated relative X-ray density measurements in Lake Lehmilampi, eastern Finland, against scanning electron microscope back-scattered images, claiming that both of these reﬂect changes in an annual deposition of detrital mineral matter. Moreover, as shown by Ojala and Francus (2002), varve analysis of back-scattered electron images also provides information on mineral grain size that is not available with X-ray densitometry. Summary X-ray radiography is a rapid and non-destructive method for observing sediment composition and sedimentary structures with variable annual to centennial resolution. However,

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Figure 8. Comparison between Nautajärvi annual mean relative X-ray density and dry bulk density of the sediment between the present and 2000 BC. Gray-scale values of 40 and 100 approximately correspond to the dry bulk density values of 0.1 and 0.4 g cm−3 , respectively.

in order to produce high-quality gray-scale images of ﬁnely laminated varved section, for example, some speciﬁc technical adjustments are required. It is recommended that a long focal distance is used and samples are as thin as possible and located directly underneath the X-ray source when analyzed. When combined with digital image analysis techniques (e.g., line-scan analysis), Xray densitometry is a very useful tool in digitally recording the number, composition and structure of varves with an annual to seasonal resolution. Line-scan digital image analysis is a fairly simple, rapid and easily repeated method for recording and studying the annual accumulation of seasonal components of clastic-organic varves from X-ray radiographs. It is possible to routinely apply these methods to study varved sequences that are thousands of years long, but operator assistance is always needed to verify the location of varve boundaries deﬁned by the program. However, in the application of these digital image analysis techniques, X-ray densitometry is one step further towards providing more objective quantitative analysis of varved sections, especially when calibrated against real densities. Acknowledgments I’m very grateful for the constructive and pertinent comments provided by Thomas Algeo, Michael Soreghan and Pierre Francus on the text. References Algeo T.J., Phillips M., Jaminski J. and Fenwick M. 1994. High-resolution X-radiography of laminated sediment cores. J. Sed. Res. 64 (A): 664–668. Axelsson V. 1983. The use of X-ray radiographic methods in studying sedimentary properties and rates of sediment accumulation. Hydrobiologia 103: 65–69. Axelsson V. and Händel S.K. 1972. X-radiography of unextruded sediment cores. GeograﬁskaAnnaler 54 (A): 34–37.

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Bodbacka L. 1985. Annually laminated sediments in two basins of Lake Mälaren (Lilla Ullfjärden and Stora Ullfjärden) studied by X-ray radiography. Geograﬁska Annaler 67 (A): 145–150. Bouma A.H. 1969. Methods for the Study of Sedimentary Structures. John Wiley and Sons, New York, 458 pp. Brauer A., Ednres C., Günter C., Litt T., Stebich M. and Negendank J.F.W. 1999. High resolution sediment and vegetation responses to Younger Dryas climate in varved lake sediments from Meerfelder Maar, Germany. Quat. Sci. Rev. 18: 321–329. Britt S.L., Bottjer D.J., Fischer A.G., Flocks J.G. and Gorsline D.S. 1992. X-radiography of horizontal core slabs: a method for greater retrieval of sediment core data. J. Sed. Petrol. 62: 718–721. Calvert S.E. and Veevers J.J. 1962. Minor structures of unconsolidated marine sediments revealed by X-radiography. Sedimentology 1: 287–295. Cooper M.C. 1997. The use of digital image analysis in the study of laminated sediments. J. Paleolim.19: 33–40. Digerfeldt G., Battarbee R.W. and Bengtsson L. 1975. Report of annually laminated sediment in Lake Järlesjön, Nacka, Stockholm. Geol. Foeren. Stockholm Foerh. 97: 29–40. Edmondson W.T. and Allison D.E. 1970. Recording densitometry of X-radiographs for the study of cryptic laminations in the sediment of Lake Washington. Limnol. Oceanogr. 15: 138–144. Francus P. 1998. An image-analysis technique to measure grain-size variation in thin sections of soft clastic sediments. Sed. Geol. 121: 289–298. Hamblin W.K. 1962. X-ray radiography in the study of structures in homogeneous sediments. J. Sed. Petrol. 32: 138–144. Harrison S.P. and Digerfeldt G. 1993. European lakes as palaeohydrological and palaeoclimatological indicators. Quat. Sci. Rev. 12: 233–248. Karlén W. 1976. Lacustrine sediments and tree-limit variations as indicators of Holocene climatic ﬂuctuations in Lappland, Northern Sweden. Geograﬁska Annaler 58 (A): 1–34. Koivisto E. and Saarnisto M. 1978. Conventional radiography, xeroradiography, tomography, and contrast enhancement in the study of laminated sediments. Preliminary report. Geograﬁska Annaler 60 (A): 55–61. Lamoureux S.F. 1994. Embedding unfrozen lake sediments for thin section preparation. J. Paleolim. 10: 141–146. Loﬁ J. and Weber O. 2001. SCOPIX — digital processing of X-ray images for the enhancement of sedimentary structures in undisturbed core slabs. Geo-Mar. Lett. 20: 182–186. Lotter A.F. and Lemcke G. 1999. Methods for preparing and counting biochemical varves. Boreas 28: 243–252. Mehl J. and Merkt J. 1992. X-ray radiography applied to laminated lake sediments. Geological Survey of Finland, Special Paper 14: 77–85. Migeon S., Weber O., Faugeres J.-C. and Saint-Paul J. 1999. SCOPIX: a new X-ray imaging system for core analysis. Geo-Mar. Lett. 18: 251–255. Ojala A.E.K. 2001. Varved lake sediments in southern and central Finland: long varve chronologies as a basis for Holocene Paleoenvironmental Reconstructions. Geological Survey of Finland, Miscellaneous Publications, Academic dissertation, 41 pp. Ojala A.E.K. 2002. Climate reconstruction from Finnish laminated lake sediments: “Palaeohydrological changes in central southern Finland detected through a 10,000 yrs long record of clastic-organic varves in Lake Nautajärvi”. 1st HOLIVAR Workshop, Lammi. Geol. Surv. Finland, Misc. Publ., pp. 87–91. Ojala A.E.K., Saarinen T. and Salonen V.-P. 2000. Preconditions for the formation of annually laminated lake sediments in southern and central Finland. Boreal Env. Res. 5: 243–255. Ojala A.E.K. and Francus P. 2002. X-ray densitometry vs. BSE-image analysis of thin-sections: a comparative study of varved sediments of Lake Nautajärvi, Finland. Boreas 31: 57–64.

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Ojala A.E.K. and Saarinen T. 2002. Paleosecular variation of the earth’s magnetic ﬁeld during the last 10,000 yrs based on an annually laminated sediment of Lake Nautajärvi, central Finland. The Holocene 12: 393–402. Petterson G., Renberg I., Geladi P., Lindberg A. and Lindgren F. 1993. Spatial uniformity of sediment accumulation in varved lake sediments in northern Sweden. J. Paleolim. 9: 195–208. Petterson G., Odgaard B.V. and Renberg I. 1999. Image analysis as a method to quantify sediment components. J. Paleolim. 22: 443–455. von Rad U., Schaaf M., Michels K.H., Schulz H., Berger W.H. and Sirocko F. 1999. A 5000-yr record of climate change in varved sediments from the oxygen minimum of Pakistan, Northeastern Arabian Sea. Quat. Res. 51: 39–53. Renberg I. 1982. Varved lake sediments — geochronological records of the Holocene. Geologiska Föreningens i Stockholm Förhandlingar 104: 275–279. Renberg I. 2000. Lake sediments as environmental archieves. In: Sandgren P. (ed.), Environmental chances in Fennoscandia during the Late Quaternary. LUNDQUA Report 37, pp. 90–95. Russ J.C. 1999. The Image Processing Handbook. CRC Press (3rd ed.) Boca Raton, 771 pp. Saarinen T. and Petterson G. 2001. Image analysis techniques. In: Last W.M. and Smol J.P. (eds), Tracking Environmental Change Using Lake Sediments: Physical and Geochemical Methods. Kluwer Academic Publishers, Dordrecht, pp. 23–39. Saarnisto M. 1986. Annually laminated lake sediments. In: Berglund B.E. (ed.), Handbook of Holocene Palaeoecology and Palaeohydrology. John Wiley and Sons Ltd, Chichester, pp. 343–370. Segerström U., Renberg I. and Wallin J.-E. 1984. Annual sediment accumulation and land use history; investigations of varved lake sediments. Verh. Int. Ver. Limnol. 22: 1396–1403. Tiljander M., Ojala A.E.K., Saarinen T. and Snowball I.F. 2002. Documentation of the physical properties of annually laminated (varved) sediments at a sub-annual resolution and their environmental interpretation. Quat. Int. 88: 5–12. Varem-Sanders T.M.L. and Campbell I.D. 1996. Dendroscan: a tree-ring width and density measurement system. Special report 10, Canadian Forest Service, Northern Forestry Centre. UBC Press, Vancouver, 131 pp. Zolitschka B. 1996. Image analysis and microscopic investigation of annually laminated lake sediments from Fayatteville Green Lake (NY, USA) Lake C2 (NWT, Canada) and Holzmaar (Germany): a comparison. In: Kemp A.E.S. (ed.), Palaeoclimatology and Palaeoceanography from Laminated Sediments. The Geological Society London, Special Publication 116, pp. 49–55. Zolitschka B. 1998. A 14,000 year sediment yield record from western Germany based on annually laminated lake sediments. Geomorphology 22: 1–17.

11. PROCESSING BACKSCATTERED ELECTRON DIGITAL IMAGES OF THIN SECTION

MICHAEL J. SOREGHAN ([email protected])

School of Geology and Geophysics Sarkeys Energy Center 100 E. Boyd St. University of Oklahoma Norman, OK 73019 USA PIERRE FRANCUS ([email protected])

Climate System Research Center Department of Geosciences University of Massachusetts Amherst, MA 01003-9297 USA Currently at INRS - Eau, Terre et Environnement 490 rue de la Couronne, Qu ébec (QC) G1K 9A9 Canada Keywords: Backscattered electron microscopy, Paleoenvironment, Paleoclimate, Methods, Image analysis, Grain size, Loessite, Textural analysis

Introduction Image analysis has developed over the last decade as an extremely useful tool in the interpretation of sedimentary rocks and sediments (e.g., Starkey and Samantaray (1994), Krinsley et al. (1998), Anselmetti et al. (1998), Francus and Karabanov (2000)). Rocks or impregnated sediment from unconsolidated cores can be imaged using backscattered electron (BSE) microscopy. Typically, these images are interpreted in a qualitative manner, but image analysis provides means to quantify compositional, structural or textural information. Indeed, image analysis takes full advantage of some properties of BSE images, such as high phase contrast and low overlapping of the elements, in order to quantify characteristics of the sediment, which is otherwise difﬁcult using regular petrographic images. Another main advantage of the method is that such measurements can be performed on samples that are not accessible with classical analytical techniques. Unlike bulk analysis, the researcher has 203 P. Francus (ed.) 2004. Image Analysis, Sediments and Paleoenvironments. Kluwer Academic Publishers, Dordrecht, The Netherlands.

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more control on the sample to be analyzed, because it is possible to “see” what is measured. For instance, single sedimentary events can be measured without the risk of contamination of the surrounding material (Francus et al. 2002b). Further, it is also possible to analyze the size, structure or texture of selected elements within a sedimentary facies, such as the biogenic fraction in a consolidated rock. A number of studies have illustrated the methods of BSE microscopy for diagenetic and provenance (modal analysis) studies of sedimentary deposits (e.g., Krinsley et al. (1998), Anselmetti et al. (1998)), but image analysis studies of BSE images for paleoclimatic and paleoenvironmental interpretations are less common (Francus 1998; Saarinen and Petterson 2001; Francus et al. 2002b). One problem with image analysis studies of geologic samples is that the materials are more difﬁcult to work with compared to many biological and medical samples, for which image analysis is more widely used. Geologic materials are generally less homogenous than biologic or medical samples and no standard procedures for analysis has yet been developed. Nevertheless, BSE microscopy image analysis holds great potential in paleoclimatic and paleoenvironmental studies of recent and ancient sediments and can be used for both, continuous (e.g., laminae thickness or type), and discrete (e.g., textural or compositional trends at sampled intervals) data. The purpose of this chapter is to outline imaging methods and techniques speciﬁc to the use of BSE images in the study of sedimentary deposits for paleoenvironmental/paleoclimatic reconstructions. In particular, acquiring BSE images requires special methodology not necessary with other imaging techniques. Then, we present one case example, which illustrates a speciﬁc application of BSE microscopy for paleoenvironmental reconstruction. This case study and previous work by Francus (1998) and Francus et al. (2002b) illustrate some of the advantages and disadvantages of using BSE images analysis, which are summarized in the discussion section of this chapter. Finally, the last section provides some recommendations regarding future studies using these methods. Image acquisition General principles of image analysis have been outlined in chapter 2, 3 and 4 of the current volume. They also apply in the case of BSE imagery. BSE imagery The nature of BSE images is described in details in electron microscopy textbooks (e.g., Goldstein et al. (1992)). BSE images can be produced by Scanning Electron Microscopes (SEM), Environmental Scanning Electron Microscopes (ESEM), and microprobes. The working principle of these three devices is identical, even if slight differences exist in acquisition parameters. In brief, electrons emitted from an electron gun and focused using electromagnetic lenses cause the emission of several signals when they interact with a specimen. Among them, some elastically scattered electrons are eventually directed back out of the specimen as backscattered electrons (Krinsley et al., 1998). The backscattered coefﬁcient, η, or the number of backscattered electrons related to the number of incident electrons, is strongly dependent on the mean atomic number of the specimen (see Fig. 2.11 in Reed (1996)). On BSE images, mineral grains such as iron sulﬁdes and oxides,

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carbonates, quartz, and biogenic silica appear decreasingly bright. Organic matter and epoxy embedding media appear dark and because of this marked contrast, BSE images of sedimentary rocks can be used as a map of porosity (Kemp et al. 2001). The production of backscattered electrons is the result of scattering of the incoming electrons with the target. As a consequence, an effective 3-dimensional volume (interaction volume) can be deﬁned, the dimension of which is dependent on several factors (beam voltage, average mean atomic number (z) of the target). In a low density low-atomic-number target, the depth of this volume is on the order of ∼2 µm for acceleration voltage of about 20 KV (Reed 1996; Goldstein et al. 1992, and references herein). This implies that the probability of overlapping objects is small compared to optical transmitted light microscopy, which integrates a 30 µm thick volume of sediment (Francus 1998). Because of this characteristic, and the intensity contrast between the resin and the specimen components, BSE images are very suitable for image analysis work. Sample preparation As for any work involving image analysis, high quality images begin with good sample preparation. Depending on whether the subject material is lithiﬁed or unconsolidated, the initial steps of sample preparation will vary; steps for preparing thin sections or rounds from lithiﬁed or poorly consolidated sediment have been outlined in a number of papers (von Merkt 1971; Murphy 1986; Camuti and McGuirre 1999; Francus and Asikainen 2001; Kemp et al. 2001). Before acquiring a BSE image, it is useful to obtain an enlarged hard copy of the specimen to locate each photograph taken hereafter, especially when a transect is needed along a sedimentary facies or when depth information is required. This also facilitates the ﬁnding of the Region of Interest (ROI) once the sample is in the instrument. For thin sections, we recommend the use of a ﬂatbed scanner with transparencies capability to capture an image of the whole thin section (Francus et al. 2002a; De Keyser 1999), whereas a regular ﬂatbed scanner or binocular microscope can be employed to image thick specimens. In newer digitally controlled microscopes, it is possible to upload the coordinates of the ROI electronically. BSE images can be obtained from unpolished samples. However, the presence of a good polish is critical, particularly if textural parameters (size, shape) are to be measured. Indeed, on unpolished samples, the backscattered coefﬁcient, η, does not solely control the signal intensity (brightness) of the specimen, but the micro-topography of the sample surface also affects the signal (Reed 1996). To illustrate the necessity of using polished sections, we took a digital BSE picture of an unpolished and subsequently polished ROI (Fig. 1). From these, we obtained binary images and basic measurements using identical image analysis procedure (Fig. 1; Table 1). From the resultant binary images, it is evident that the polished section contains less noise within the sedimentary matrix and within the large detrital grains. Grain boundaries are sharper, and more ﬁne details that were apparently indistinguishable from noise in the unpolished section are visible in the matrix. Also, note that the wall of the diatom on the unpolished image (Fig. 1C) is discontinuous and thinner relative to the polished section (Fig. 1D). For older microscopes having detectors off the axis, the difference in quality between the two samples is explained in Figure 2. On unpolished or poorly polished samples, grains or features in the sedimentary matrix form

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Figure 1. BSE images of unpolished (A) and polished specimens (B). Identical standard imaging procedures have been applied to produce the corresponding binary images (C and D). Laguna del Hornillo, Central Spain, Holocene sediments. Scale bar is 200 µm and image resolution is 1 pixel/µm (Courtesy J. Vegas). Table 1. Measurements obtained from images C. and D. of Figure 1 P%2 mean Ri 3

mean D0 1

median D0

C. unpolished 10.598 µm

6.687 µm

15.206 µm 5.537 µm

4.06

0.478

9.135 µm

7.237 µm

10.231 µm 5.055 µm 157.435 µm 6.35

0.476

Images

D. polished

Std Dev

Mode D0

Max D0 147.35 µm

1 D is the equivalent disk diameter such as computed in Francus (1998). Polishing the section allows detection of 0

more small grains (smaller mode), but also increases the size of large grains (Max D0 and median D0 are both larger). 2 P% is the phase percentage (Francus 1998). The polished section contains more objects. 3 R = A/L2 . A = surface area measured by counting enclosed pixels; L = long axis of the best ﬁtting ellipse. R is a i i

shape index = 1 for spheres. In this case, polishing does not modify the mean shape of the grains. The effect of polishing the thin section on measurements is signiﬁcant but seems to be complex and needs further testing.

irregular topographic highs (Fig. 2). With a detector located to one side of the specimen, the side of the hill directly facing the detectors appears brighter (Reed 1996) because it has a more favorable detection geometry. Due to its angle, it also has a greater emission area (larger BSE production) compared to a surface normal to the incident beam. On the other hand, the BSE emitted on the opposite side of the hill remain undetected resulting in a shadow effect. This highlights the necessity of polishing prior to imaging; working

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Electron beam

Electron beam

BSE detector

BSE detector

BSE (A.)

BSE

BSE

BSE (B.)

Figure 2. Backscattered electron along a ﬂat sample with an off-axis detector (A). Along a topographic “hill” (B), the slope facing the detector is brighter, while the opposite one is shadowed. Redrawn from Reed (1996).

down to a grit size of 1 µm or less, although the ﬁnal hand-polishing stage will depend on sample composition. With newer microscopes or microprobes having quadrant or annular BSE detector conﬁguration, the issue of irregular topography is quite different, although less critical. The sides of the hill have a higher BSE production because their surface area is relatively larger, triggering signiﬁcant “spurious contrast” (Goldstein et al. 1992). However, in either case, unpolished samples are also more susceptible to charging effect (Goldstein et al. 1992). Polished sections are subsequently coated with a 100–150 Å layer of carbon to ensure sufﬁcient conductivity to prevent the charging of the sample, as sedimentary samples are poorly conductive material. For thin sections, we found that a customized sample holder signiﬁcantly improved image quality (Fig. 3) in comparison with simply ﬁxing the glass on a 1 cm diameter aluminum stub because conductivity is ensured more equally across the surface of the specimen. For slabs, it is more difﬁcult to customize a sample holder because slabs can be of variable shape and size. Another problem in using slabs is that good electrical conductivity between the specimen and the stub is harder to achieve because of the sharp edges of the slabs. This is not a problem with ESEM, as coating is not necessary with this type of microscope. Image intensity As with other image analysis applications, evaluating and optimizing the acquisition system’s settings (contrast, brightness, and magniﬁcation) for the speciﬁc scientiﬁc question(s) to be answered is critical. In the case of BSE imaging, image intensity (or gray level value) depends on several factors. Production of BSE is proportional to the primary electron beam current. Higher current equates to higher signal to noise ratio and better phase contrast, but with a decreased resolution (Goldstein et al. 1992). As most studies of sediment in thin section do not require high magniﬁcation, resolution can be compromised in favor of greater

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signal. A wider spot size produces a brighter image. The working distance between sample and detector is also important. A shallow working distance produces a brighter image, due to greater detector efﬁciency; a long working distance, however, incorporates a wider surface area at low magniﬁcation. Further, at low magniﬁcation it is more likely that image deformation will occur due to lens aberrations. The ﬁnal adjustments to enhance image quality are made via signal processing. Typically, by adjusting contrast and brightness controls, the direct current (DC) level and alternative current (AC) amplitude components of the signal are set up after collection (Goldstein et al. 1992). In most modern SEMs, a digital value can be attributed to contrast and brightness, and be noted as metadata. The parameters mentioned above are easy to control and can be strictly maintained between working sessions. Unfortunately, additional factors that are difﬁcult to control inﬂuence the images intensity values and are discussed in Lamoureux and Bollmann (this volume). For example, variation in the supply of electricity may be visible on slow scan mode image acquisition, pointing out the need for a stabilized power supply to the microscope. Slight modiﬁcations of the electron gun and column alignment, as well as an aging cathode and column/aperture contamination are also potential sources of variation in intensities in the acquired images. This highlights the need for some sort of calibration material to be imaged at the beginning and end of a working session to ensure comparability of the results. Pieces of reference material (e.g., resin, glass, quartz, calcite, iron oxides) can be embedded in the edge of the sample holder (Fig. 3), and be used in the same way a color chart is used in core photography or density wedges are used in X-ray calibration. Finally, it is important to note that the ideal settings for one device do not compare with another instrument, because of differences in the type of electron source, sensitivity of the detectors, the type of vacuum, and the geometry of the column and the chamber (more details in Lamoureux and Bollmann (this volume)).

Figure 3. Photograph of a thin section holder speciﬁcally designed for BSE imagery. Four equally spread out screws ensure an equal conductivity on the surface of the thin section and allow for easy sample change procedure. Size of the holder is 7.5 × 2 cm.

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Image acquisition In most SEMs, the digital signal is acquired directly from the TV scan interfaced directly to a digital frame grabber. Images acquired in this manner are inherently noisy, and of limited resolution. Better images are obtained by the integration of several scans or frame averaging that improves signiﬁcantly the signal-to-noise ratio (Krinsley et al. 1998). In most recent microscopes, digital images acquisition systems allow the acquisition of good quality images, typically 1280 × 960 pixels. If the results are not satisfactory, especially with older SEMs, an external scanning interface unit (SIU) can be used. External scanning control is provided by routing out the output from the microscope’s scan generator through the SIU to the microscope’s scan coil ampliﬁers. This is designed to switch all the required scan signals from the inside microscope to those provided by the SIU. These devices allow for higher digital quality with resolutions up to 32000×32000 pixels with considerably greater depth (12 or 16 bits, i.e., 212 or 216 gray level values). Digital images of a calibration grid are used to check the quality of the image, e.g., the amount of electronic noise, “squareness” of pixels, or presence of systematic disturbances (Lamoureux and Bollmann, this volume; Nederbragt et al., this volume). Image processing Once an image is acquired, subsequent processing includes four primary steps: calibration, ﬁltering, segmentation and thresholding. The previous chapters as well as many manuals and papers describe these operations in great detail (e.g., Russ (1999)). The following section provides a general outline of some of the available techniques and procedures that are particularly applicable to textural analysis as it pertains to BSE microscopy of sediments and sedimentary rocks. Calibration A set of digital images of a calibration grid is acquired for every magniﬁcation that will be used in further work to check the accuracy of the scale bar provided by the SEM. One set is necessary for every working distance used, as the size of the ﬁeld of view will be slightly different. An intentionally blurred photograph of ﬂat uniform metal part (Fig. 4) can be used to correct for uneven illumination. Procedures for spatial calibration and correction for uneven illumination are outlined in Nederbragt et al. (this volume). Filtering BSE image ﬁltering is a process that increases the signal-to-noise ratio within an image in order to enhance regions of interest (e.g., grains). Sources of noise include: 1) random electronic instrument noise, and errors due to the digitizing process (scanning); 2) uneven “illumination” caused by beam shape and alignment, instrument charging, or detector orientation, 3) inherent variation in geologic substance, and 4) non-normal orientation or a poorly polished sample. Good acquisition and calibration practices described in the previous sections can eliminate most noise due to types 1), 2), and 4). However, it may

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Figure 4. BSE Image of the metal stage (A.) is processed, and then the resulting image (B.) is used to capture the repartition of light in the ﬁeld of view and can be used for image correction as described in Nederbragt et al. (this volume). Scale bar is 250 µm and image resolution is 1 pixel/µm. In this case, the Photoshop magic wand tool is used to select black patches. The selection is then replaced with 40% gray, and then a Gaussian blur (40 pixels radius) is applied. The lower panel (C.) displays the intensity proﬁle for image B., each point of the plot being the average grey level value of each pixel column in image B. Uneven illumination is in this case very small (2 levels of gray values).

still be necessary to deal with noise inherent to the geological samples viewed in BSE mode. Indeed, most geologic materials are inhomogeneous, even within single phases, so that some ﬁltering is almost always necessary to smooth regions that are presumably part of the same phase. It is important, however, to test and evaluate how each ﬁlter affects

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the image (Starkey and Samantaray 1991) and attempt to keep ﬁltering to a minimum, because ﬁltering changes the value of each pixel (the original data are altered), and so, theoretically, analyses and measurements of unﬁltered images would be best in order to obtained unbiased results. Of course, if the research objectives require measuring the natural inhomegeneity within a sample, ﬁltering is not appropriate. General ﬁltering techniques are described comprehensively in Russ (1999) and in Nederbragt et al. (this volume). For reasons detailed in Nederbragt et al. (this volume), we favor the use of median ﬁlters or hybrid median ﬁlters because they are efﬁcient in removing pixel scale noise. In addition, they have the advantage of not displacing or blurring distinct boundaries, so that the ﬁlters can be applied repeatedly (Huang et al. 1979; Russ 1999). Image segmentation and thresholding In terms of paleoenvironmental and paleoclimatic studies of sediments, segmentation and thresholding refers to the selection of speciﬁc mineral grains, or grains in total (relative to sediment matrix) so that the abundance, size and/or shape of the grains can be counted or measured. Segmentation may require the use of complex edge ﬁnding ﬁlters, which scan an image and look for abrupt changes in gray level values that deﬁne the boundary between two phases (Russ 1999). These ﬁlters (such as Sobel, Kirsch or Chei) are commonly available in image processing software packages, or as third party plug-ins, and are commonly used in conjunction with other ﬁlters or processing steps. The speciﬁc ﬁlter chosen as an edge ﬁnding ﬁlter is dependent upon the nature of the image itself and often requires some trial and error. Russ (1999) illustrated a number of examples of different edge ﬁnding techniques that can be tested on a subject image. One issue speciﬁc to BSE microscopy is that, dependent on the polish of the sample, the edge of the grain may exhibit a different gray level relative to the interior of the grain. This difference in gray level between the grain and rim results from variation of surface detector angle caused by beveling at the grain edge. Accordingly, the edge ﬁnding ﬁlter may accentuate the rim at the boundary between the grain interior and the beveled edge and not the grain boundary itself, which will affect the subsequent measurement of the grain (Fig. 5). Thresholding can be accomplished in a number of different ways (Nederbragt et al., this volume), but the main goal is to produce an image easily utilized for measurements or characterization. Because the signal from the detector is proportional to the average atomic number of the scanned phase, the resultant gray level from the image can be used to distinguish speciﬁc mineral phases (Pye 1984; Krinsley et al. 1998). If the image contained a perfect, homogenous substance with no attendant instrumental noise, then the speciﬁc gray value of the grain in the image could be selected and changed to black pixels, making thresholding quite straightforward. However, in real cases, variations occur in gray levels within a phase of interest, either because of natural variation of the substance, image noise, variation in sample-beam distance or angle, or a combination of these. Variation in intensity even within a single phase requires that a range of gray levels is selected to encompass the segmented region prior to thresholding. Therefore, the cumulative histogram of BSE image’s gray levels is typically analyzed, either qualitatively or quantitatively to determine the thresholding level or range. One or more modes in the histogram will generally represent the gray levels of the most common phase(s) within the image (Fig. 6). If the scope of the study requires only that sediment grains are segmented relative to matrix, then thresholding

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Figure 5. Edge ﬁnding ﬁlter (Kirsch Filter) applied to two BSE images of lithiﬁed siltstone. The top left image is an original BSE image and the top right image is the same image after the edge ﬁnding ﬁlter is applied. Note that the ﬁlter delineates most of the grain boundaries very well. The bottom left image is another original BSE image of a lithiﬁed siltstone, but with a poor polish. The box represents the enlarged view at bottom right in which the same edge ﬁnding ﬁlter was applied. Note that the grains with beveled edges, because of the poor polish, are not as well resolved, with boundaries both at the beveled edge and at the edge of the grain. All images except lower left are 250 µm across; lower left image is 125 µm across.

requires selecting the gray level at some deﬁned point between the mode represented by the grains and the mode represented by the matrix (Fig. 6) and converting all pixels outside the range to black. However, if the scope of the study requires speciﬁc phases to be identiﬁed (e.g., quartz and feldspar, Fig. 6), then thresholding requires selecting only the gray level values to a consistently deﬁned point on either side of the mode represented by that phase. Besides thresholding based on brightness (gray levels) alone, segmentation and thresholding can in some cases be accomplished through analysis of the textural and shape differences between regions of interest and the background. One obvious case is the comparison of sedimentary matrix to clastic grains; the matrix will exhibit high frequency variation in gray level relative to grain interiors. In this case, the difference in texture would

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Figure 6. BSE image of a lithiﬁed siltstone in which quartz is the dominant phase (dark gray grains) of the framework grains. The image also contains a number of feldspar grains (light gray grains). The histogram depicts the cumulative distribution of gray levels of the entire image from 0 (black) to 255 (white). The largest mode reﬂects the interior of the quartz grains, although individual pixels with the same gray level value as quartz may also reside within the regions of matrix. The secondary mode reﬂects the feldspar grains. Image is 250 µm across. Histogram is a screen capture from Adobe Photoshop .

allow for segmentation. Another example is the segmentation of quartz in the presence of dolomite. Both quartz and dolomite exhibit nearly identical atomic intensities, and therefore appear on BSE images with nearly the same gray level values. However, because of their relative differences in hardness, the quartz grains are typically better polished and therefore exhibit less high frequency variation in gray levels within grain interiors compared to dolomite (Fig. 7). By using ﬁlters that accentuate the differences in texture, the quartz grains can be segmented relative to the dolomite, allowing for subsequent thresholding (Fig. 7). Differentiation of phases of similar atomic densities but differing composition can be easily performed by Energy Dispersive Spectroscopy (EDS) mapping as well, which is available in most recent SEMs and Wavelength Dispersive Spectroscopy (WDS) mapping on microprobes, but these methods involve higher costs due to the longer machine time use. Image measurement Image measurement is comprehensively described in chapter 4. Methods of measuring “grain size” from thin sections have been discussed and investigated in a number of studies (e.g., Krumbein (1935), Friedman (1962), Harrell and Ericksson (1979), Van den Berg et al. (2002)). BSE microscopy has been used for granulometric studies because it resolves individual grains and allows for quantifying their morphology. However, two factors particular to these methods must be considered. First, with standard BSE detectors, the smallest grains that can be detected will always be ∼2 µm, because of the size of the interaction volume of the backscattered electrons. Although, with careful set-up, some BSE detectors can be set to pass only the electrons that have the highest energy, and thus reach a much higher resolution (Goldstein et al. 1992). In practice, most detector do not allow high resolution work. In

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Figure 7. BSE image (left) of unconsolidated silt grains with certain phases labeled: qtz = quartz; dol = dolomite. Note that the quartz and dolomite grains exhibit almost the same gray level value, however, the quartz is uniform in texture relative to the dolomite. This reﬂects in part the better polish on the surface of the quartz grains relative to the dolomite grains. Image on right represents a ﬁltered image that was subsequently thresholded so that the quartz grains were segmented, but dolomite grains are mostly eliminated. A Haralick ﬁlter was employed followed by an edge ﬁnding ﬁlter to produce the thresholded image, which was then cleaned up using a median hybrid ﬁlter. Image is 314 µm across.

addition, setting up the microscope for high resolution in BSE mode is very restricting. At 200× magniﬁcation, a 2 µm particle is represented by 15 pixels for a 1280 × 960 pixels wide image (1 pixel = 0.5 µm). Therefore, attempting to resolve particles smaller than 15 pixels on an image is contra productive. The second factor to consider in working with BSE images is that the sample needs to be representative of the sedimentary fabric. In laminated or varved sediments, Francus et al. (2002b) showed that measurements can be signiﬁcantly repeated from 2 sediment cores separated by 100 meters. The number of grains in single images of lake and marine sediments can be greater than 2000. However, in other settings, like sandy or loess deposits where the objects of interest are less numerous, it might be necessary to develop a sampling strategy (Buchter et al. 1994) that allows capture of the variability of the sedimentary facies, as we outline in the upcoming case study. Case study: grain size analysis of upper Paleozoic loessites Introduction Grain size analysis is one key proxy used for paleoclimatic analysis of loess-paleosol sequences in the Chinese Loess Plateau. Grain size analysis of the quartz fraction in particular (Porter and An 1995; Xiao et al. 1995) has been used as a proxy for variations in wind strengths within these loess-paleosol successions because quartz is less susceptible to diagenetic changes during soil forming processes. To date, however, such analyses have been applied only to Plio-Pleistocene loess successions, primarily because of the lack of well studied pre-Pleistocene loess sequences and because of difﬁculties involved with grain size measurements of lithiﬁed loess (loessite). The goal of this case study is to illustrate

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how combined BSE microscopy and image analysis can be applied to document grain size variations within very ancient loessite successions. Similar to the Quaternary, the Late Paleozoic is well known as a time of signiﬁcant glaciation, marked at high (paleo)latitudes by widespread and unequivocal evidence for continental glaciers, and at low latitudes by pervasive and classic Pennsylvanian “cyclothems” typically consisting of intercalated marine and continental strata that record the repeated waxing and waning of the Gondwanan ice sheets (Crowell 1978; Veevers and Powell 1987). The glacial-interglacial climatic ﬂuctuations that drove glacioeustasy were also recorded in low latitudes of Pangea as fundamental shifts in depositional environments, reﬂecting changes between relatively arid glacial and more humid interglacial conditions (e.g., G. Soreghan (1994), (1997)). Within the Eagle basin (central Colorado, USA) thick successions of loessite (eolian silt) accumulated punctuated by numerous paleosol horizons (Johnson 1989; G. Soreghan et al. 1997). The Eagle basin was located in western equatorial Pangea during Late Pennsylvanian-Early Permian time (ca. 300 Ma). Pedologic, geochemical, and magnetic studies of these loessite-paleosol sequences indicate that the two depositional systems behaved much like that of the Quaternary Chinese Loess Plateau, reﬂecting probable glacialinterglacial ﬂuctuations that operated in western equatorial Pangea (G. Soreghan et al. 1997; 2002; Tramp 2000). In addition to “icehouse” conditions, however, the paleogeography of late Paleozoic Pangea has led many to suggest extreme seasonality and mega-monsoonal circulation patterns (e.g., Parrish (1993)). M. Soreghan et al. (2002) employed provenance analysis of several upper Paleozoic loessite deposits of the western U.S. to document apparent monsoonal circulation in western equatorial Pangea. Accordingly, loessite of late Paleozoic western Pangea potentially records the inﬂuence of both icehouse and monsoonal conditions, analogous to today. The following reﬂects our methodology for analysis of quartz grain size within loessite-paleosol couplets of these upper Paleozoic loessites in order to assess their temporal variation, and possible relation to atmospheric circulation (wind strength and variation) in western equatorial Pangea during late Paleozoic time. Methods The Colorado study section consists of over 700 m of loessite and interbedded paleosols comprising the Maroon Formation (Fig. 8). This unit has been previously investigated and interpreted as windblown silt (Johnson 1989); the unit has also been studied in terms of detailing a paleoclimatic record from combined rock-magnetic and sedimentologic analysis (G. Soreghan et al. 1997; Tramp 2000). The loessite is well lithiﬁed, and not easily disaggregated to allow standard grain size analysis. Accordingly, we utilized image analysis of backscattered electron images of the loessite to measure grain size characteristics of quartz grains. Initially, nine loessite-paleosol couplets, three each from the base, middle and top of the Maroon Formation section were targeted, in order to examine both shortterm (loesssite-paleosol) and long-term (through the entire formation) trends in quartz grain size (Moreland et al. 2002). Polished rounds of 5 to 9 samples were prepared for each of the nine couplets from each section. Polishing and sample preparation followed standard procedures, with a ﬁnal hand polishing using 0.25 µm diamond paste grit. BSE imaging was performed using a Cameca SX50 electron probe microanalyzer at the University of Oklahoma. Beam conditions were 20 kV acceleration and 10 nA sample current measured

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Figure 8. Location map and paleogeographic map of the Eagle Basin, showing the location of the loessite (Maroon Formation) sampled in this study. Note the inferred wind direction (northwesterlies). Modiﬁed from Tramp (2000).

at the Faraday cup. The acquisition parameters used with the Cameca SX50 high resolution BSE detector generate quality images at higher magniﬁcation yet with low current, which was necessary for these ﬁne grained sediments. During imaging, 8–12 digital images of each sample were acquired directly into 1024 × 1024 pixel arrays. Each image was then digitally analyzed and ﬁltered using Adobe Photoshop to highlight grain outlines of approximately 800 quartz grains per sample (80–100 grains per image); the processing steps are outlined below. We focused on quartz grains alone, owing to its resistance to chemical weathering that may have occurred in both pedogenic and diagenetic environments (cf., Porter and An (1995); Xiao et al. (1995)). In BSE mode, quartz grains can be identiﬁed as uniformly gray grains with smooth surfaces and their grain boundaries are generally distinct. A series of ﬁltering steps outlined below, however, were required to adequately segment quartz grains from both the matrix as well as other non-quartz grains. After an image (Fig. 9A) was imported into Adobe Photoshop a Laplacian ﬁlter (3 × 3 with a central value of +9 and surrounding values of −1) was applied to a copy of the image. This ﬁlter enhances contrast at edges of grains and has the added advantage of increasing the noise of the matrix relative to grain interiors (Fig. 9B), which allowed for better segmentation after additional processing. A Hybrid Median ﬁlter was then applied to the same copy of the image to further smooth the gray levels of the grain interiors relative to the matrix (Fig. 9C).

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The next step involves thresholding at a level to segment the quartz grains relative to other mineral phases that are brighter (more dense). By thresholding at a gray level less than the average gray level of these non-quartz grains, the quartz grains will be segmented. For this step we used a qualitative analysis of the histogram, and selected for thresholding the gray level value corresponding to the base of the quartz peak (Fig. 10). This value changed from image to image depending upon the relative proportion of matrix to grains as well as probable variations in image acquisition parameters. However, the thresholding value did not vary by more than 10%. Figure 9D depicts the resultant image after thresholding on the selected gray level value. Although the processing segmented quartz grains relative to most other non quartz grains, the resultant image contains abundant spurious pixels that require further processing. A second copy of the original image was then processed to better deﬁne the grain boundaries and to eliminate most matrix. A Haralick ﬁlter, which is an edge ﬁnding ﬁlter, was applied in order to deﬁne grain boundaries, regardless of the grain type (Fig. 9E). The resultant image was then smoothed through a hybrid median ﬁlter that was applied three times in succession. This median ﬁlter eliminates many of the spurious pixels within the regions of matrix, as well as along grain boundaries (Fig. 9F). Next, both processed images were superimposed, using a Boolean “AND”. This process examines the pixel value of both images at each x-y location, and if both images contain a pixel at that location that is “on,” or black, then the pixel is left black. However, if either or both images contain a pixel that is “off,” or white at that location, then the pixel is turned white. As a result, the quartz grains, which were thresholded in both images stay highlighted whereas non-quartz grains are eliminated because they are not thresholded in the ﬁrst image (Fig. 9G). The boundaries of the grains are controlled mainly by the second ﬁltered image, which more accurately reﬂects the cross-sectional area of the grain. Finally, the superimposed image was ﬁltered using an Opening ﬁlter and a Hybrid Median ﬁlter, both of which further eliminate spurious pixels (Fig. 9H). The fully processed and ﬁltered image reasonably segments only quartz grains and outlines their grain boundaries. However, there are some caveats and additional complications in terms of the use of the resultant image for grain size analysis. First, very small quartz grains (<4 µm) are not well imaged and were sometimes eliminated by the processing steps. In addition, clumps of matrix may have survived the processing steps and remained in the thresholded image. Second, quartz grains were sometimes in contact, or the processing steps joined two grains that are actually discrete. Also, authigenic quartz (quartz cement) was present in some samples and could not be resolved from detrital quartz in normal BSE images. In these cases, the processing produced artiﬁcially larger grain areas because grains were joined, or cement was included with the grain. Because of these complications, each processed image was visually compared to the original image. Grains were manually separated if the processing joined them. Also non-quartz pixels were eliminated by hand if they appeared to represent matrix. Quartz grains touching the edge (boundary) of the image were also eliminated (Pirard, this volume). Finally, if quartz cement was excessive, the image was not used for further analysis. Following image processing, we used the National Institute of Health’s (NIH) freeware package to measure the grain area, perimeter, and major and minor axes of the imaged quartz grains. In all cases, grains with an area of less than 20 pixels were not counted because of the resolution issues previously discussed in Pirard (this volume).

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Figure 9. Series of images illustrating the various ﬁltering procedures used in this study. A: original BSE image of lithiﬁed loess of the Maroon Formation (all images are 500 µm across). B: Image in A after Laplacian ﬁlter (3 × 3 array) was applied. This ﬁlter accentuated the textural difference between the grains and the matrix. C: Image in B after a hybrid median ﬁlter was applied; note that the grain interiors are relatively uniform, but the matrix still contains high frequency variation in gray levels. D: Image (binary) in C after thresholding on the gray level depicted in Figure 10. Note that the quartz grains are segmented, but non-quartz grains are left unsegmented. E: Image in A after an edge ﬁnding ﬁlter (Haralick) was applied to a duplicate of original image. This ﬁlter segments most grains from the matrix, although some matrix remains. F: Same image in E after a hybrid median ﬁlter was applied (three times in succession); this eliminates most of the matrix and smoothes the grain boundaries. G: Thresholded image after image in F and image in D were combined using a Boolean “AND”. This procedure allowed most of the matrix to be eliminated (because of steps in E and F) as well as segmentation of only quartz grains (steps in B through D). H: Final image after image in G was smoothed using a hybrid median ﬁlter and an opening ﬁlter. The next step is to superimpose the ﬁnal image on the original in order to quality check and manually eliminate any additional spurious pixels and to remove quartz grains that are touching the edge of the image.

Figure 10. Histogram of BSE image in Figure 9(A). Thick line depicts the thresholded level chosen for thresholding resulting in Figure 9D. Dominant mode represents the quartz grains, whereas the subtle secondary mode to the right represents the superposition of a mode reﬂecting feldspar grains plus matrix. The thresholding level was chosen at the minimum between these two modes.

Results and discussion Because of excessive quartz cement within predominately the loessite facies in three of the nine loess-paleosol couplets, these proﬁles were not included in the subsequent analysis. In the remaining six proﬁles, the averaged median grain area of quartz grains was coarser within the samples from the loessite facies relative to the samples from the overlying paleosol (Fig. 11). In some cases, the median grain area of the quartz within the loessite was more than double the median grain area of the quartz within the paleosol; however, in other cases this difference was less than 10% (Fig. 11). Further, in some cases, the ﬁning trend through the loessite into the superimposed paleosol was nearly uniform (Fig. 12A) although in other proﬁles, the ﬁning was much less uniform with a maximum near the middle of the loessite interval (Fig. 12B). As noted earlier, the measured sizes and size distributions cannot be converted directly into actual grain sizes and thus quantitative analyses of the

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Figure 11. Bar graph of the average median grain area (µm2 ) for six loessite-paleosol couplets from the Maroon Formation. The values at the bottom of each loessite-paleosol couplet give the stratigraphic level (above the base of the section) for each pair. In each case the loessite exhibits a larger median grain area than the paleosol.

differences can not be made with the present dataset. Nevertheless, assuming that the shapes of the grains did not vary over time, and that the imaged slices represent a random cut through the sample, then the relative differences in measured median grain area do reﬂect real relative changes in quartz grain size. We follow Porter and An (1995) and Xiao et al. (1995) in suggesting these relative changes in the grain size of quartz grains reﬂect relative changes in wind strength, and thus infer that the general ﬁning in paleosols relative to underlying loessites reﬂects decreasing wind strengths during times of pedogenesis (interglacials) relative to times of signiﬁcant eolian silt accumulation (glacials). Hoang et al. (2002) showed a similar general pattern of grain size variation between loessites and superimposed paleosols from roughly coeval strata within the Paradox basin of Utah, using the same methodology. In summary, grain size analysis on lithiﬁed loessite is possible using digital image analysis of BSE images. The methods outlined here are provisional and will undoubtedly be reﬁned with additional testing. Nevertheless, our study suggests that techniques applied for paleoclimatic analyses in Plio-Pleistocene loessite may also be applicable to very ancient loessite successions.

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Figure 12. Stratigraphic proﬁle of two of the loessite-paleosol intervals of the Maroon Formation. A) Loessite-Paleosol couplet 33 m above base of section. B) Loessite-Paleosol couplet 684 m above base of section. Vertical scale is in meters and the median grain area (µm2 ) for each sample in the proﬁle determined through image analysis is plotted to the right of each section at the sampled horizons. The small “x” pattern on each proﬁle depicts observed sedimentologic features inferred to reﬂect soil forming processes (slicknesides, blocky peds, root traces, etc.).

Discussion and recommendations for BSE image analysis Advantages of using BSE microscopy for imaging include the ability to: 1) derive both compositional and textural information from the same image 2) use high magniﬁcation for analyzing ﬁne grained material, and therefore obtain information that was not accessible previously due to sampling limitations; 3) possibility of selection of the object of interest, based on their characteristics (mineralogy, shape, or size). The biggest problem in BSE imagery, however, remains keeping acquisition conditions constant, although newer digitally controlled instruments provide much better control of current stability. In addition, the technique is relatively time consuming compared to classical grain size techniques, especially considering the time for sample preparation and image acquisition. For most core work, we favor the use of thin section or polished rounds compared to impregnated chips because with thin sections or rounds it is not necessary to unglue specimens from stubs and recoat them between work sessions. In addition, thin sections and rounds are easier to handle due to their even thickness (no refocusing of sample) and customized sample holders allow the analysis of several samples each working session, which facilitates work ﬂow. As in all grain size techniques, some limitations, however, still exist (Last 2001). The “real” grain size cannot be determined using BSE microscopy image analysis techniques

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because the ﬁnest phases (<2 µm) are not resolvable; further, like any study involving 2D cuts of 3D grains, the resultant measurements do not directly correspond to the 3D volume. Stereological corrections allow for improvement of the measurements but are still of limited use in natural samples because the shape of the grains is variable and unknown (Sahagian and Proussevitch 1998). When performing BSE image analysis, it is important to report the following meta data in the methods section: whether the samples are polished or unpolished; the KV, working distance and magniﬁcation of the image acquisition; the digital image resolution; and the lower cut-off (e.g., 15 pixels). Other data, more speciﬁc to the machine used, are also useful to allow reproduction of the analysis, e.g., spot size, brightness and contrast values, and amount of current in the Faraday cup. Finally, the issue of the representative nature of the samples analyzed should be carefully addressed and evaluated. Future direction The current state of image analysis techniques is not limited by image analysis algorithms, or computer and SEM capabilities. Rather, it is restricted by lack of agreement of protocols to retrieve textural parameters. Once a set or range of protocols is standardized, semiautomated procedures of image ﬁltering and measurement can be developed. These semiautomated procedure will have to include a calibration procedure, by embedding standards in the microscope stage or the sample holder. As in microprobe work, standards should be chosen according to the samples analyzed. In the case of lake or marine sediments, standards might include polished pieces of glass, quartz, carbonate and iron oxide. Doing so, it should be possible to calibrate the intensity for each working session allowing for more rapid data collection, and to favor intercomparison of analyses. Currently, long series of annually resolved data are still tedious to produce (Francus et al. 2002b); for example, acquiring and analyzing 100 images per week is a rapid pace. Once semi-automated, one can expect to reach 1000 images per week, and therefore very long and high resolution time-series are possible. However, the selection of the ﬁeld of view will always require the competence of a sedimentologist. Assisted classiﬁcation procedures are in development but it seems that fully automated classiﬁers are still out of reach. Summary Image analysis of sedimentary particles using backscatter electron (BSE) microscopy shows great promise in paleoclimatic and paleoenvironmental studies. Prior to the last few years BSE microscopy has been used primarily for compositional (provenance) studies. Our preliminary work on Paleozoic loessite, as well as previous work on recent sediments (Francus 1998; Francus and Karabanov 2000), suggests that BSE microscopy image analysis is an effective tool for deriving textural data for use as a paleoclimate proxy. Our data on the Paleozoic loessite shows that we are able to document changes in grain size of quartz through several loessite-paleosol couplets. In each case, the quartz was coarser in the loessite facies relative to the overlying paleosol, which is similar to grain size trends observed in the Quaternary Chinese Loess Plateau. Image acquisition is a critical step in this methodology, however, special precautions are needed to make sure that 1) the samples are

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suitably prepared, 2) the acquisition instrument’s settings are controlled and maintained, and 3) the acquisition system provides an output of suitable resolution. Processing is similar to other types of imagery subjected to image analysis, and includes calibration, ﬁltering, and image segmentation and thresholding. An important component of processing is testing how different ﬁlters affect grain boundaries, particularly if grain size or grain shape is to be measured. In terms of image measurements, the magniﬁcation is an important consideration, and should be consistent; with standard BSE detectors, grains smaller than approximately 2 µm can not be resolved because of the size of the interaction volume of the backscatter electrons. As the case study illustrates, measurements of grain size or grain perimeter in this methodology do not translate into actual grain size information because of stereological considerations, however, relative changes in grain parameters yield useful information. The two biggest drawbacks of the present methodology are that it is difﬁcult to keep acquisition conditions constant, and that data collection is time consuming. As instruments with BSE capabilities improve with more digital controls, acquisition will become much more stable, and as protocols are developed, it will be possible to semi-automate the procedure, allowing for a much faster rate of data collection. Acknowledgments Funding was provided by NSF grant EAR-0001052. We thank G. Morgan and J. Vegas for help with sample preparation and BSE image acquisition and G. Soreghan for helpful discussion of Pangean climate. K. Moreland and N. Hoang performed the image analysis and image measurements on the ancient loessite samples. Pierre Francus is supported by the University of Massachusetts. We would like to thank Drs. F. Anselmetti and R. Behl and an anonymous reviewer for providing extremely helpful reviews of the manuscript. Metadata Image in Figure 1: JEOL JSM-5410 Scanning Electron Microscope @ 20 KV, working distance 20 mm; spot size: 20; magniﬁcation ×100. Image acquisition on a 4Pi digital acquisition system with a dwell of 20, in a 1240 × 960 pixels images. Image in Figure 4: Philips XL30 Lab6 @ 15 KV; working distance 20 mm; spot size: 4.8; magniﬁcation ×100; scan speed 968 lines/frame; image averaged = 2. Images in Figures 5–7 and 9: Cameca SX50 electron probe microanlayzer @ 20 KV; working distance 20 mm; Figures 5–6 and 9: magniﬁcation ×150; Figure 7: magniﬁcation ×125. References Anselmetti F.S., Luthi S. and Eberli G.P. 1998. Quantitative characterization of carbonate pore systems by digital image analysis. Am. Assoc. Pet. Geol. Bull. 82: 1815–1836. Buchter B., Hinz C. and Fluhler H. 1994. Sample-size for determination of coarse fragment content in a stony soil. Geoderma 63: 265–275. Camuti K.S. and McGuire P.T. 1999. Preparation of polished thin sections from poorly consolidated regolith and sediment materials. Sed. Geol. 128: 171–178.

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Porter S.C. and An Z. 1995. Correlation between climate events in the North Atlantic and China during the last glaciation. Nature 375: 305–308. Pye K. 1984. Rapid estimation of porosity and mineral abundance in backscattered electron images using a simple SEM image analyzer. Geol. Mag. 121: 81–84. Reed S.J.B. 1996. Electron Microprobe Analysis and Scanning Electron Microscopy in Geology. Cambridge University Press, Cambridge, UK, 201 pp. Russ J.C. 1999. The Image Processing Handbook. CRC Press, Boca Raton, Florida, 771 pp. Sahagian D.L. and Proussevitch A.A. 1998. 3D particle size distribution from 2D observations: stereology for natural applications. J. Volcan. Geoth. Res. 84: 173–196. Saarinen T. and Petterson G. 2001. Image analysis techniques. In: Last W. and Smol J. (eds), Tracking Environmental Change Using Lake Sediments: Physical and Geochemical Methods. Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 23–39. Soreghan G.S. 1994. Stratigraphic responses to geologic processes; Late Pennsylvanian eustasy and tectonics in the Pedregosa and Orogrande basins, ancestral Rocky Mountains. Geol. Soc. Am. Bull. 106: 1195–1211. Soreghan G.S., Elmore R.D., Katz B., Cogoini M. and Banerjee S. 1997. Pedogenically enhanced magnetic susceptibility variations preserved in Paleozoic loessite. Geology 25: 1003–1006. Soreghan G.S., Elmore R.D. and Lewchuk M.T. 2002. Sedimentologic-magnetic record of western Pangean climate in upper Paleozoic loessite (lower Cutler beds, Utah). Geol. Soc. Am. Bull. 114: 1019–1035. Soreghan M.J., Soreghan G.S. and Hamilton M.A. 2002. Paleowinds inferred from detrital zircon geochronology of upper Paleozoic loessite, western equatorial Pangea. Geology 30: 695–698. Starkey J. and SamantarayA.K. 1991.An evaluation of noise reduction ﬁlters, with particular reference to petrographic images. J. Comp.-Assist. Microsc. 3: 171–188. Starkey J. and Samantaray A.K. 1994. A microcomputer-based system for quantitative petrographic analysis. Comp. Geosci. 20: 1285–1296. Tramp K.L. 2000. Integrated sedimentologic, geochemical, and rock magnetic data as a high resolution record of pedogenesis in the Pennsylvanian Maroon Formation loessite (Colorado). M.S. thesis, University of Oklahoma, 212 pp. Van den Berg E.H., Meesters A.G.C.A., Kenter J.A.M. and Schlager W. 2002. Automated separation of touching grains in digital images of thin sections. Comp. Geosci. 28: 179–190. Veevers J.J. and Powell C. McA. 1987. Late Paleozoic glacial episodes in Gondwanaland reﬂected in transgressive-regressive depositional sequences in Euramerica. Geol. Soc.Am. Bull. 98: 475–487. von Merkt J. 1971. Zurverlässige Auszählungen von Jahresschichten in Seesedimenten mit Hilfe von Grob-Dünnschliffen. Arch. Hydrobiol. 69: 145–154. Xiao J., Porter S.C., An Z., Kumai H. and Yoshikawa S. 1995. Grain size of quartz as an indicator of winter monsoon strength on the Loess Plateau of Central China during the last 130,000 yr. Quat. Res. 43: 22–29.

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Part III: Advanced Techniques

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12. AUTOMATED PARTICLE ANALYSIS: CALCAREOUS MICROFOSSILS

JÖRG BOLLMANN ([email protected]) PATRICK S. QUINN MIGUEL VELA BERNHARD BRABEC SIEGFRIED BRECHNER MARA Y. CORTÉS HEINZ HILBRECHT DANIELA N. SCHMIDT RALF SCHIEBEL HANS R. THIERSTEIN

Department of Earth Sciences ETH and University Zurich Sonneggstrasse 5, 8092 Zurich Switzerland Keywords: Neural networks, Particle recognition, Automated microscopy, Microfossils, Morphometry, Calcareous nannofossils, Planktic foraminifera, SEM, Light microscopy

Introduction Automated particle analysis is a common method in biology (e.g., analysis of cell size and shape), quality control (e.g., wafer inspection systems) and in forensic sciences (e.g., analysis of gunshot residues). Within Geoscience, particle analysis is often applied to the characterization of sediments (Felix 1969; Schwarcz and Shane 1969; Ehrlich and Weinberg 1970), to quantify the morphology of fossils (Kennett 1968; Bé et al. 1973; Hecht 1976; Bollmann 1997; Knappertsbusch et al. 1997) or to analyze the assemblage composition of microfossils (Imbrie and Kipp 1971). In numerous studies, quantitative analyses, statistical treatment, and subsequent interpretation of microfossil assemblages have demonstrated the potential of these approaches in interpretation of the history of regional and global climate, the oceans, and of the evolution of the biosphere (e.g., Imbrie and Kipp (1971), CLIMAP (1976), Lipps (1993), Westbroek et al. (1993), Lazarus et al. (1995)). However, the manual collection of a statistically signiﬁcant quantity of unbiased, reproducible data is time consuming and thus, automated microfossil analysis and species recognition has been a long-standing goal in micropaleontology (COSOD II 1986). In recent years, increasing computing power and the development of digitally controlled microscopes has offered a realistic opportunity to develop efﬁcient robots for the automated 229 P. Francus (ed.) 2004. Image Analysis, Sediments and Paleoenvironments. Kluwer Academic Publishers, Dordrecht, The Netherlands.

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analysis of microfossils. However, there are currently but a few applications in micropaleontology that take advantage of fully automated image acquisition, particle analysis, and recognition (e.g., Ratmeyer and Wefer (1996),Young et al. (1996), Dollfus (1997), Beaufort et al. (2001), Bollmann et al. (2002a), du Buf and Bayer (2002)). The automatic recognition of particles such as microfossils can be divided into two main tasks: image acquisition and particle recognition. Recognition of particles is purely software-based whereas automated image acquisition requires the communication between a computer and a microscope. Automated image acquisition is the ﬁrst step towards automated particle analysis, however, the fully automated acquisition of images can assist in manual data analysis. The automated collection of high quality images, for example, of plankton preparations with the Scanning Electron Microscope (SEM), is time saving and permits optimal utilization of the SEM as overview images can be stored on CD-ROMs and processed manually anywhere with a computer (Bollmann et al. 2002a). Furthermore, samples can be re-examined without an SEM and different scientists can analyze the same sample for quality control or comparison of taxonomic concepts. To efﬁciently acquire images of calcareous microfossils in the size range of 63 µm to 2000 µm (e.g., planktic foraminifera) with an incident light microscope and in the size range of 1 µm to 30 µm (e.g., calcareous nannofossils) with a SEM and with a transmitted light microscope, three robots have been developed and tested over the last ﬁve years by the micropaleontology group at the ETH Zürich in collaboration with Focused Electrons and Ions (FEI) AG, LEICA Switzerland and Soft-Imaging Software (SIS). In addition, a Microsoft Windows NT -based neural network simulator was developed for the online and ofﬂine classiﬁcation of microfossils from digital images. The three automated image acquisition systems have been used successfully in various applications (Brechner 2000; Bollmann et al. 2000; Bollmann et al. 2002a; Schmidt 2002; Schmidt et al. 2003) and clearly demonstrate the ability of automated microscopes to speed up the arduous process of collecting images of microfossils and to provide morphometric data of consistent high quality. This paper aims to outline what criteria need to be taken into account for building robots to acquire digital images automatically with different types of microscopes. We share here our experience gained during the construction of three automated systems with special focus on their applicability and limitations. Furthermore, we give a brief description of a neural network classiﬁer used for the identiﬁcation of calcareous microfossils. Automated image acquisition All three currently operational systems at the Geological Institute of ETH Zürich automatically scan predeﬁned sample areas and capture either overview images (e.g., for plankton and sediment counts) or detailed images of single objects (e.g., for microfossil recognition with a neural network simulator or for morphometry). All systems have a similar basic setup consisting of a microscope with motorized stage, a digitizing unit, and PC with a remote control (for details see Fig. 1). In the following section, we describe the most important features necessary for automated image acquisition and subsequent recognition using an incident light microscope (Automated Light Microscope Fossil Analyzer (ALFA), Fig. 2), transmitted light microscope (Computer Guided Nannofossil Identiﬁcation System (COGNIS Light), Fig. 3),

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Figure 1. General set-up of the three microscope types for automated image acquisition.

Figure 2. Photograph of the incident light microscope set-up. Left: A: Ring light; B: Microscope; C: CCD video camera; D: Glass tray with level holder; E: Computer controlled motorized X, Y stage; F: Computer; G: Video frame grabber. Right: Close up of the six glass trays. A: Glass tray; B: adjustable feet for leveling of the glass tray; C: Black velvet. For details on components used see A1.

and scanning electron microscope (Computer Guided Nannofossil Identiﬁcation System (COGNIS), Fig. 4) for automated calcareous nannofossil analysis. A list of the most important software control functions is given in Table 1 and all components for the different microscopes and a detailed technical description of the systems is given in the Appendix.

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BOLLMANN ET AL. Table 1. List of the most important software functions for automated image acquisition with an incident light microscope, a transmitted light microscope, and a scanning electron microscope. Command Set/Get X, Y , Z stage position Set/Get Rotation stage Digitize Image Set/Get Polarizer position On/Off Light Set/Get Bulb current Set/Get Final lens current On/Off High tension Get/Set Spot size Get/Set Contrast Get/Set Brightness Set Auto Contrast & Brightness Set Autofocus Get/Set Line time Get/Set Filament current Get/Set Magniﬁcation

Incident LM X

Transmitted LM X

X

X X X X

SEM X X X

X X X X X X X X X X

Figure 3. Photograph of the transmitted light microscope set-up. Left: A: Slow Scan CCD camera; B: Microscope body; C: Computer controlled motorized X, Y , Z, axis; D: motorized ﬁlter exchangers; E: Computer with control software and frame grabber. Right: Close up of the stage. For details on components used see A2.

Sample preparation We emphasize that high quality sample preparation is essential for successful automated acquisition and recognition of microfossils. We strongly recommend ﬁrst optimizing the sample preparation before applying complex manipulations and algorithms to digital images, for example ﬁltering or particle separation. Isolated non-overlapping particles are required for the automated recognition of calcareous microfossils. In order to avoid measuring aggregates of sand-sized particles with the incident light microscope a small amount of material (e.g., sieved foraminifera sand) is evenly distributed on a sample tray. The usual procedure for the preparation of calcareous nannofossils in the light microscope (LM) and the SEM is to mix a small amount of sediment with water, smear it on a glass cover slip, and mount it on a microscope slide (Bown and Young 1998,

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Figure 4. Remotely controlled Philips XL30 scanning electron microscope in combination with the imaging software analySIS3.0 . A: SEM Column; B: Microscope control computer; C: Computer with remote control and digital beam control. For details on components used see A3.

p. 17). So-called “smear slides” are quick and convenient for the routine manual analysis of calcareous nannofossils, and this method is widely used in research and industry. However, for the automatic analysis of calcareous nannofossils with the LM and SEM, the distribution of material on smear slides is far too uneven, both horizontally and vertically. We have therefore developed a technique for the production of evenly distributed slides (Bollmann et al. 1999). The method involves disaggregating the sample material, suspending it in water or alcohol, and spraying this onto a cover slip. The sprayed residue produces an even distribution of particles, the density of which can be controlled by altering the quantity of suspensions used per slide. We recommend using alcohol instead of water for SEM preparation because the alcohol evaporates without producing a rim of precipitates around the particle that interfere with the detection of objects. For LM preparations, we use fast UV-setting NORLAND mounting media instead of CANADA balsam in order to prevent the suspension of particles during mounting. This keeps most of the particles in one focal plane, reduces the number of steps required by an autofocus procedure, and therefore, increases the total efﬁciency of the system (Fig. 5). Segmentation and illumination The ﬁrst step in detecting and analyzing individual particles on digital images is to separate (segment) the objects from the background. There are several approaches to segmenting

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Figure 5. Schematic of sample preparations. Numbers 1 to 4 refer to individual particles in a slide; A: Top view of a sprayed sediment suspension mounted for SEM or LM application. B: Side view of A when the cover slip is mounted onto a glass slide using Canada Balsam for use with an incident light microscope. — Note that all particles lie in different focal planes; C: Side view of a sprayed sediment suspension mounted with NORLAND UV glue. — Note that all particles lie more or less in one focal plane. D: Top view of C. — Note that the size of the particles look identical now in this top view.

images (details of the algorithms are given by France et al. (this volume)). We use automated thresholding techniques to separate foreground from background with all our systems. Thresholding uses the gray value distribution (frequency histograms) of an image to distinguish between objects and the background (see Fig. 6 and France et al. (this volume)). Constant light intensity, uniform illumination within a ﬁeld of view, and high contrast are prerequisites for the optimal segmentation and detection of objects within an image. These conditions should be stable during operation of the robots over a time span of 1 to 12 hours. These requirements are the same for all types of microscopes although the light sources and imaging techniques may be different. Microscope illumination is affected by several factors such as the light source, optics, and the digitizing device. We recommend ﬁrst optimizing the light conditions before applying digital imaging procedures to correct for inhomogeneous illumination, for example, shading correction and contrast enhancement/equalization (see

Figure 6. Example of automated thresholding and particle detection. Left: Coccoliths in an image acquired with a SEM. Right: Gray value distribution of the image. — Note that all detected particles are shown in white. Scale bar = 4 µm.

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Nederbragt et al. (this volume)) as each ﬁlter procedure can produce artifacts and reduces the image information. Illumination for incident light microscopy In order to obtain homogeneous, shadow-free illumination, we used a ﬁber optic ring-light (Cold Light Source) attached to a stereomicroscope (Fig. 2 left). In addition, we have constructed a low-reﬂectance glass tray to enhance the detection of the objects. The glass tray is mounted about three centimeters above a black velvet cloth (see Fig. 2 right). This design provides a homogeneous dark background (low reﬂectance) as the black velvet cloth below the tray absorbs reﬂected light. Bright objects are therefore easily detected and the largest outline of an object can be automatically identiﬁed even if the contrast and/or the sharpness is very low. Black painted metal trays, widely used for microfossil analysis, are not suitable for the automated detection of objects because they reﬂect light at varying intensities. Depending on the inclination, light is reﬂected from small irregularities on the surface of such trays, and therefore, it is very difﬁcult to calculate a gray-value threshold that can be applied for object segmentation of all objects in one ﬁeld of view. The lifetime of the bulb is about 2900 hours but may be reduced to 420 hours if the bulb is switched on and off daily (for technical details see Appendix A1). Illumination for transmitted light microscopy Transmitted light microscopes are usually equipped with halogen bulbs that last about 120 hours. The light intensity of such bulbs decreases slowly during their lifetime and remains more less constant over an operation time of 12 hours. In-homogeneous illumination is a minor problem with transmitted light microscopes. However, light intensity often decreases from the center to the border of a ﬁeld of view depending on the quality of the objectives and the overall optics (Fig. 7). Therefore, it may be necessary to reduce the area of interest until the illumination is more or less homogeneous. We recommend using Plan Apochromat objectives because they minimize the inhomogeneous illumination.

Figure 7. In-homogeneous illumination on a transmitted LM. Left: Image recorded in XPL. Right: Binarized image shown left. — Note that the light intensity decreases from the center to the border. Scale bars = 10 µm.

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In order to identify calcareous nannofossils, transmitted light, phase contrast, and crossed polarized light (XPL, crossed nicols) in different orientations, is required. In crossed polarized light, it is desirable to rotate specimens with respect to the direction of the crossed nicols as distinct features, for example the bridge elements of the coccolith genus Gephyrocapsa, are only visible at certain orientations of the crossed nicols (see Fig. 8B). As a high precision rotating motorized stage was considered to be too difﬁcult to build and too slow for collecting images automatically, our microscope was extended by two motorized polarizing ﬁlter exchangers, one above and one below the sample stage (see also Fueten (1997)). Each ﬁlter carousel is equipped with ﬁve polarizing ﬁlters offset by 9◦ from each other. In addition, it has one position for phase contrast (Fig. 8). Illumination for SEM Constant illumination with an SEM over an operation time of 12 hours is difﬁcult to obtain for several reasons. These include (a) movement of the ﬁlament/gun with respect to apertures in the column, in which drift from the center position produces lower illumination, (b) the stability of the ﬁlament saturation, (c) position of the samples with respect to the detector, and (d) charging of the sample. In our opinion, the most suitable systems for automated operation over several hours are warm ﬁeld emission gun systems (Schottky Field Emitter) because of the stability of their gun system and the long lifetime of the ﬁlament (for details see Lamoureux and Bollmann (this volume)). However, we strongly recommend performing extensive tests of the stability over several weeks before deciding which SEM or gun system to invest in. Camera, frame grabber, and slow scan digitizer In order to convert images for automated processing, a camera and digitizer are necessary. The basic principle is to transform an image with a camera/detector into a continuous electrical analog signal, then into a discrete digital signal. There are two basic systems for image acquisition: slow scan CCD cameras/digitizer and TV cameras in combination with a video framer grabber. In order to choose the best camera for the task to accomplish, the most important characteristics of CCD cameras to consider are: the pixel resolution, light sensitivity, the speed of the image transfer to the computer, and the programmability of certain functions such as direct memory access for fast image access, the adjustment of gain/offset for contrast enhancement or the adjustment of the exposure time. For details on the different systems see Lamoureux and Bollmann (this volume). Digitizing images with incident light microscope Light intensity on low magniﬁcation incident light microscopes does not usually require a sophisticated camera equipped with a highly sensitive CCD chip. Therefore, we equipped our incident light microscope with a simple black and white TV CCD video camera that is connected to a video frame grabber (16 bit, 50 Hz, PAL, 768 × 576 pixels). The light intensity can be automatically controlled via software by adjusting gain and offset of the frame grabber or simply manually by adjusting the light intensity of the ring light. The size of microfossils analyzed varies from 63 µm to 2000 µm and a pixel resolution of 768 × 576

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Figure 8. A: Schematic diagram of the polarizer and analyzer ﬁlter exchanger. The arrows indicate the orientation of the polarizing ﬁlter. PH = Phase contrast; B: Series of images of same coccolith specimen, Gephyrocapsa oceanica, in ﬁve different positions of the crossed polarizing ﬁlter (each offset by 9◦ ). — Note that the calcite bridge (distinguishing feature) crossing the central area is only visible in image 5.

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provides a pixel size ranging from 8.01 µm to 1.38 µm at 65× and at 400× magniﬁcations, respectively. Digitizing images with transmitted light microscopes In order to capture images with a transmitted light microscope in the low light condition of crossed nicols (XPL) or in ﬂuorescent light requires a sophisticated camera system. Such cameras are equipped with highly light sensitive CCD chips. The exposure time of the camera can be programmed and often two or more pixels of the CCD chip can be combined to increase the light sensitivity (so called binning). We equipped our transmitted light microscope system with a high sensitive black and white slow scan camera with programmable exposure time and binning of up to 8 pixels. The pixel resolution of 1280 × 1024 (12 bit) provides segmented objects with a minimum size of 1 µm at 23 by 23 pixels image resolution for reliable image processing, for example in a artiﬁcial neural network classiﬁer. Digitizing images with SEM Most modern SEMs are equipped with digital imaging units and images can be directly accessed by an external program. However, it may be easier to use an external digital beam control to digitize images as it simpliﬁes the integration of image acquisition and digitizing functions into the image analysis software that controls the SEM and the image processing (for details see Soreghan and Francus (this volume), Lamoureux and Bollmann (this volume)). Automated stage In order to scan predeﬁned sample areas a microscope must be equipped with a motorized, computer-controlled stage. A mechanical precision of 1 to 5 µm is sufﬁcient for the analysis of microfossils in the size range of 63 µm to 2000 µm (e.g., foraminifera) with an incident LM. The mechanical precision in the X and Y directions for the analysis of calcareous nannofossils should be around 1 µm on a SEM and a transmitted LM. The precision in the Z direction should be around 0.01 µm for autofocus applications for all systems. The stage should be controllable via a set of software functions that can be integrated in an acquisition procedure such as a C-program. Functions such as Get/Set X, Y , R (Rotation), and Z (Height) coordinates, should be accessible via high level software functions using a Dynamic Link Library (DLL) that use the serial interface (RS232, IEEE) or the Ethernet port. From a programmer’s point of view, it is very important that a function, for example “Set stage position” or “Get stage position”, is conﬁrmed (Returns) when the position is arrived at and not when the command was received. Without a return value, or simply an “Acknowledge Return” after receiving the command, it is difﬁcult to keep track of the stage position. Modern stages offer these functions. However, some older SEM stages only allow access to the stage via a terminal program (RS232 interface) and all communication between the computer and the stage has to be programmed. This can be quite an elaborate task, especially if the documentation is imperfect. Some software and microscope companies offer a stage control already integrated into their microscope and imaging software. However, many of these systems are difﬁcult to tailor to suit speciﬁc tasks.

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Autofocus Another prerequisite for automated image acquisition is a precise and fast autofocus. The basic principle of an autofocus is to move an object into the focal point without any human interference. There are two ways to do this: 1. adjusting the focal distance by moving the lenses (incident LM, SEM) and 2. adjusting the distance between an object and the objective by moving the Z-axis of the stage (all microscopes). References to the most commonly used autofocus algorithms are given by France et al. (this volume). Most microscopes already offer a built-in autofocus function that can be activated via a computer. However, most of these autofocus functions are slow and not very reliable for the analysis of individual objects in a ﬁeld of view because they only calculate an overall focus value for each image and not for each individual object in an image. In order to automatically adjust the working distance on a microscope, several functions must be controllable by a computer. These are the Z axis (coordinate) of the stage (all microscopes), the distance between body tube and stage (incident LM), objective lens current (SEM), the automated digital image acquisition and the focus value calculation (on all microscopes). Autofocus with incident light microscopes Focusing three-dimensional objects is inherently problematic if the object is larger than the depth of focus as they have several focal planes depending on the depth of focus. Therefore, it has to be known which part of the object should be in focus if the object is larger than the depth of focus. The depth of focus depends on the magniﬁcation, the aperture of the objective, and the size of the objects. If single isolated objects have to be focused, the Z-axis of the stage or the body tube of an incident light microscope must be motorized in order to move the object into the focal plane. However, for the incident light microscope we constructed a sample tray that can be leveled with three adjustable feet (Fig. 2 right). This prevents objects from traveling out of the focus range over a predeﬁned scanning area, for instance of 105 × 65 mm. Therefore, there is no need for an autofocus function. The disadvantage of this set up is that only objects within a certain size range are in focus because of the limited depth of focus. Autofocus with transmitted light microscopes Most commercially available autofocus systems for transmitted light microscopes work on a complete ﬁeld of view or on a predeﬁned area within a ﬁeld of view that cannot be altered while the system is running. Therefore, these systems cannot focus on speciﬁc isolated objects, such as coccoliths or diatoms, lying in different planes within one ﬁeld of view on a slide (Fig. 5). In order to overcome this problem, we have developed an autofocus routine for our transmitted light microscope that enables focussing on each single object within a ﬁeld of view individually. The system ﬁrst detects all objects within a ﬁeld of view and calculates focus values for each single object (based on a gray value gradient, for details see France et al. (this volume)). Subsequently, the Z-axis of the stage is adjusted stepwise (e.g., ±50 steps of 0.1 µm step size) up and down and the focus value of each object is calculated after each step. All images and related focus values are stored in memory until the best focus value is obtained. Subsequently, the image with the highest focus value is saved to disk.

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Autofocus with SEM Most modern SEMs are equipped with an autofocus system. As with transmitted light systems, these AF functions work either on a complete ﬁeld of view or a smaller predeﬁned area that cannot be changed during operation. In addition, most autofocus functions are too slow for a rapid collection of images and not precise enough for acquisition of focused objects at high magniﬁcation. Therefore, we have developed an autofocus routine that is suited to the automated collection of single objects, such as coccoliths, on a ﬂat surface with our SEM system (COGNIS-SEM). In contrast to the COGNIS-Light system, we do not use the Z-axis of the stage to move an object into focus as it is too slow and not precise enough at high magniﬁcations. Instead, our COGNIS-SEM system adjusts the electrical current of the ﬁnal lens to change the working distance or the focal point, respectively. However, the basic principle of focusing is the same as on LMs. The COGNIS system ﬁrst detects all objects within one ﬁeld of view at low magniﬁcation (e.g., 1500×) using the gray value information within the image. Then it calculates the X and Y coordinates of each object, moves it into the center of the ﬁeld of view, and calculates the maximum magniﬁcation (screen ﬁlling objects). The maximum magniﬁcation is then set and subsequently the lens current is changed stepwise (e.g., ±1 step of 1.0 µm step size at a magniﬁcation of 30,000×) up and down while a focus value is calculated based on gray value frequencies in a TV live image. The lens current associated with the highest focus value is then set and the step size is reduced by 50% (0.5 µm). This procedure is repeated until the focus value stays constant and an image of the object is taken, for example in slow scan mode and saved to disk. The focus value is calculated by the frame grabber on live images by analyzing the gray value frequencies in an image. The frame grabber calculates a new focus value every ca. 700 ms. In order to prevent the system from running out of focus, the focus procedure is only performed if objects are detected. Furthermore, upper and lower focus limits can be set depending on the magniﬁcation. Automated classiﬁcation There are two main approaches to the automated analysis and classiﬁcation of images of individual sedimentary particles. These are structural/statistical techniques and the application of artiﬁcial neural networks. Statistical or structural approaches use complex algorithms to analyze, for example, the shape and interior of objects. They are particularly suited to the analysis of grayscale two-dimensional images of calcareous microfossils (e.g., Belyea and Thunell (1984), Healy-Williams (1983; 1984), Burke et al. (1987), Hills (1988), Garratt and Swan (1992), Yu et al. (1996)). However, in order to successfully identify several microfossil taxa in a sample using such techniques, it is necessary to apply many different image analysis algorithms, each tailored to resolve a speciﬁc shape or textural feature. Such an approach suffers from being highly complex and very inﬂexible if new taxa have to be identiﬁed. In order to automate identiﬁcation more efﬁciently, a versatile system is needed. Artiﬁcial intelligence (AI) and in particular, artiﬁcial neural networks (ANN’s), represent such a solution (see also France et al. (this volume)). Artiﬁcial neural networks are self-learning systems of simple interconnected processors, which mimic the biological nervous system. They operate on the principle that many small computational units are more powerful than a single large processor. The constituent units

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(or neurons) in an ANN have very little power, instead, it is within the connections between the various neurons where the power ofANN’s lies. Rather of being programmed to carry out a speciﬁc task, ANN’s learn by example. Training an ANN in this way involves presenting it with a training dataset of groups of images of known objects such as microfossil species and letting it work out similarities and differences between them. Neural networks actually learn by altering the strength (or weight) of the connections between their neurons. The mathematics behind ANN’s, particularly in terms of the way they are trained, is complex, however digestible introductions to the subject include Weiss and Kulikowski (1991, Chapter 4), Bishop (1995), Ripley (1996), and Schalkoff (1997). There are several different types of ANN’s which can be applied to different tasks. Artiﬁcial neural networks used to analyze images usually consist of two or more layers of neurons, which may be connected in various ways. Dollfus and Beaufort (1999) have developed a so-called “fat” neural network (SYRACO, Système de Reconnaissance Automatique de Coccolithes), based on the work of LeCun (1987), which was applied to identify calcareous nannofossil images in the study of Beaufort et al. (2001). Brechner (2000) compared this and other types of neural networks and found that a so-called convolutional artiﬁcial neural network (CNN) architecture similar to that of LeCun et al. (1990) was the best solution to classifying images of calcareous microfossils. Convolutional neural networks, a comprehensive description of which is presented in LeCun and Benigo (1995), are especially good at dealing with natural variation in objects, including translation, rotation, and distortion. Based on the investigations of Brechner (2000), we have developed a Microsoft Windows-based program (COGNIS), with an artiﬁcial neural network simulator, which allows the user to construct CNN’s for the classiﬁcation of grayscale images. During the training of a CNN with COGNIS, various parameters can be controlled, including the initial value of the weights between the neurons, and the number of times the training dataset is passed through the network, to produce a reliable CNN for a certain application. After training, the applicability of a CNN to its particular classiﬁcation task can be tested by presenting it with a separate dataset of images (classiﬁcation dataset). COGNIS can thus classify and transfer images classiﬁed into the speciﬁc class folders, where they can then be examined by the operator. We call the percentage of images fed to a CNN, which are correctly classiﬁed the classiﬁcation success. A classiﬁcation success of 100% means that all images of class X within a classiﬁcation dataset are correctly classiﬁed as class X. However, the identical CNN might also classify images of other classes as class X. The percentage of images incorrectly assigned to class X among all images assigned to class X is called the error rate. The classiﬁcation success and the error rate are measures of the capability of a CNN. We choose this distinction, because in many of our applications we are interested also if images of objects can be “enriched” in output folders with no signiﬁcant losses. There are several approaches to test the capability of a CNN (for details see Schalkoff (1997)). In order to assess the capabilities of CNNs constructed and trained with COGNIS, we utilized the Olivetti Research Laboratory (ORL) Database of Faces available at the archive of ATT Laboratories, Cambridge. This dataset consists of 10 different poses of 40 people (Fig. 9). Depending on the testing method used, the error rate varied between 14% to 3% which is comparable to the results achieved by the CNN of Lawrence et al. (1997) using the same ORL database.

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The performance of COGNIS CNN’s in classifying coccolith images was then tested using a dataset of SEM images collected from Holocene sediment samples. The training dataset contained a total of 979 images of 48 × 48 pixels in size belonging to 14 Holocene coccolith species (Fig. 9, Table 2). Training took several hours, after which the trained CNN was tested with a separate classiﬁcation dataset of 715 images of the same 14 species (Table 2). The CNN achieved an overall classiﬁcation success of 82% (proportion of images to be classiﬁed that ended up in the right class bin) and had an error rate of 37% (proportion of incorrectly classiﬁed images), indicating that the COGNIS CNN was also capable of classifying images of coccoliths. In this test, the error rate for the individual species varied from 3% to 88% (Table 2) and the classiﬁcation success varied from 34% to 86%. Whilst some species of coccoliths are likely to be more easily recognized than others, the individual error rates seem to be inversely proportional to the number of images of each species in the training dataset, which was determined by the abundance of these taxa in the Holocene sediment samples. One application of such a system for the automated identiﬁcation of coccoliths would be to search for specimens of single rare calcareous microfossil species in sediments for morphological measurements to develop oceanographic proxies (Bollmann et al. 2002b)

A. Faces

1.

2.

3.

4.

B. SEM nannofossil

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

C.

F. profunda

1.

2. Figure 9. Images from the datasets used for the classiﬁcation and training of CNN’s in this study. Numbers refer to number of classes in each data set. A. Faces CNN. Only four of the 40 classes are shown. The images come from the Olivetti Research Laboratory Database of Faces available at the archive of ATT Laboratories, Cambridge. B. SEM nannofossil CNN. Examples of the nannofossil taxa in the 14 classes. For the species Rhabdosphaera clavigera, side (8) and top views (9) were treated as separate classes due the presence of a distinctive spine. Species names are listed in Table 2. C. LM F. profunda CNN. Examples from the two classes: F. profunda images with and without associated particles (upper row), and non-F. profunda particles, including other calcareous nannofossil species and calcite particles (lower row).

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Table 2. Summary of convolutional neural network training and classiﬁcation datasets and results for CNN’s used in this study. A. SEM nannofossil CNN and B. LM F. profunda CNN’s. Training data refer to all images used for the training of the CNN; Classiﬁcation data refer to all images used for the classiﬁcation. — Note: There is no overlap between training and classiﬁcation data sets. The classiﬁcation success reﬂects the number of correctly classiﬁed images with respect to the total number of images within a speciﬁc class of the classiﬁcation data set. In contrast, the error rate reﬂects the proportion of images that was not correctly classiﬁed with respect to the number of classiﬁed images in a certain class. Training Data

Classes

Images (No.)

A. SEM nannofossil CNN 1. Calciosolenia murrayi 2. Calcidiscus leptoporus 3. Coccolithus pelagicus 4. Discosphaera tubifera 5. Emiliania huxleyi 6. Florisphaera profunda 7. Gephyrocapsa sp. 8. Rhabdosphaera clavigera 9. Rhabdosphaera clavigera spine 10. Syracosphaera pulchra 11. Thorosphaera ﬂabellata 12. Umbilicosphaera foliosa 13. Umbilicosphaera sibogae 14. Umbellosphaera tenuis

38 90 82 46 104 79 144 52 67 42 56 37 101 41 979

Results

Classiﬁcation Data

Images (No.) 9 45 16 10 284 37 38 15 47 13 11 7 168 15 715

Classiﬁed Images (No.) 15 45 15 14 291 36 34 15 24 9 25 26 141 25

Classiﬁcation success Correctly classiﬁed Images (No.) (%) 6 39 7 7 272 32 28 13 16 7 6 3 138 9 583

Average B. Florisphaera profunda CNN F. profunda non-F. profunda particles

67 87 44 70 96 86 74 87 34 54 55 43 82 60

Error rate Incorrectly classiﬁed Images (No.) (%) 9 6 8 7 19 4 6 2 8 2 19 23 3 16 132

82 1000 1000 2000

142 1950 2092

660 1432

132 1031

93 72

60 13 53 50 7 11 18 13 33 22 76 88 2 64 37

528 401

80 4

or test evolutionary models (Knappertsbusch 2000). Collecting images of rare species manually can take several hours on a microscope, and therefore, substantial automated enrichment of desired taxa would be beneﬁcial to such studies. To achieve, this the CNN must reliably identify a single species among all other coccolith and non-coccolith particles in a sample. Towards this end, a CNN was trained using a dataset containing 2000 images of only two classes of objects, collected automatically with the COGNIS-Light system (Table 2, Fig. 9). The ﬁrst class was composed exclusively of images of the coccolith species Florisphaera profunda and the other class contained a random selection of all other coccolith and non-coccolith particles, encountered in the same sediment sample. Training this CNN took considerable time (ca. 30 hours) due to the large size of the training set

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and the variability in the second class. The trained CNN was then tested using a separate classiﬁcation dataset of 2092 different images from the same sample captured automatically using the COGNIS-Light system. In this test, the CNN achieved a classiﬁcation success of 93% for F. profunda and 72% for all other particles, respectively (Table 2). Whilst the CNN correctly classiﬁed 132 images of F. profunda in the classiﬁcation set, 528 other, non-F. profunda particles were also classiﬁed with them (error rate of 80% for F. profunda). While the error rate in this example was 80%, the procedure resulted in an almost three-fold enrichment of F. profunda, whilst it failed to recognize only 7% (10 images) of this species. This represents a signiﬁcant outcome and demonstrates that such an approach has clear practical beneﬁts for reducing the time taken in searching for specimens of rare taxa. What can be improved? We have demonstrated that it is possible to automate the process of collecting calcareous microfossil data (Brechner 2000; Bollmann et al. 2000; Bollmann et al. 2002a; Schmidt 2002; Schmidt et al. 2003), however, there is still a need to improve the overall performance of image acquisition and particle recognition of these systems. From our point of view the main bottleneck is currently the speed of autofocus and the error rate with ANN’s. The speed of autofocussing in the various systems is highly dependent on the velocity of the stage or ﬁnal lens current adjustment, the communication between the motorized stage and the PC and the rate of focus value calculation. The major limitations with the SEM system are the calculation rate of a new focus value of every ca. 700 ms and the mechanical movement of a detected object into the center of the ﬁeld of view. Faster communication between SEM and PC would greatly speed up this process. Furthermore, it would be desirable to determine the focus values of several individual particles from live overview images while changing the ﬁnal lens current or the Z-axis of the stage. Similar improvements would also beneﬁt the transmitted light microscope system. In addition, a data transfer rate faster >10 MHz between the camera and computer would be desirable and improved light sensitivity of the CCD could help decrease the exposure time. Some companies already offer microscopes that can be controlled entirely by computer. However, there are limits to the speed and efﬁciency of mechanical systems. In contrast, AI andANN’s are rapidly expanding branches of science. New concepts and the development of improved software are to be expected. Artiﬁcial neural networks are now making signiﬁcant inroads into many aspects of the earth and environmental sciences (Swaby 1990; Malmgren and Nordlund 1997; Malmgren and Winter 1999; Belgrano et al. 2001; Beaufort et al. 2001). They have also been applied to the identiﬁcation of dinoﬂagellates (Culverhouse et al. 1996) and pollen (France et al. 2000; France et al., this volume). However, to our knowledge, there is currently no commercially available software for the recognition of calcareous microfossils and no existing particle recognition systems can be easily adapted to suit this purpose. We have tested the CNN capabilities of COGNIS on reﬂected light microscope images of foraminifera collected by the ALFA system and found that their classiﬁcation is complicated by the need to combine information from different orientations of the same specimen (i.e., umbilical, spiral and side views). In this respect, foraminifera present a completely different classiﬁcation task to calcareous nannofossils. Foraminifera have been the subject of several studies using structural/statistical methods of image analysis (e.g.,

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Yu et al. (1996)). However, our on-going investigation represents on of the ﬁrst attempts at using CNN’s for their recognition. The COGNIS ANN simulator is very versatile and can potentially be used for the classiﬁcation of non-microfossil sediment particles. It can also be used to investigate and analyze various environmental data sets such as primary production time-series (Belgrano et al. 2001) or temperature and precipitation (Malmgren and Winter 1999). We emphasize that the recognition of calcareous microfossil particles with CNN’s is highly dependent on types of object classes and the quality of the images used for training and classiﬁcation. Producing optimal CNN’s for speciﬁc recognition tasks requires a great deal of experimentation and practice. Future lines of investigation include: the combination of several CNN’s in a hierarchical fashion, to achieve higher recognition of several different particles in single samples and to cope with different views of a single particle type, for example, with foraminifera. The integration of numerical data, such as particle size within CNN’s trained with two-dimensional images to recognize morphometrically-deﬁned microfossil taxa. The idea of connecting several ANN’s to improve their capabilities seems to be the way forward (see also France et al. (this volume)) and is currently being investigated at the ETHZ. The F. profunda CNN described above indicates that a high classiﬁcation success can be achieved for single species. Therefore, it may be possible to connect two or more such CNN’s together in a parallel or pyramidal arrangement to classify several species in a single sample with greater success. Summary Manual collection of a statistically signiﬁcant quantity of unbiased and reproducible data on microfossils is time consuming. Therefore, fully automated operating robots are needed that recognise and analyze calcareous microfossils. Here, three robots were described that automatically capture images of microfossils with an incident light microscope, a transmitted light microscope, and a scanning electron microscope. In addition, a Microsoft Windows NT -based universal artiﬁcial neural network simulator was described for the online and ofﬂine classiﬁcation of microfossils from digital images. Acknowledgments We thank the reviewers Luc Beaufort and Phil Culverhouse for their valuable comments. Manuel Schneidereit (SIS Münster) and Rudolf Schmid (FEI Switzerland) helped solving several hardware and software problems. Robert Hofmann, Marcel Mettler, and Urs Gerber constructed the camera stand and the levelling trays for the ALFA system. We are grateful to Ursi Brupbacher for proof reading of the manuscript. Appendix: system description There are currently three systems operational at the Geological Institute of ETH Zürich. All systems automatically scan predeﬁned sample areas and capture either overview images (e.g., for plankton and sediment counts) or detailed images of single objects (e.g., for microfossil recognition and morphometry). Images are archived on CD-ROMs and can

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be either manually or automatically processed on any computer. Two of these systems, the incident LM and the SEM are currently used for automated image acquisition and morphometry only. The third system, a transmitted light microscope, is capable of both automated image acquisition and morphometry, and the online classiﬁcation of microfossils with neural networks. All systems have a similar basic setup consisting of a microscope with motorized stage, a digitizing unit, and PC with a remote control (for details see Fig. 1). Details of each system are described in the following. A1. ALFA, Incident light microscope The system consists of a black and white CCD video camera attached to a Wild MZ3 incident light stereomicroscope equipped with a motorised stage (Fig. 2a). The light source is a ﬁber optic ringlight (Volpi Intralux 4000, Cold Light Sources). The system is driven by a C-program developed at the ETH Zurich running under the imaging software analySIS3.0 . Several high-level imaging functions such as the automatic calculation of a gray-value threshold for object segmentation, detection of objects and extraction of morphological parameters were implemented in the C-program. The motorized stage is controlled via a serial interface (RS232) and image capturing is carried out with a video frame grabber (Grabbit SIS, 16 bit, 50 Hz, PAL, 768×576 pixels). We used the so called automater module provided by analySIS 3.0 to deﬁne the scanning area of a motorized stage (Märzhäuser L-Step 3 stage) and the automatic image analyzing procedures. The AUTOMATER module can be used to deﬁne the stage path (scanning area) and the automatic image analyzing procedures (macros) without any further programming knowledge. This package supports several stages, cameras, and microscopes from different companies (e.g., FEI , LEO and Olympus ). All components and their suppliers are listed in Table A1. In order to overcome elementary problems of ambiguously deﬁned and focused objects, a low-reﬂectance glass tray was constructed (Fig. 2 right, for details see sections “Autofocus with incident light microscopes” and “Illumination for incident light microscopy”). The system captures about 1000 images per hour, sharpens them, deﬁnes the object boundaries, and extracts the morphological parameters for each object, for example, diameter, area, perimeter, mean gray values, and roundness. This system has been successfully applied in several projects to document the size variability of planktic foraminifera assemblages over the last 65 million years (e.g., Schmidt (2002)). In this study, ca. 800 samples with 1.5 million images were captured and analyzed. The ALFA system is the ﬁrst step towards a fully automated robot, which also classiﬁes and recognizes particles such as foraminifera using a neural network classiﬁer. The current design of the system enables a broad application for automated granulometry in the size range from 63 µm to several mm and it is planned to extend the system to perform with online classiﬁcation for planktic foraminifera. A2. COGNIS Light, transmitted light microscope The heart of the system is a LEICA DMRXA transmitted light microscope equipped with three objectives (HCX Plan APO, Oil 100×/1.35 PH3, PL APO, Oil 40×/1.25 PH3, Pl APO,

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Table A1. List of all components and their suppliers used for the ALFA system. Item

Brand

Supplier

Light microscope

WILD MZ3

Leica Mikrosysteme Vertrieb GmbH, Lilienthalstrasse 39-45, D-64625 Bensheim, Germany, e-mail: [email protected]

Light System

Ring light Volpi Intralux 4000

Volpi AG, Wiesenstrasse 33, CH-8952 Schlieren-Zürich, e-mail: [email protected]

CCD Video Camera

no name

Special glass tray

custom made

Motorized stage

Märzhäuser L-Step 3 , 30 cm × 30 cm

PC, Intel Pentium II 233 MHz, 128 mb Ram, 2 Gigabyte Harddisk

Märzhäuser Wetzlar, In der Murch 15, D-35579 Wetzlar, Germany, [email protected] SIS, Soft-Imaging Software GmbH, Hammer Str. 89, D-48153 Münster, Germany, e-mail: [email protected]

Frame Grabber

Grabbit , SIS

ditto

Imaging Software

analySIS 3.0

ditto

Operating System

Windows 95

Microsoft

Controlling Software

Automater/personally developed

20×/0.60, PH2) and a LEICA DMSTC motorized stage (Märzhäuser 100 × 100 mm), which can house up to 3 slides (75 × 25 mm), and is controlled via a joystick or using a computer (Fig. 3). Furthermore, the standard microscope stand was extended by the addition of a polarizer and analyzer ﬁlter exchanger (for details see section “Illumination for incident light microscopy”). Attached to the trinocular head of the microscope is a highly sensitive, slow scan CCD camera (PCO SensiCam 1280×1024×12 bit resolution). The microscope is connected via a RS232 interface to a DELL Precison 530 1 GHz Dualprocessor PC (running Microsoft Windows 2000 ) and controlled by the COGNIS program developed at the ETH. COGNIS has a Windows-based menu system, which can be divided into three parts; microscope control, image analysis and neural networks (for details on the NN functions see A4). The complete system is capable of collecting images of coccoliths and other microfossil groups, from standard (75 × 25 mm), coverslipped, light microscope slides. The time taken to scan a slide varies considerably and is dependent on numerous factors. These include the density of the slide (i.e., the number of objects per frame), the user-deﬁned object capture settings (e.g., light dependent thresholds, size of objects), and the number and type of ﬁlter positions in a particular scan. In the numerous tests carried out

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Table A2. List of all components and their suppliers used for the COGNIS Light system. Item

Brand

Supplier

Transmitted Light Microscope

LEICA DMRXA

Leica Mikrosysteme, e-mail: [email protected]

Motorized Analyzer carousel with 5 analyzer positions each with a 9◦ offset, 1 position for phase-contrast

built in

ditto

Motorized Polarizer carousel, 5 polarizer positions with a 9◦ offset

custom made

ditto

Light System

12 Volt 100 Watt Halogen

ditto

CCD Video Camera

PCO SensiCam, 1280 × 1024 × 12 bit

PCO, Germany, [email protected]

Motorised stage

Märzhäuser 10 × 10 cm with 3 slide holder

Märzhäuser, [email protected]

Dell Precison 530, Intel Pentium 1 GHz Dualprozessor, 1 Gb Ram, 2 × 78 Gb Harddisk

Dell

Dell

Imaging Software

personally developed

Operating System

Windows 2000

Controlling Software

personally/DLLs provided by leica and PCO

Microsoft

so far, the rate of capture has been about one frame per minute. A single frame measures 40× 50 µm and contains 20–40 objects.All components and their suppliers are listed in TableA2. A3. COGNIS, scanning electron microscope The system consists of a Philips XL30 Lab6 Scanning Electron Microscope and a SIS ADDA II slow scan interface with 4000 × 4000 × 12 bit resolution. It is remotely controlled via the RS232 interface and a C-program running under the imaging software analySIS3.0 . Most microscope functions were implemented in this C-program developed at the ETH Zurich and combined with several high-level imaging functions that are already available within analySIS3.0 , such as the automatic calculation of a gray-value threshold for object segmentation, detection of objects and extraction of morphological parameters. Up to ten samples can be processed in a batch and the system automatically scans over a predeﬁned area of each sample capturing either overview images or detailed images of single objects at maximum magniﬁcation. In continuous scanning mode the system captures a maximum of 1000 images per hour. A typical batch run of, for example, three plankton samples each with 2100 overview images (slow scan images with 1400 × 1040 × 12 bit, line time 1.64 ms) at 2000× magniﬁcation, takes about 9 hours whereas a batch run with

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Table A3. List of all components and their suppliers used for the COGNIS system. Item

Brand

Supplier

Scanning microscope

Philips, XL30 LaB6

FEI Company,

Gun System

LaB6

ditto

Motorized stage

Internal 5 cm × 5 cm

ditto

PC, Intel Dual Prozessor, 400 MHz, 256 mb Ram, 2×76 Gb Harddisk

Dell Precision 410

Dell

Frame Grabber, Slow scan interface

Grabbit 756 × 578 × 16 bit, SIS, ADDA II 4000 × 4000 × 12 bit, SIS

SIS, e-mail: [email protected]

Imaging Software

analySIS 3.0

ditto

Operating System

Windows NT4.0 Service Pack 5

Microsoft

Controlling Software

personally developed/DLLs provided by SIS

10 sediment samples with each 1000 overview images (TV-Mode, 768 × 576 × 8 bit) takes about 11 hours. In a second mode, the system collects focused, centered images of individual particles at a maximum magniﬁcation of 30,000. In this mode, the system currently captures approx. 120 images/objects per hour. This system has been successfully applied in several projects to collect images of coccoliths with constant high quality for testing a statistical and neural network coccolith classiﬁer (Brechner 2000) and to collect overview images of plankton ﬁlter samples and sediment samples for counting of coccoliths (Bollmann et al. 2000; 2002a). It is planned to extend the system to perform online classiﬁcation of coccoliths. All components and their suppliers are listed in Table A3. A4. COGNIS artiﬁcial neural net work simulator The COGNIS neural network simulator is a user-friendly, Microsoft Windows-based program which permits the construction and training of ANN’s for various classiﬁcation tasks. The user has full control of the size, number, and connectivity of each layer and is guided through a set of sub-windows during the production of a network. Neural networks are essentially mathematical constructs and the COGNIS ANN simulator displays the ﬁnished NN in a format that is easy to visualize. Training is carried out with a training dataset ﬁle (.dsf), which can be produced within the program, from images in tagged image format (.tif), as well as tables of numerical data. During training, the user has full-control of all parameters, for example, the initialization of weights in the network and the number of times the training dataset is fed through the CNN. Trained networks can be saved, as can their corresponding dataset ﬁles, for further training or subsequent classiﬁcation. Classiﬁcation with CNN’s is performed from raw images of different sizes, which are

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adjusted to ﬁt the network, or by constructing a classiﬁcation dataset ﬁle for this purpose. With the classiﬁcation of images, copies of each classiﬁed image are placed in a subfolder corresponding to one of the output various categories of the CNN. In this way, the results of such a classiﬁcation can be checked visually using any graphics program that displays tif ﬁles. A text ﬁle (.txt) summarizing the results of the classiﬁcation is produced. The COGNIS ANN simulator is fully integrated with all other functions of the COGNIS program, including image processing, tagging and archiving facilities as well as the light microscope control options. On-line CNN classiﬁcation is now capable with the latest version of the COGNIS program. Using this function, which links the ANN simulator with the automatic collection of particles with the COGNIS-Light system, images are fed directly into a maximum of three pre-trained neural networks for instant classiﬁcation. References ATT Laboratories Archive, Olivetti Research Laboratory Database of Faces, http://www.uk.research. att.com/facedatabase.html. Bé A.W.H., Harrison S.M. and Lott L. 1973. Orbulina universa d’Orbigny in the Indian Ocean. Micropaleontology 19: 150–192. Beaufort L., de Garidel-Thoron T., Mix A.C. and Pisias N.G. 2001. ENSO-like forcing on oceanic primary production during the Late Pleistocene. Science 293: 2440–2444. Belgrano A., Malmgren B.A. and Lindahl O. 2001. Application of artiﬁcial neural networks (ANN) to primary production time-series data. J. Plankton Res. 23: 651–658. Belyea P.R. and Thunell R.C. 1984. Fourier shape analysis and planktonic foraminiferal evolution: The Neogloboquadrina - Pulleniatina lineages. J. Paleontol. 58: 1026–1040. Bishop C.M. 1995. Neural Networks for Pattern Recognition. Clarendon Press, Oxford, 482 pp. Bollmann J. 1997. Morphology and biogeography of Gephyrocapsa coccoliths in Holocene sediments. Mar. Micropaleontol. 29: 319–350. Bollmann J., Brabec B., Cortés M.Y. and Geisen M. 1999. Determination of absolute coccolith abundances in deep-sea sediments by spiking with microbeads and spraying (SMS method). Mar. Micropalaeontol. 38: 29–38. Bollmann J., Cortés M.Y., Lenz B., Llinas O., Müller T. and Reuter R. 2000. Distribution of living coccolithophores North of the Canary Islands: Vertical, seasonal and interannual variations. EOS Transactions AGU 81 48: F204. Bollmann J., Cortés M.Y., Haidar A.T., Brabec B., Close A., Hofmann R., Palma S., Tupas L. and Thierstein H.R. 2002a. Techniques for quantitative analyses of calcareous marine phytoplankton. Mar. Mircropaleontol. 44: 163–185. Bollmann J., Henderiks J. and Brabec B. 2002b. Global Calibration of Gephyrocapsa coccolith abundance in Holocene sediments for paleotemperature assessment. Paleoceanography 17: 7–1 to 7–9. Bown P.R. and Young J.R. 1998. Techniques. In: Bown P.R. (ed.), Calcareous Nannofossil Biostratigraphy. British Micropalaeontological Society Publication Series, pp. 16–28. Brechner S. 2000. Automatic coccolith classiﬁcation and extraction of morphological features in SEM images. Selected Readings in Vision and Graphics 5, Hartung-Gorre Verlag, Konstanz, 205 pp. Burke C.D., Full W.E. and Gernant R.E. 1987. Recognition of fossil freshwater ostracodes — fourier shape analysis. Lethaia 20: 307–314. CLIMAP Project Members, 1976. The surface of the ice-age earth. Science 191: 1131–1137. COSOD II Working Group Members, 1986. Report of the Second Conference on Scientiﬁc Ocean Drilling (COSOD II). Strasbourg. European Science Foundation.

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Lipps J. 1993. Fossil Prokaryotes and Protists. Blackwell Scientiﬁc Publications, Boston, 342 pp. Malmgren B.A. and Nordlund U. 1997. Application of artiﬁcial neural networks to paleoceanographic data. Palaeogeogr. Palaeoclim. Palaeoecol. 136: 359–373. Malmgren B.A. and Winter A. 1999. Climate zonation in Puerto Rico based on principal components analysis and an artiﬁcial neural network. J. Climate 12: 977–985. Ratmeyer V. and Wefer R. 1996. A high resolution camera system (ParCa) for imaging particles in the ocean: System design and results from proﬁles and a three-month deployment. J. Mar. Res. 54: 589–603. Ripley B.D. 1996. Pattern Recognition and Neural NetwSorks. Cambridge University Press, Cambridge, 403 pp. Schalkoff R.J. 1997. Artiﬁcial Neural Networks. MIT Press and The McGraw-Hill Companies Inc., New York, 421 pp. Schmidt D.N. 2002. Size variability in planktic foraminifera. Ph.D. thesis, ETH No. 14578, 121 pp. Schmidt D.N., Renaud S. and Bollmann J. 2003. Response of planktic foraminiferal size to late Quaternary climate change. Paleoceanography 18: 17–1 to 17–12. Schwarcz H.P. and Shane K.C. 1969. Measurement of particle shape by Fourier analysis. Sedimentology 13: 213–231. Swaby P. 1990. Integrating artiﬁcial intelligence and graphics in a tool for microfossil identiﬁcation for use in the petroleum industry. Proceedings of the 2nd Annual Conference on Innovative Applications of Artiﬁcial Intelligence, Washington, 203–218 pp. Weiss S.M. and Kulikowski C.A. 1991. Computer systems that learn: classiﬁcation and prediction methods from statistics, neural nets, machine learning and expert systems. Morgan Kaufmann Publishers Inc, San Francisco, California, 223 pp. Westbroek P., Brown C.W., Van Bleijswijk J., Brownlee C., Grummer G.J., Conte M., Egge J., Fernandez E., Jordan R., Knappertsbusch M., Stefels J., Verdhuis M., Van der Wal P. and Young J.R. 1993. A model system approach to biological climate forcing. The example of Emiliania huxleyi. Glob. Planet. Change 8: 1–20. Young J.R., Kucera M. and Chung H.-W. 1996. Automated biometrics on captured light microscope images of Emiliania huxleyi. In: Moguilevsky A. and Whatley R. (eds), Microfossils and Oceanic environments. Aberystwyth Press, Aberystwyth, pp. 261–280. Yu S., Saint-Marc P., Thonnat M. and Berthold M. 1996. Feasibility study of automatic identiﬁcation of planktic foraminifera by computer vision. J. Foraminiferal Res. 26: 113–123.

13. SOFTWARE ASPECTS OF AUTOMATED RECOGNITION OF PARTICLES: THE EXAMPLE OF POLLEN

I. FRANCE ([email protected])

FCS Caerau Llansadwrn, Gwynedd LL57 1UT Wales A. W. G. DULLER ([email protected])

picoChip Designs Ltd. Riverside Buildings 108 Walcot Street Bath, BA1 5BG UK G. A. T. DULLER ([email protected])

Institute of Geography and Earth Sciences University of Wales Aberystwyth, Ceredigion SY23 3DB Wales Keywords: Pollen, Classiﬁcation, Neural network, Automation, Microfossil, Autofocus

Introduction This chapter concerns the automated recognition of microscopic objects. The primary author has a background in computer science, not palynology; accordingly, the research reported here developed a novel image recognition system for the pollen classiﬁcation problem. Pollen provides a challenging target for image recognition systems for three reasons: (a) the narrow depth of ﬁeld requires accurate focusing on individual objects; (b) the high intra-class variability caused by the unconstrained orientation of the particles makes the recognition system’s job much harder; (c) the large number of pollen types requires a ﬂexible, extensible system. Given these difﬁculties, it is not surprising that an automated pollen classiﬁcation system has not yet been devised. Most of this work is applicable to the automated recognition of other microscopic objects, provided the objects are separate and not touching. In other applications, where 253 P. Francus (ed.) 2004. Image Analysis, Sediments and Paleoenvironments. Kluwer Academic Publishers, Dordrecht, The Netherlands.

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the objects are overlapping or touching and cannot easily be separated, other techniques are necessary in order to extract and recognise individual objects. If this is the case in your application, the literature on image analysis of blood cells is probably a good starting point (Di Ruberto et al. 2002). This chapter starts by describing a basic automated stage and camera set-up. Next, it discusses image acquisition, including correction for non-uniform illumination, foreground/background separation, and autofocusing. The chapter then brieﬂy discusses feature extraction (this is discussed in more detail elsewhere in this book). Finally, it provides a case study of a pollen recognition system developed by the authors. The case study includes a short review of other pollen recognition systems, followed by a description of the image analysis neural network, Paradise, which the authors used for the classiﬁcation. Results of a large experiment are presented. This experiment involved over 2000 images of pollen grains that were collected using the automatic techniques described in this chapter. The ﬁnal section looks forward to possible developments and future work. Acquisition of microscopic images This section discusses the basic requirements of a system for automatically acquiring images of objects on microscope slides. A basic set-up Figure 1 shows the elements required. The automated stage allows the computer to scan the slide and, importantly, to focus the images. A CCD camera attached to the microscope sends images to the computer system.

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The level of magniﬁcation of the microscope is important. The choice is determined to a large extent by the size of the objects one wishes to study. Higher magniﬁcations obviously provide a larger image, and thus a higher resolution. However, at higher magniﬁcation the objects can be harder to ﬁnd and the depth of focus is smaller; these factors can increase processing time considerably.

Acquiring the images There are three issues which must be addressed before images of individual objects on the slide can be obtained: the need to correct for non-uniform illumination of the slides, the need for automated focusing on the objects, and the need to separate individual objects from the background. Normally, the correction for non-uniform illumination is performed ﬁrst. Whether one should focus the entire image and then ﬁnd individual objects, or ﬁnd the objects and focus each of them individually, depends upon the nature of the material on the slides.

Correcting non-uniform illumination Unlike the case of many imaging applications, highly accurate analysis of the illumination is not necessary here. Microscopes are designed to reduce the non-uniform nature of the lighting. Nonetheless, some adjustment is sensible. Figure 2 shows a representation of an image of blank space taken with the microscope. The grey-level has been converted into height so as to emphasise the non-uniformity. The user obtains an image of a blank area of the slide in order to have an estimate of the lighting changes over the slide. This image is smoothed using a 5 × 5 averaging ﬁlter to reduce noise (Nederbragt et al., this volume). Then, in order to correct for the uneven illumination, the smoothed image is subtracted, on a pixel-by-pixel basis, from each new image obtained during the run. The non-uniformity of the lighting has not been observed to change during the course of a run; this is fortunate, since it means that the single image collected at the start of the run is sufﬁcient. If the circumstances are such that the lighting can change, the required corrections are more complex. Figure 3 illustrates the effect of the correction for non-uniform illumination upon a sample image.

Foreground / background discrimination The object segmentation takes place after non-uniform illumination has been corrected. This process separates the foreground objects from the background. In many applications, the background is uniform, whereas the objects of interest display variations in grey-scale intensity. In such circumstances, a simple variance measure can be used to distinguish between foreground objects and the background.

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The variance, var(i, j ) of the area around the pixel at (i, j ) can be calculated using: ! " " i+s j +s 2 1 "

var(i, j ) = 2 # I (k, l) − M(i, j ) , (1) w k=i−s l=j −s

Figure 2. The blank background image displayed as a landscape with the vertical direction representing the grey-level. Note the non-uniform nature.

Figure 3. Left: original image. Right: image after correction for non-uniform illumination. Note the more uniform nature of the background, especially the reduction of the bright spot just below the center of the image. Scale bar is 50 µm.

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where w = the width of the window used to calculate the variance, s = (w/2) − 1, I (x, y) = the value of the image pixel at (x, y), and M(x, y) = the mean value of the image in the window around the point (x, y). Figure 4 shows the result of this operation on an example image. A window width of 7 pixels was used to calculate the variance.

Figure 4. Left: original image. Right: image after variance analysis. Scale bar is 50 µm.

Having obtained the variance image, a common technique for clustering data, the kmeans algorithm (Umbaugh 1998), can be used to partition the image into 2 sets. A ﬁxed number of classes are selected, and each is assigned a centre. Data points are then assigned to the class whose centre is closest to the data point. An iterative algorithm then attempts to alter the class centres so that: (1) Each centre is the mean of the data points which are assigned to its class; (2) Each sample is in the class whose centre it is closest to. There are many techniques for achieving this in the literature. In our application, the initial clusters are chosen to be at 1 and 10, so as to produce an output in which pixels allocated to Cluster 1 can be taken as being background (lowest variance) and pixels assigned to Cluster 2 can be taken as being objects (highest variance). The result of this operation on the image in Figure 4 is the binary image shown in Figure 5. Here, pixels, which the algorithm has

50 µm Figure 5. The result of the k-means clustering algorithm.

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selected as possibly belonging to foreground objects, are in white; possible background pixels are in black. To extract the objects, pixels that are connected to each other can be linked to form groups of connected components. These components can then be ﬁltered by size to remove noise pixels or objects, which are too large to be of interest (in the pollen application, organic detritus and charcoal are often found; these are large and can be easily removed at this stage). Focusing The focal depth of most microscopes is not sufﬁcient to ﬁnd all objects within the same focal plane. In many cases, the objects being analysed are larger than the focal depth of the microscope. This is especially true when higher magniﬁcations are used (see also Bollmann et al. (this volume)). The image obtained from the camera can vary immensely with the focal position. Figure 6 shows a single grain of pollen photographed at different focal depths, which demonstrates the variability in image obtained.

Figure 6. A pollen grain captured at different focal points. Individual images are 40 µm accross.

Focusing must be performed before any other discrimination takes place; this is because badly focused objects can look like smears on the slide. There is a considerable amount of literature devoted to the problem of auto-focusing microscopes: Groen et al. (1985), Firestone et al. (1991), and Santos et al. (1997) give good reviews and comparisons of the most commonly used methods. These methods use a “focus function” to evaluate the quality of the focusing at each focal depth. The best focal depth is taken as being that depth at which the focal function is a maximum. Unfortunately, these methods are concerned with focusing on an object which has a unique “best plane”. These methods typically use objects such as a grid from an electron microscope and a lymph node tissue section. Many microscopic objects, such as pollen grains, do not ﬁt this type; they can be large, translucent, or both, and often have several surfaces and features that can be focused on at different depths. In all the studies, measures utilising the high-frequency content of the image were among the best focus functions evaluated. It is easy to see why this was the case. For a

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normal optical microscope, the blurring due to defocusing can be modelled as a convolution of the focused image with a Gaussian blurring ﬁlter B where each element of the ﬁlter, Bij , is given by Bij = KA e−A(i

2 +j 2 )

,

(2)

where A is inversely proportional to the amount of defocusing, and KA is a normalising constant that forces the sum of the elements of the ﬁlter to be 1. Figure 7 shows an image of a hand convolved with this blurring function. The values for A are 1, 10, and 20, with KA being 6.28, 62.51, and 125.66 respectively. This Gaussian convolution is equivalent to a low-pass ﬁlter being applied to the image. As the focal plane of the microscope is moved further from the focal plane of the object, the high-frequency component is increasingly attenuated by the low-pass ﬁltering of the blurring ﬁlter. A plot of the high-frequency content of an image against the focal position will show a peak at the focal plane of the object. Figure 8 shows this for a simulated situation. A white bar 5 pixels wide and 20 long was convolved with the blurring function to create a number of images corresponding to a range of different focal positions. The high frequency content of each image was calculated using 2D difference ﬁlter (see Umbaugh (1998)), and the results were graphed.

Figure 7. A hand image convolved with the blurring function with three different sets of parameters. Left: A = 1, KA = 6.28. Middle: A = 10, KA = 62.51. Right: A = 20, KA = 125.66.

The situation is more complex when features lie in several focal planes. Figure 9 shows the graph obtained when two bars are simulated, lying at −5 and +5 in the focal direction. This graph has two peaks, roughly situated at the focal planes for each of the bars. The minimum in the centre corresponds exactly to the average of the two focal planes. Figure 10 shows a set of graphs obtained from pollen grains; these graphs show the multimodal nature of the high-frequency focus function. The central focus position can be obtained by differentiating the focus function (with smoothing to suppress noise) and selecting the central zero-crossing of the derivative. We compared the focus position chosen by the algorithm with that chosen by a human operator. The algorithm was applied to 16 pollen grains from 4 species — Nymphaea alba, Crataegus monogyna, Plantago lanceolata and Polemonium caeruleum. The user focused on the pollen grain and recorded the focal setting; the focus was then altered so that the pollen grain was blurred; the auto-focusing procedure was then initiated. The average difference between the focus point chosen by the user and the point selected by the computer was 20 units, with a standard deviation of 17. Visual inspection reveals that this error is acceptable:

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Figure 10. Left column: focus function for real pollen grains. Right column: Numerical differential of the focus function. Top row: Nymphaea alba. Bottom row: Crataegus monogyna. The vertical line in each image represents the focus position chosen by a human operator. The horizontal lines show the derivatives selected by the algorithm.

Figure 11. A pollen grain captured at different focal positions. The left and right images are captured at +/− 20 focal units of the central image. Scale bar is 10 µm.

it amounts to less than 10 percent of the distance from the front of the pollen grain to the back. Figure 11 illustrates this with images of a pollen grain captured at the chosen focus point and at focal points 20 units on either side. Figure 12 shows examples of pollen grain images captured before and after application of the auto-focusing procedure.

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10 µm Figure 12. A number of pollen grains captured after auto-focusing. Top: before auto-focusing. Bottom: after auto-focusing.

Feature extraction Once a good quality digital photograph is obtained, it is possible to measure the image to extract the features that will be used to distinguish between different types of objects. There are many different measurements that can be made from digital images; Pirard (this volume) has dealt with a number of these techniques. Standard measurements include size and shape measures such as area, perimeter length, ratio of major and minor axes, and thinness ratio (see, for example, Umbaugh (1998)). In some cases the roughness of the edge of the object can be important; in such cases the fractal dimension can be taken (Huang et al. 1994; Jin et al. 1995). In many cases the surface texture of microscopic objects is useful as a classiﬁcation feature. There is a large literature on texture features; for a review, see Zhang and Tan (2002). This collection of extracted features can be used as the set of inputs to classiﬁcation systems such as those described in the next sections. Example: pollen classiﬁcation using a neural network The remainder of this chapter describes a microscopic image analysis system that has been developed to identify different types of fossilised pollen grain. Such a system has been frequently called for (see, for example, Stillman and Flenley (1996), Green (1997)), but a viable system requires much future work. There have been several investigations into the automation of microfossil counting, but most have concentrated on the classiﬁcation stage. Additional complications of automated image acquisition often lead to poor quality images of microfossils, and this can reduce the performance of a classiﬁer. Many techniques rely upon the surface structure of the objects of interest, in this case the pollen grains. This structure is not readily visible under optical microscopes; Scanning Electron Microscopy (SEM) must be used to obtain ﬁne detail. Vezey and Skvarla’s (1990) work, although not intended to be used for the automation of pollen counting, shows that a very high level of inter-species discrimination is a possibility when SEM images are used.

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Witte (1988) and Ping Li et al. (1998) have investigated the use of images obtained with an optical microscope. Witte used texture features, which had been found by Langford et al. (1990) to be successful with SEM images. The results were not very encouraging with the lower resolution obtained with optical microscopy. Ping Li used a combination of shape measures and a neural network (a multi layer perceptron, see later) to classify the pollen grains. The results were good, but the number of images used was lower than that required to give a reliable indication of the performance of the network. Haykin (1999) shows that if, when using a multi layer perceptron, one requires an error rate of less than 10%, one needs at least 10 times as many training examples as there are weights in the network. The classiﬁcation methods employed by the systems reported create ﬁxed classiﬁers based on the training data. If a new pollen type needs to be added, these methods require that the entire data set, old images and new, be used to retrain the classiﬁer. This retraining has to be performed by an expert in image processing.

Neural networks A neural network is an interconnected network of processing elements called neurons. These processing elements are modelled on the neurons of the brain. There are many varieties of neurons used in neural networks. All have a number of inputs and a single output (Fig. 13). Each input has a weight associated with it. The output of the neuron is a function of the inputs and the weights.

w1 Inputs

Output

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Figure 13. An artiﬁcial neuron. Each input has a weight associated with it as indicated by w1, w2 etc.

A common function used in the multi-layer perceptron is shown below. y=f

wi xi ,

(3)

i∈inputs

where y is the output of the neuron, wi is the value of the weight on input i, xi is the value of the ith input, and f () is the output function, which is often used to restrict the output to a desired range. A common neural network is the multi-layer perceptron (MLP) (see Fig. 14). In this network the neurons are arranged in layers. Each layer’s output acts as the next layer’s input. Typically, three layers are encountered: an input layer, a hidden layer, and an output layer. Each neuron in a layer takes its inputs from all of the neurons in the previous layer — this is known as a fully connected network. To train an MLP on a microfossil classiﬁcation task with, for example, 5 different output classes (types of object), one would create a network with 5 neurons in the output layer.

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Input Layer

Hidden Layer

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Figure 14. A fully connected 3 layer network.

In such a network, each output neuron would correspond to a different class of objects, and the neuron with the highest output value would be used to determine to which class the network decided an input belonged. The number of neurons in the input layer would usually equal the number of features extracted from the image in the earlier processing stages. The number of neurons which would be required in the hidden layer is an open question: it would have to be determined by trial and error. The training procedure is called back-propagation. A training example is presented to the network inputs and the resulting output is calculated. This is compared with the desired answer and an error is calculated. This error is then used to change the weights of the neurons, so that the next time the example is presented, the output should be closer to the desired output. The training set is presented to the network many times until the network has learned to recognise it effectively. This type of network is called a supervised network, since a supervisor needs to determine the correct class for each of the training examples. Once trained, the weights of the multi-layer perceptron must be ﬁxed. Any attempt to train the network with new data leads to it forgetting the old data. Unsupervised networks are another common type of network. These networks are selforganising; they group the training data according to their own internal deﬁnitions of similarity; they do not use externally imposed deﬁnitions. The adaptive resonance theory (ART) networks of Carpenter and Grossberg (Carpenter et al. 1991) are examples. These networks analyse their inputs and separate them into different classes. If a new input does not ﬁt any existing class, the network creates a new class. This process is controlled such that the network can learn to classify new data at any time without forgetting the original data. The Paradise neural network The work reported here uses the Paradise neural network developed by Banarse et al. (2000); it is loosely based on Fukushima’s (1980) Neocognitron and Carpenter and Grossberg’s (Carpenter et al. 1991) ART networks. Paradise is an unsupervised network and comprises three layers, each of which performs a different task (see Fig. 15). The ﬁrst layer, the feature extraction layer (FE layer), is responsible for detecting lowlevel features in the image. The operator determines these features before the training

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Classification Cell Layer

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Figure 15. An overview of the Paradise neural network architecture.

begins. In the network used here, the neurons are oriented Gabor ﬁlters (see, for example, Umbaugh (1998)); each is tuned to detect edges at a particular orientation and scale. The FE layer contains a plane of neurons for each feature. Within each plane the neurons have identical sets of weights. Each neuron is positioned over a point in the input image; its output represents the strength of the feature at that point in the input image. Figure 16 shows the output of two feature extraction planes (using Gabor ﬁlters oriented at 0◦ and 90◦ ), when they are used to ﬁlter a simple square image and a typical pollen image. The second layer, the pattern detection layer, is responsible for the detection of larger patterns built up from groups of features detected in the ﬁrst layer. These patterns might represent the edge of a microfossil object, or some detail of the internal structure. Each pattern is recognised by a pattern detection module (PDM); this is centred over a point in the image and recognises its pattern in an area around that point. The patterns are determined during the training procedure. The ﬁnal layer, the classiﬁcation layer, performs the classiﬁcation of the images.

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Figure 16. The output of the feature extraction layer. Top: a simple square. Bottom: a pollen image. From left to right: the input image; the output from the 0 degrees ﬁlter; the output from the 90 degrees ﬁlter; the sum of the outputs. Scale bar = 10 µm.

Table 1. Number of images in the training and testing sets. Taxa Plantago lanceolata Rumex acetosella Conopodium majus Dactylis glomerata

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364 517 225 600

363 517 224 600

Each neuron in this layer takes its input from a sub-set of the PDM outputs, thus giving a high output when the patterns to which it is connected are present in the image. The object class is determined by the neuron with the highest output in the classiﬁcation layer. It is the dynamics of this layer that give the network its ﬂexibility. If an image is not recognised by the network, the classiﬁcation layer creates a new neuron; this is trained on the unrecognised image and forms the basis for a new class. This ability allows the network to learn to classify new objects at any point in its life cycle; in theory it permits new pollen taxa to be added when required without retraining. This description of the Paradise network has been brief. For comprehensive treatment see Banarse (2000), France (2000), France et al. (2000). Data set and results We tested the network with 4 different pollen types. We prepared the pollen slide with a strong dilution; this was to ensure that the grains were sparsely distributed. We use an automatic collection procedure as outlined earlier in this chapter. We then randomly split the images into training and testing sets. Table 1 shows the pollen taxa and the number of images collected. Figure 17 shows a selection of images obtained for each of the pollen types.

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20 µm Figure 17. A selection of the images obtained for each pollen type. Clockwise: Plantago lanceolata; Rumex acetosella; Dactylis glomerata; Conopodium majus.

Training the network The network training takes advantage of a useful feature of the Paradise network: two or more trained networks can be combined to produce a new, larger network, one that recognises the images of the original networks. In this trial, four networks are trained, one for each pollen taxon. Each network produces a number of classes, each of which recognises a different view of the pollen type on which it was trained. These classes are then labelled by the operator with the pollen type upon which they were trained. Thus a distinction is made between the internal classes of the networks and the external classiﬁcation of pollen type. These four networks are then combined to produce a recognition network that is used to classify the test set. Table 2, below, shows the results. Note that the network rejects images that it cannot classify; if the network were training, it would create a new class at this point, but during testing it rejects such images as unknown. Accordingly, Table 2 shows the reject rate of the classes as well.

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FRANCE, DULLER AND DULLER Table 2. Recognition and rejection rates for the test sets. Taxa Plantago lanceolata Rumex acetosella Conopodium majus Dactylis glomerata

Correctly recognised

Incorrectly recognised

Rejected

302 (83.2%) 430 (83.2%) 193 (86.2%) 515 (85.8%)

48 (13.2%) 62 (12%) 21 (9.3%) 45 (7.5%)

13 (3.6%) 25 (4.8%) 10 (4.5%) 40 (6.7%)

Table 3. The internal class numbers and the pollen taxa which these classes recognise. Internal class 0–17 18–21 22–32 33–47

Pollen Taxa Plantago lanceolata Rumex acetosella Conopodium majus Dactylis glomerata

Figures 18 and 19 show a selection of the pollen grains classiﬁed in each of the networks internal classes. In these images, the numbers on the left hand side indicate the internal class number followed by the number of images that were recognised by that class. Table 3 shows the pollen taxa to which these internal classes correspond.

Future directions Scaleability and reliability The work presented here on pollen analysis needs to be tested on larger data sets, with more pollen species. Although the network can in theory be trained to recognise extra pollen taxa, this has not been thoroughly tested. Interference could occur between the pollen taxa and this may cause the network performance to drop. The network parameters may constitute another problem. Many parameters need to be set by the operator during training. At present, trial and error is the only method available for determining these parameters, but some possibilities for automated parameter setting have been suggested by France (2000). This problem is common to many types of neural network. The use of large data sets is essential for testing and training any classiﬁer. The more data one has, the better. Ideally, such data should represent the real world situation to which the system will be applied. Only in such circumstances can one have conﬁdence in the results of the trial. Large public data sets are also necessary for comparing different classiﬁers. Unless the tests are conducted on the same data, it is impossible to assess the relative abilities of competing solutions.

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Figure 18. Images from the test set which were recognised by the Paradise network (Part 1 of 2). For each image, the number on the left is the class number followed by the number of images recognised by that class.

Human accuracy

It is sometimes forgotten that, when analysing systems such as this, there is a need to compare the system with a trained human operator. This gives a baseline for future work.

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Figure 19. Images from the test set which were recognised by the Paradise network (Part 2 of 2). For each image, the number on the left is the class number followed by the number of images recognised by that class.

We are not aware of any studies to determine the accuracy of human counts on pollen, but a similar study was carried out by Culverhouse (1994) on images of plankton. Foreground / background separation The technique given here is sufﬁcient for a wide range of situations. Problems arise in only three situations: when the background is not sufﬁciently uniform, when the objects are likely to be clustered together, or when the objects are likely to be obscured by debris.

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Note that, in the latter case, the recognition of partial images is a major research topic in computer vision. For more information see, for instance, work by Martinez (2000) on the recognition of partially occluded faces. Summary This chapter looked at the use of automatic techniques for the analysis of microscopic objects. It showed all stages of the analysis, from the initial hardware set-up, through the focusing procedure and object detection, to the ﬁnal classiﬁcation of the objects. It presented a case study of a pollen classiﬁcation system that can be trained on a sample of images of pollen grains. The system was based on a ﬂexible neural network architecture: such networks trained on individual species can be combined to produce a discriminator for the set of species. The chapter presented results based on a trial with a large number of images. Experience in the face recognition community has shown that, for small data sets, it is easy to get good results; problems arise when attempts are made to scale up techniques to realistic amounts of data. Comparing the results of different techniques is also problematic. Large public datasets are required along with protocols for testing the recognition systems. References Banarse D., France I. and Duller A.W.G. 2000. Analysis of a self-organising image recognition neural network. Adv. Eng. Softw. 31: 937–944. Carpenter G., Grossberg S. and Rosen D. 1991. Art 2a — an adaptive resonance algorithm for rapid category learning and recognition. Neural Networks 4: 493–504. Culverhouse P.F., Ellis R., Simpson R., Williams R., Pierce R.W. and Turner J.T. 1994. Automatic categorization of ﬁve species of Cymatocylis (Protozoa, Tintinnida) by artiﬁcial neural network. Mar. Ecol. Progr. Series 107: 273–280. Di Ruberto C., Dempster A., Khan S. and Jarra B. 2002. Analysis of infected blood cell images using morphological operators. Image Vision Comp. 20: 133–146. Firestone L., Cook K., Culp K., Talsania N. and Preston Jr. K. 1991. Comparison of autofocus methods for automated microscopy. Cytometry 12: 195–206. France I. 2000. Application of pattern recognition techniques to palynological analysis. Ph.D. thesis, University of Wales, Bangor, 182 pp. France I., Duller A.W.G., Duller G.A.T. and Lamb H.F. 2000. A new approach to automated pollen analysis. Quat. Sci. Rev. 19: 537–546. Fukushima K. 1980. Neocognitron: A self organising neural network model for a mechanism of pattern recognition unaffected by shift in pattern. Biol. Cybern. 36: 193–202. Green D.C. 1997. The environmental challenge for numerical palynology. INQUA subcommision on data handling methods, Newsletter 15: 3–6. Groen F.C.A., Young T.I. and Ligthart G. 1985. A comparison of different focus functions for use in autofocus algorithms. Cytometry 6: 81–91. Haykin S. 1999. Neural Networks — A Comprehensive Foundation. Prentice-Hall, London, 206–208. Huang Q., Lorch J.R. and Dubes R.C. 1994. Can the fractal dimension of images be measured. Pattern Recognit. 27: 339–349. Jin X.C., Ong S.H. and Jayasooriah 1995. A practical method for estimating fractal dimension. Pattern Recognit. Lett. 16: 457–464.

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Langford M., Taylor G.E. and Flenley J.R. 1990. Computerised identiﬁcation of pollen grains by texture. Rev. Palaeobot. Palynol. 64: 197–203. Li P., Flenley J.R. and Empson L.K. 1998. Classiﬁcation of 13 New Zealand pollen patterns using neural networks. Proc. Int. Conf. on Image and Vision computing, Auckland, 120–123. Martinez A.M. 2000. Recognition of partially occluded and/or imprecisely located faces using a probabilistic approach. Proc. IEEE Int. Conf. Computer vision and pattern recognition. Santos A., De Solorzano O., Vaquero J.J., Pena J.M. and Malpica N. 1997. Evaluation of autofocus functions in molecular cytogenic analysis. J. Microsc. 188: 264–272. Stillman E.C. and Flenley J.R. 1996. The needs and prospects for automation in palynology. Quat. Sci. Rev. 15: 1–5. Umbaugh S.E. 1998. Computer Vision and Image Processing. Prentice Hall International Editions, 515 pp. Vezey E.L. and Skvarla J.J. 1990. Computerised feature analysis of exine sculpture patterns. Rev. Palaeobot. Palynol. 15: 187–196. Witte H.J.L. 1988. Preliminary research into possibilities of automated pollen counting. Pollen Spores 30: 111–124. Zhang J.G. and Tan T.N. 2002. Brief review of invariant texture analysis methods. Pattern Recognit. 35: 735–747.

14. MULTIRESOLUTION ANALYSIS OF SHELL GROWTH INCREMENTS TO DETECT VARIATIONS IN NATURAL CYCLES

ERIC P. VERRECCHIA ([email protected])

Institut de Géologie Université de Neuchâtel Rue Emile Argand 11 2007 Neuchâtel Switzerland Keywords: Wavelet transform, Spectral analysis, Fourier analysis, Power spectrum, Shell growth, Freshwater clams, Environmental record

Introduction In the last ten years, wavelet transform has become a standard method of spectral analysis for digital signals and images. Its ability to cope with both spatial and frequency localizations and its low cost in terms of computational complexity are the main reasons for its success. This paper provides an introduction to multiresolution analysis, which is closely related to discrete wavelet transform. Multiresolution is also called multiscalar analysis, because of its ability to extract information at various scales. Wavelet transform has been compared to a mathematical microscope (Burke Hubbard 1995). An application of multiresolution analysis is taken from environmental sciences, using shell growth increments to illustrate variations in environmental conditions. After a short overview of the reasons that have led to the concept of wavelet analysis, special emphasis will be put on the use of wavelet and scaling bases. The reconstruction technique, which allows a particularly simple and natural presentation of the results, will be also discussed. Spectral analysis The principle of spectral analysis Spectral analysis of a given signal (variations of an element’s concentration through time, variations of bed thickness, etc.) is mainly based on the decomposition and the projection of the initial raw signal onto a new space, where it is possible to distinguish the various elements (signals or functions) composing the initial data. In other words, spectral analysis is a kind of principal component analysis in which each signal is decomposed into a sum of elementary signals projected onto a new orthogonal space (equivalent of principal components). Each 273 P. Francus (ed.) 2004. Image Analysis, Sediments and Paleoenvironments. Kluwer Academic Publishers, Dordrecht, The Netherlands.

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axis (each principal component) in this space represents a part of the signal variance. Obviously, the initial signal can be reconstructed by summing all its elementary signals (the sum of all principal component variance is equal to the total variance of the initial data set). Each decomposition can be inverted for signal reconstruction: the reconstruction is the operation going from the space of projection back to the initial signal space. However, during reconstruction, the initial signal can also be ﬁltered by using only part of its decomposition, ignoring for example signals bearing low information (low variance). Therefore, the principle of spectral analysis is the following: the raw signal is projected onto another space where it can be decomposed in a new orthonormal basis where each element includes a part of its variance, and then some part of the decomposition elements are selected to reconstruct a ﬁltered signal by an inverse method. A corollary of this principle is that it can provide information on the elementary signals that contain the most important part of the initial signal information (the most important variance). Therefore, it is possible to identify which signals are the most important components of the raw initial signal. If the initial signal is a function of time, it will be possible to detect the main frequencies composing it. In terms of paleoenvironments, this means that some important natural periodic events, such as tides, sun spots, or Milankovitch cycles, can be detected from natural variables recorded through time (bed thickness, calcium carbonate content, major or trace elements concentrations, etc., see Schwarzacher (1993)). The most conventional method used for spectral analysis is Fourier analysis. Fourier analysis Fourier analysis is based on the principle that a composite signal of a period T can be decomposed into a sum of constant and trigonometric functions between 0 and 2π , and respectively of periods T , T2 , T3 , . . . , Tn , according to the expression: 2π 2π t + ϕ1 + A2 · cos 2t + ϕ2 Sn (x) = A0 + A1 · cos T T 2π 2π (1) 3t + ϕ3 + · · · + An · cos nt + ϕn . +A3 · cos T T The different values of An are called the amplitudes of the various n harmonics, which are the n trigonometric elements of the sum. Therefore, the harmonics are elementary sinusoidal functions of periods T , T2 , T3 , . . . , Tn with their associated ϕn , which are the phases at the origin, i.e., the difference between the origin and the starting point of the function on the Oy axis. The Fourier series is characterized by a graph or a bar chart, called a spectrum, on which each harmonic is plotted in function of its associated amplitude. Let us take a simple example to illustrate the relationships between a signal and the spectrum of its Fourier series. The graph in Figure 1 gives the shapes of a series of sinusoids of increasing frequencies (1F, 2F, 3F, 5F , and 7F ). Imagine that we sum all of these functions, but we subtract the ﬁfth one and we double the values of the third one. The composite signal obtained is deﬁned by the following equation: f (x) = sin(x) + sin(2x) + 2 sin(3x) − sin(5x) + sin(7x).

(2)

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The Fourier spectrum of this composite signal (see Fig. 2) is the picture of the value (the amplitude) of each function (each harmonic) we have summed. Therefore, the spectrum is supposed to give the amplitudes of the various harmonics in ascending order, i.e., harmonics 1 (for the ﬁrst frequency, called the fundamental harmonic), 2 for the second frequency, and so on. In equation (2), the frequency of the signal is given by the successive values in front of the variable x and the amplitude by the multiplicative coefﬁcient in front of the function. In conclusion, the ﬁrst, the second, and the seventh harmonics have an amplitude of 1, whereas the fourth and the sixth harmonics, have an amplitude of 0 (they do not appear in the equation, i.e., the sum). The third harmonic has an amplitude of 2 and the ﬁfth harmonic an amplitude of −1. Nevertheless, because − sin(5x) = sin(5x + π ), the amplitude is considered to be 1, but the phase is π. All the other harmonics have a phase equal to 0. The Fourier spectrum of the function given in equation (2) is a bar chart showing only the amplitudes (Fig. 2). The function given in equation (2) describes a stationary signal, which means that the signal is invariant through translation. In this case, the solution of the Fourier analysis is

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trivial. But for non-stationary signals, such as natural images, the solution is not obvious and the interpretation is often fairly complex. The spectrum loses all the local information and therefore makes the interpretation in terms of space (or time) almost impossible (Fig. 3). To summarize, Fourier analysis, and its operator the Fourier transform, allows space to be changed by projecting the signal into Fourier space where it is represented by the various frequencies composing the original signal. The Fourier transform of a signal is given by: +∞ f$(ω) = T Fourier f (ω) = f (t)e−iωt dt, (3) −∞

where f$(ω) describes the spectral behavior of the function f (t). Nevertheless, during the integral (or summation) calculation, all time and space location information is lost for non-stationary signals. Other methods have to be found to keep local information and frequencies. Wavelet transform The advantage of wavelet transform In the Fourier transform of a signal, the information given is a spectrum in which the main harmonics and their respective amplitudes can be seen. Nevertheless, the local information is lost and the spectrum is an image of the signal as a whole. For example, a bird song can be considered as a succession of various notes. By analyzing this “song signal” using the

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Figure 3. Fourier portrait and its Fourier transform. On the top right: moduli (amplitudes). On the bottom right: phases.

Fourier transform, it is possible to determine if these notes are present in the song and their respective amplitudes. However, Fourier analysis is not capable of determining at what time a particular note appears in the song, i.e., the location information is lost. This lack of location information in Fourier analysis has been noticed by Gabor (1946). An attempt to keep the spatial location of information characterized by some speciﬁc spectral properties led to the concept of the sliding windowed Fourier transform. The associated transform to this operator is called the short time Fourier transform (STFT) or windowed Fourier transform. The function, or moving window g(s − t) where t is the translation parameter, is applied to the signal and the Fourier transform is applied to the signal within the window as the window is moved. The general formula of this transform is (see for example Truchetet (1998) or Addison (2002)): +∞ f (s)g(s − t)e−iωs ds. (4) T STFT f (t, ω) = −∞

This transform is identical to the conventional Fourier transform, but with a multiplication of the exponential member by a window function. The t parameter is a translation parameter allowing the preservation of the time aspect of the signal during the transform. Therefore, the signal is analyzed in a window of a ﬁxed dimension. The tiling in the spatiofrequency domain is the same for all frequencies. Unfortunately, the window is too narrow for low frequencies, but not narrow enough for high frequencies. In conclusion, this analysis is not optimal: it is obvious that a good frequency accuracy at high frequency needs less space (for a given number of periods) than at a lower frequency. To conclude on short time Fourier transform, the result is an analysis taking into account the time domain, but in

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which the quality of the frequency analysis is good only for average frequencies (neither low nor high). The tiling aspect of the time-frequency domain is illustrated in Figure 4. In the conventional Fourier transform, the signal is decomposed into various frequencies, but the graph does not give any information on the location of these frequencies. In the STFT, the regular tiling preserves part of local but ﬁxed information on the frequencies, although it is not accurate for low or high frequencies. On the contrary, this trade off between spatial and spectral resolution is naturally provided by wavelet transform, in which stretching and translation of a unique analyzing function, called the “mother wavelet”, is used to scan the whole spatio-frequency domain.

Wavelet transform theory The continuous wavelet transform has the following expression: 1 T wavelet fa,b (t) = √ a

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the frequency: the smaller a, the less temporally wide the wavelet (the analyzing function), therefore, the higher the central frequency of the spectrum (Truchetet 1998; see Fig. 4). Historical examples of such mother wavelets are given by Morlet’s wavelet: x2 1 ψ(x) = √ e− 2 e−iω0 x 2π

(7)

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transform (DWT) of a continuous signal f (t) (Addison 2002): +∞

−j −j T dwt fj,n (t) = a0 2 f (t)ψ a0 t − nb0 dt. −∞

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The choice of a0 = 2 and b0 = 1 leads to the dyadic transform. It is certainly the most commonly used wavelet transform and an example of its application will be given later. Nevertheless, other possibilities exist, such as rational values for a0 . In this case, it is common to call j the scale of resolution. A major point is that these transformations can be extended to signal analysis in two or more dimensions. In addition, under given conditions, the wavelet transform has an inverse transform (IWT) like the Fourier transform (IFT). For example, this inverse wavelet transform allows results to be displayed after multiresolution analysis. Multiresolution analysis What is multiresolution analysis? The principle of the multiresolution approach is based on a theory deﬁning linear operators allowing analysis of a signal at various scales. The most well known method is based on (j ) Mallat’s dyadic algorithm (Mallat 1989a, b, c). A signal an including n components at n scale j (Fig. 6A) is split into two signals with 2 components, the signal of details and the signal of approximation. Each of these two signals are obtained by applying two ﬁlters on (j ) an , h˜ and g, ˜ their size becoming n2 by suppression of one out of two points. The obtained approximation signal becomes the signal of the scale i + 1. Reconstruction of the signal at the scale i from signals at the scale i + 1 is obtained by an inverse process: insertion of null samples in order to get signals of size n, application of two ﬁlters (conjugates of the former ones), and then summation of the two obtained signals (Fig. 6A). In other words, the multiresolution approach is a sort of mathematical microscope that can be used to observe a signal from near or far. This zoom-in effect is driven by a scale function that dilates through the various scales. The signal projected onto this function gives a representation of the original signal at a higher scale. This representation (projection coefﬁcients) leads to a backward zooming from the original signal, explaining the term of approximation coefﬁcients used in such operations. To reconstruct the signal from the approximation coefﬁcients, it is necessary to project the original signal onto an orthonormal subspace (to keep all the information). The function generating this second vectorial space is a wavelet. To summarize, the signal is projected onto a scale function, creating an approximation signal, and onto a wavelet to get back all the information lost during the ﬁrst projection. This second projection includes all the details of the original signal. Finally, the scale function is a sort of low pass ﬁlter, whereas the wavelet is a high pass ﬁlter. Therefore, details are the high frequencies of the signal. The multiresolution scheme used in this paper has been proposed by Mallat and Meyer (Mallat 1989a, b, c; Meyer 1990) and is based on an orthonormal projection of the signal to be analyzed onto a series of embedded closed subspaces Vj with Vj ⊂ Vj −1 . The orthogonal complement of Vj in Vj −1 is Wj with Vj −1 = Vj ⊕ Wj , as explained above and illustrated in Figure 6. An orthogonal wavelet basis exists for these subspaces. This

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multiresolution analysis is dyadic if f (x) ∈ Vj ⇒ f (2x) ∈ Vj −1 . The an are called the coefﬁcients of the approximation function (or approximation coefﬁcients) and the j dn , the wavelet coefﬁcients (or the detail coefﬁcients) for the scale j . Mallat (1989b) has demonstrated that the projection onto each subspace can be performed by a simple convolution product between the digital signal constituted by the coefﬁcients and a unique digital ﬁlter. Taking the scaling function ϕ(x), a wavelet function ﬁlter ψ(x) allowing the multiresolution analysis has to be found such that it is orthonormal to ϕ(x) (Daubechies 1988; Viscito and Allebach 1991). By only considering the bi-orthogonality between ϕ(x) and ψ(x), the ﬁlters can be built as recursive ones with a low number of coefﬁcients (Delyon 1993). This is exactly the case if a B-spline function is chosen for ϕ(x). An illustration of multiresolution analysis In order to illustrate the concept of multiresolution analysis, a natural signal will be decomposed at ﬁve different scales, each of them being characterized by its detail and approximation coefﬁcients. The natural signal (s) is built using successive thicknesses of

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210 layers of varved sediments, deposited in a proglacial lake during the Last Glacial Maximal in the Jura Mountains (France). The thickness in mm is plotted on the y axis and the number of successive laminae is on the x axis (Fig. 7). The mother and scaling wavelets used for the analysis are the Haar wavelets, as shown in Figure 5 and deﬁned in equation (8). The various approximation coefﬁcients (the following an with n ∈ [1, 2, 3, 4, 5]) and detail coefﬁcients (the following dn with n ∈ [1, 2, 3, 4, 5]) have been calculated using the convolution between the Haar scaling wavelet and the Haar mother wavelet, respectively. The results are given in Figure 7. It is obvious that the approximation coefﬁcients, from a1 to a5 following the various scales, has a smoothing effect on the initial signal. Compared to the Fourier transform which affects the signal as a whole, this smoothing effect does take into account the distribution of the various peaks, depending on their location, i.e., the local impact (or contribution) of the various frequencies composing the signal. In addition, a signal at a given scale, e.g., 2 is the sum of the detail and approximation coefﬁcients of scale 3. The scale-time tiling given in cf s represents the value of the wavelet coefﬁcient at each scale (from 1 to 5). The tiles are wider at scale 5 because they represent a more dilated function than at scale 1, for example. The lighter the color of the window, the higher the

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Figure 8. Principle of wavelet and multiscalar analysis. During the wavelet analysis step, a raw image, e.g., at scale 5 (Sc. 5), is ﬁltered into two sub-images constituting the image at scale 4 (Sc. 4), and resulting from the combination of approximation and detail coefﬁcients. This analysis can be performed until scale 1 (Sc. 1), each time by analyzing the detail coefﬁcient image of the former scale level. In the reconstruction step example, only detail coefﬁcients at scale 1 are kept to rebuild the ﬁltered image.

coefﬁcient (in absolute value). Note that all the detail coefﬁcients are centered on the y = 0 axis. A general cascade algorithm As seen in the paragraph above, the reconstruction of details at scale j is performed by taking the coefﬁcients dj , computed by the analysis of the signal s, and cancelling all the other coefﬁcients for each of the other scales. These coefﬁcients will constitute the approximation at the zero scale of the projection of the signal s on the subspace Wj (see Fig. 6B, C and D). Technically, the method is divided into two main steps (Fig. 8). First a multiresolution analysis, according to the Mallat algorithm (see Fig. 6A), is processed to compute the approximation and detail coefﬁcients at scale j , giving aj and dj . Then, a reconstruction synthesis is made using only the coefﬁcients of approximation and/or detail, corresponding to the explored scale. The result provides a non-subsampled view of the projection at a given scale j . This will be critical to detect variations without losing any information as demonstrated in the following natural example. Application to growth increment detection Methodology The method described above has been used to extract growth increments at various resolutions from Holocene freshwater shells in order to demonstrate that they are able to record environmental ﬂuctuations during their growth. Anodonta cygnae L. is a freshwater mussel that has a maximum 18 year lifespan (8–10 years on average). During the biomineralization of their shell, they record environmental variations at various scales, as marine shells do (Rhoads and Pannella 1970). Nevertheless, freshwater environments do not provide

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the buffered conditions that the ocean does and it is often difﬁcult to link shell growth increments with periodic and/or regular environmental conditions (Downing et al. 1992). In this particular case, it seems that the best method for environmental signal deconvolution remains wavelet analysis. The orthonormal basis used in this application is built using cubic B-splines, a symmetric function (Olkkonen 1995). The image is decomposed using multiresolution analysis. At this stage, an approximation of the target projection is reconstructed. For example, the result of the computation for the reconstruction, in which the approximation coefﬁcients have been deleted from the largest scale, is equivalent to the reconstruction of the approximation of f − Aj f (Diou et al. 1999). Since the projection operator is linear: a0 (f − aj f ) = a0 f − a0 (aj f )

(10)

therefore, a0 (f − aj f ) = aj f + a1 f + d2 f + · · · + dj f − aj f, a0 (f − aj f ) = d1 f + d2 f + · · · + dj f. This principle is illustrated in Figure 8, showing the two steps, i.e., coefﬁcient extraction using wavelet transform and reconstruction at the various selected scales using either detail or approximation coefﬁcients. An analysis of detail coefﬁcients at different scales will be performed on the prismatic layer of an Anodonta cygnae L. shell. Consequently, the prismatic layer’s microtopography has to be recorded as a range image, i.e., a grey level image in which the grey level is related to the relative altitude of each pixel. Detection of the main cycles related to environmental variations will be performed at various scales of resolution, using the relative differences in the microtopography of this prismatic layer. From the raw range image (Fig. 9A), wavelet analysis is used to extract detail coefﬁcients and to reconstruct the ﬁltered image at a given scale (Fig. 9B). A microtopography signal is extracted from this new image in one or two dimensions (Fig. 9C) and a spectral analysis is performed to detect the main cycles (Fig. 9D). Before any mathematical treatment, the shell topography (Fig. 10A) has to be cleaned in diluted hypochlorite to remove the organic periostracum, because the prismatic layer develops under this organic matrix. The prismatic layer records the various rates of CaCO3 deposition (Fig. 10B, C), reﬂecting the environmental conditions during organism ontogenesis. In order to obtain the most detailed information possible from the shell microtopography, the clean shell surface is scanned using a Replica 500 3D scanner. This scanner is of the stripe sensor type and uses the optical triangulation method to generate the range image. The spatial resolution of the scanner is 20 µm in z (altitude) and 50 µm in the x and y plane (Toubin et al. 1999). The range image dimensions (Fig. 9A) are 512 × 128 × 256 (x, y, and z, i.e., the number of grey levels). Each dimension is obviously a power of 2. The scanned prismatic shell layer is approximately 2.5 cm long and 0.7 cm wide. Because of the chosen algorithm and the image dimension (x = 27 ), a maximum of seven levels of resolution (or scale) is possible. For each scale, approximation and detail coefﬁcients can be extracted. Figure 11 shows an example of the differences between image reconstruction using either approximation or detail coefﬁcients. On the left, the approximation coefﬁcients essentially record the general curvature of the shell, whereas the detail coefﬁcients show an obvious cyclicity on the right hand side.

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Figure 9. Method used in this paper.A) Raw range image obtained with a 3D scanner. B) Multiscalar analysis using wavelets: the raw image has been studied at seven different levels of resolution, each of them being characterized by detail and approximation coefﬁcients. Here, the image represents the reconstruction using detail coefﬁcients at scale 4. C) From the ﬁltered image, a grey level line can be sampled to show the variation of detail coefﬁcients at scale 4. D) From this 1D signal, a conventional Fourier spectral analysis can be performed in order to detect cycles.

Before performing the wavelet analysis on the raw range image, one problem is still pending. What is the signiﬁcance of a growth ring? In other words, what is the relationship between pixels, prisms and time? An investigation on the prism growth rate of A. cygnae L. is necessary in order to determine the signiﬁcance of the growth increments. Growth increment calibration Bivalves show differently colored bands (annuli) that are thought to be due to environmental variations such as relative content of calcium and organic matter caused by temperature or anaerobiosis (Downing et al. 1992). These factors are mainly related to climatic and seasonal variations (cold temperatures, rain and runoff waters, etc.). For example, annual winter rings can be packed as a single thick and dark annuli due to decreasing biogenic activity (cold temperature) and high dilution of calcium during rainy months. Other species simply show growth cessation during winter (after September) because the mussel becomes endobenthic, passing the winter buried in the sediment (McCuaig and Green 1982). In

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20 mm

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Figure 10. Example of an Anodonta cygnae L. specimen. A) General view of shell’s external surface of the freshwater mussel. Growth rings are obvious. The black rectangle shows the approximate position of the 3D scanned surface. B) Scanning electron microscope (SEM) view of a clean surface (the organic periostracum has been removed). Multiple annuli appear, some of them being fused, showing a thicker accumulation of calcium carbonate. C) SEM view showing microtopography of the shell. The surface is constituted by the top of the prismatic layer. Three very high frequency annuli can be observed. These annuli can be detected by the resolution of the 3D scanner.

addition, some Anodonta form an average of 0.65 to 0.42 annulus yr−1 , and the rate of formation of these annuli can vary systematically with body size (McCuaig and Green 1982). Because of the difﬁculty to relate growth rings to a particular time line, due to clam ontogenesis as well as their volatility to record seasonal variations, investigations have been made on the growth of A. cygnae L. sampled in a man-made lake at Saint-Ciergues, 70 km north of Dijon (France). The lake environment is characterized by a semi-continental climate with cold winters, mild summers, 80 to 100 days of frost and 800 to 1000 mm of precipitation per year. Sediments are mainly constituted by calcareous muds originating from the marly watershed. The best method to evaluate the growth rate is to consider each dark ring as a mark without any particular signiﬁcance in terms of time for the moment. A population of 14 individuals of the same area have been used to plot increments. Increments have been identiﬁed using the variable darkness of lines on the shell surface. In “Anodonta, rings are especially clear” (McCuaig and Green 1983, p. 437). The Ford-Walford plot (Walford 1946) is used to calculate an unbiased index of growth, k, because it is based on the regularity

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Figure 11. Example of results obtained by wavelet and multiresolution analysis on a shell range image. Left, from top to bottom: image reconstructed using approximation coefﬁcients at scale 7. Pseudo 3D projection of the image showing the general curvature of the shell. Cross section based on approximation coefﬁcients showing the general curvature of the shell. The plateau corresponds to a juvenile stage, when growth is fast. Right, from top to bottom: image reconstructed using only detail coefﬁcients at scale 7. Pseudo 3D projection of the image showing that the general curvature of the shell is not visible anymore. The analysis “ﬂattens” the shell. Cross section based on detail coefﬁcients showing at least three main growth rings at this scale. One pixel represents two days of growth.

rather than the annularity of growth increments. The growth of a bivalve shell is generally described by von Bertalanffy’s (1938) equation:

Lt = L∞ 1 − e−k(t−t0 ) ,

(11)

where Lt represents the length of the organism at time t (age), L∞ , the asymptotic length, i.e., the theoretical maximum length an organism would reach at an inﬁnite age, k, Brody’s growth constant depicts the rate at which the organism’s size approaches L∞ , and t0 , the theoretical time at which we have L0 (Anthony et al. 2001). The higher the k value, the more slowly growth approaches the limiting length (Walford 1946). The equation’s parameters can be estimated using linear regression analysis of the Ford-Walford plot (Anthony et al. 2001). Therefore, a 1−b

(12)

k = − ln b.

(13)

L∞ = and

As Anthony et al. (2001) noted, in the absence of a known age-at-length relationship, t0 of equation (11) is impossible to estimate. Anthony et al. (2001) propose a reinterpretation of

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von Bertalanffy’s equation by introducing the parameter L0 instead of t0 as suggested by Southward and Chapman (1965), leading to the following equation: Lt = L∞ − (L∞ − L0 )e−kt

(14)

L0 is still difﬁcult to estimate, but Anthony et al. (2001) propose to take the glochidia (mussel larvae) as a plausible approximation of size at t = 0. This size is around 0.35 mm in the case of A. cygnae L. (Bauer 2001). Equation (14) can be rearranged in terms of time as a function of length, as proposed by Anthony et al. (2001): ) * ) * (Lt − L∞ ) 1 t = ln − × − . (15) (L0 + L∞ ) k The Ford-Walford plot provides the values for a = 8.577 and b = 0.937 used in equations (12) and (13). In the Anodonta samples from Saint-Ciergues, k = 0.065 (log k = −1.18) and L∞ = 135.935 mm. The value of k for this kind of freshwater mussel is low but consistent with the ones given by Bauer (2001, p. 236, e.g., log k = −1.02) or calculated by Anthony et al. (2001, p. 1352, e.g., k = 0.055 for the freshwater Unionidae Lampsilis siliquoidea). In addition, the ecological environment of the Saint-Ciergues lake probably provides not more than 260 days of active biomineralization for A. cygnae L., due to long winter cold conditions. Using all this information, it is possible to approximate the mean growth rate of A. cygnae L. at Saint-Ciergues. The part of the shell that has been 3D scanned belongs to the juvenile and medium period of growth. The total distance from the umbo to the end of the range image is 33 mm (Fig. 10A). The general curvature of the scanned part is shown in Figure 11 by the approximation coefﬁcients. There is a plateau, corresponding to the end of the fast juvenile growth, followed by a slope attributed to a slower development of the shell. Nevertheless, a mean growth rate can be calculated, providing an approximation for the general growth constant. Using equation (15), the age of the shell from the umbo to the end of the part scanned can be calculated with L0 = 0.35 mm, L∞ = 135.93 mm, k = 0.065, and Lt = 33 mm. The result gives an age of 4.31 years. This ﬁgure is perfectly reasonable: on Figure 11, the detail coefﬁcients shows three main increments and, on Figure 10A, it can be seen that at least one more major annulus can be added to the 3D scanned zone. It seems likely that, in this case, the major increments could be related to annual rings. Another age has been calculated on the largest and oldest A. cygnae L. sampled at Saint-Ciergues using the same variables but with Lt = Lmax = 95.5 mm. The result gives an age of 18.69 years. This ﬁgure is still reasonable regarding the oldest possible age for A. cygnae L. Using these ages, it is possible to calculate an approximation of the growth rate in µm per day. Considering that biomineralization is effective 260 days a year, the shell part between the umbo and the end of the scanned zone has a mean growth rate of: 33, 000 = 29.4 µm · d−1 . 4.31 × 260

(16)

This ﬁgure has to be considered as a sort of an average between the juvenile fast growth step and its slower development in the older part. If the total shell is included in the calculation, a ﬁgure of 19.37 µm · d−1 is obtained. For the part of the shell studied (the 2.5 cm scanned), a mean of 25 µm · d−1 seems perfectly reasonable. This rate is also conﬁrmed for this shell

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Figure 12. Reconstructed images at different scales (7, 5, 4, 3 and 1) showing the various frequencies of growth increments. Images have been built using detail coefﬁcients for each scale.

size by extrapolation of Ravera and Sprocati (1997)’s growth curve for A. cygnae L. from northern Italy. To our knowledge, there is no other information available in the literature. Consequently, a range image pixel has to be considered as an integration of two days of growth on average (the xy plane resolution of 50 µm divided by the biomineralization rate 25 µm · d−1 ). Results of spectral analysis Today, spectral analysis is a routine method to extract cyclicity from signals. It has been used with various success on marine shells, demonstrating the existence of semi-annual, monthly (with modulations) or fortnight periodicity (e.g., Rosenberg and Runcorn (1975)). The multiresolution analysis facilitates “noise” removal by focusing on each scale of the shell record. It also drastically diminishes the interactions of frequencies due to missing or superimposed increments or random phase changes during shell growth, which obviously result in spurious peaks in the power spectrum. Nevertheless, as in conventional spectral analysis on natural objects, each milestone of natural cycles is characterized by a family of frequencies rather than a single and isolated peak (Fig. 12).

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The frequency f is calculated as follows, n being an integer increment from 1 to 256: f =

n . 512

(17)

1 × 2. f

(18)

Therefore, the period is given by: P =

Multiplying the expression by 2 allows the conversion of a period measured in pixels into a period expressed in days. The spectral analysis of the images at the various scales gives the following results: •

At scale 7: two main frequencies appear at 5.86 × 10−3 (or 341 days) and 7.81 × 10−3 (or 256 days). The ﬁrst one can be considered as the annual signal, whereas the 256 day period is obviously an artifact of the dyadic algorithm (256 = 28 ).

•

At scale 6: the same artifact at 256 days is still present, with a sub-harmonic of the 341 day period at 170 days (f = 11.72), conﬁrming the semi-annual peak.

•

At scale 5: two major peaks are detected, but they are difﬁcult to interpret. They correspond to periods of 113 days (f = 17.57 × 10−3 ) and 102 days (f = 19.53 × 10−3 ).

•

At scales 4, 3 and 1: the monthly modulation starts to appear at scale 4 at f = 56.64 × 10−3 (35 days), at scale 3 at f = 82.03 × 10−3 (25 days), and conﬁrmed at scale 1 at f = 66.84 × 10−3 (30 days) and f = 82.03 × 10−3 (25 days). These monthly modulations have also been observed in marine bivalves (Dolman 1975). It is surprising to ﬁnd harmonics around the 28 day lunar month in terrestrial environments. This points out a possible inﬂuence of lunar tides in lakes.

•

At scales 3 and 2: the fortnight cycle (Dolman 1975) is strongly represented by a family of three peaks, at f = 115.23 × 10−3 (17 days) at scale 3, and at f = 132.81 × 10−3 (15 days) and f = 148.43 × 10−3 (13 days) at scale 2.

•

At scale 1: in addition to the monthly cycle described above, three other peaks conﬁrm periods already observed: the 341 day one and the artifact period at 256 days, accompanied by its 128 days (27 ) sub-harmonic.

Conclusion The multiresolution analysis using B-splines seems to be well adapted to extract spatial as well as frequency information from natural objects. Reconstruction of an image with given approximation or detail coefﬁcients at chosen scales allows the ﬁltration of a speciﬁc frequency band from the initial range image and visualization of the result, keeping spatial information. These results reveal details that are drowned out in the original raw signal. However, there is still a lot of work to do to develop new wavelet ﬁlters with better accuracy. In addition, multiresolution analysis based on the dyadic method remains a limited approach

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for scale resolution (which has to be a power of 2). Detection of natural cycles in natural objects using wavelet transform and multiresolution analysis is not only a challenge but also a promising ﬁeld for research in paleontology as well as in sedimentology. The researcher interested in the use of wavelet transform, but not in computer programming, can ﬁnd an extremely useful and free wavelet toolbox, called “Wavelab”, composed of Matlab routines and functions. Wavelab can be found at this website: http://www-stat.stanford.edu/ wavelab/. Mathworks Inc., who distribute Matlab software, also developed a powerful and user friendly “Wavelet toolbox”. But this toolbox is not free. A lot of software information and absolutely brilliant explanations of the use of wavelet transform can be found in Addison (2002). Summary Conventional spectral analysis is mainly based on Fourier transform. This kind of transform provides excellent information in terms of frequencies (with their associated amplitudes) constituting the original signal, but does not keep the spatial information: it is possible to determine the elementary bricks that compose the signal, but not the way they are ordered along the signal. This limitation of the method has been noticed by Gabor (1946) who proposed a sliding window along the signal, in which the Fourier transform could be performed. In this way, part of the local (spatial) information is not lost. Nevertheless, this time-frequency tiling is still rigid and not really appropriate for natural complex signals. In the eighties, mathematicians introduced the concept of wavelet transform. The wavelet is a localized function, sort of a probe, capable of dilation (spreading out of the wavelet along the Oy axis) and translation (along the Ox axis). The transformation of the original signal by the wavelet results in coefﬁcients, which are another expression of the signal. In addition, the wavelet transform acts as a mathematical microscope. In the discrete wavelet transform, two wavelets are used: the mother wavelet (the probe) and the scaling function. Therefore, it is possible to observe the signal at various scales, which is equivalent to the extent of the smoothing effect on the signal. This results in approximation coefﬁcients computed by the scaling function. However, the mother wavelet will provide the detail coefﬁcients. In conclusion, the signal is decomposed in two series of coefﬁcients for each scale of observation. This extremely powerful tool has been used to detect cycles in the growth of lacustrine shells. By removing detail and/or approximation coefﬁcients at different scales, and using image reconstruction (the wavelet transform has an inverse wavelet transform), annual, seasonal, tidal (monthly), and fortnight cycles in shell growth increments can easily be detected. Because of the very low amplitude of some of these cycles, it would not be possible to detect them without using the scaling effect and the detail coefﬁcients associated with the lower scales. This method is much more powerful than the conventional Fourier transform when the aim of the study is to look for speciﬁc local periods and scale-sensitive information. Acknowledgments The author is indebted to many colleagues and doctoral students who helped him with the tough concept of wavelet transform. Professors F. Truchetet and A. Diou (Le2i, CNRS,

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University of Burgundy, France) have been the main contributors, as well as Drs C. Dumont and M. Toubin. Dr A. Quinquis substantially improved the ﬁrst draft of this manuscript. Dr P. Francus is particularly acknowledged for his patience and kindness during the chapter editing. This work has been partly funded by the Swiss National Foundation. References Addison P.S. 2002. The Illustrated Wavelet Transform Handbook. Institute of Physics Publishing, Bristol, 353 pp. Anthony J.L., Kesler D.H., Downing W.L. and Downing J.A. 2001. Length-speciﬁc growth rates in freshwater mussels (Bivalvia: Unionidae): Extreme longevity or generalized growth cessation? Freshwater Biol. 46: 1349–1359. Bauer G. 2001. Framework and driving forces for the evolution of Naiads life histories. In: Bauer G. and Wächtler K. (eds), Ecology and Evolution of the Freshwater Mussels Unionoida, Springer Verlag, Berlin, Ecol. Studies 145, pp. 234–255. Burke Hubbard B. 1995. Ondes et ondelettes, la saga d’un outil mathématique. Pour la Science, Belin, Paris, 236 pp. Daubechies I. 1988. Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. 41: 919–996. Delyon B. 1993. Ondelettes orthogonales et bi-orthogonales. IRISA, Rennes, Publ. Int. 732, 24 pp. Diou A., Dumont C., Laligant O., Toubin M., Truchetet F., Verrecchia E.P. and Abidi M.A. 1999. Multiscale analysis of range image: Its use for growth increment characterization. Opt. Eng. 38: 2016–2021. Dolman J. 1975. A technique for the extraction of environmental and geophysical information from growth records in invertebrates and stromatolites. In: Rosenberg G.D. and Runcorn S.K. (eds), Growth Rhythms and the History of the Earth’s Rotation, John Wiley and Sons, London, pp. 191–221. Downing W.L., Shostell J. and Downing J.A. 1992. Non-annual external annuli in the freshwater Anodonta grandis grandis and Lampsilis radiata siliquoidea. Freshwater Biol. 28: 309–317. Gabor D. 1946. Theory of communication. J.I.E.E. London 93: 429–457. Mallat S. 1989a. Multiresolution approximations and wavelet orthonormal bases of L2(R). Trans. Am. Math. Soc. 315: 69–87. Mallat S. 1989b. Multifrequency channel decomposition of images and wavelet models. IEEE Trans. Acoustic Speech and Signal Proc. 37: 2091–2110. Mallat S. 1989c. A theory for multiresolution signal decomposition: The wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 11: 674–693. McCuaig J. and Green R.H. 1982. Unioid growth curves derived from annual rings: A baseline model for Long Point Bay, Lake Erie. Can. J. Fish. Aquat. Sci. 40: 436–442. Meyer Y. 1990. Ondelettes et Opérateurs I. Hermann, Paris, 215 pp. Olkkonen H. 1995. Discrete binomial splines. Graph. Models and Image Proc. 57: 101–106. Ravera O. and Sprocati A.R. 1997. Population dynamics, production, assimilation and respiration of two fresh water mussels: Unio mancus Zhadin and Anodonta cygnae Lam. Mem. Ist. Ital. Idrobiol. 56: 113–130. Rosenberg G.D. and Runcorn S.K. (eds) 1975. Growth Rhythms and the History of the Earth’s Rotation. John Wiley and Sons, London, 559 pp. Southward G. and Chapman D. 1965. Utilization of Paciﬁc halibut stocks: Study of Bertalanffy’s growth equation. Rep. Int. Pac. Halibut Comm. 39, 33 pp. Rhoads D.C. and Pannella G. 1970. The use of molluscan shell growth patterns in ecology and paleoecology. Lethaia 3: 143–161.

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Schwarzacher W. 1993. Cyclostratigraphy and the Milankovitch Theory. Elsevier, Amsterdam, Dev. in Sedim. 52, 225 pp. Toubin M., Dumont C., Verrecchia E.P., Laligant O., Diou A., Truchetet F. and Abidi M.A. 1999. Multi-scale analysis of shell growth increments using wavelet transform. Comp.. Geosci. 25: 877–885. Truchetet F. 1998. Ondelettes pour le Signal Numérique. Hermès Sci. Publ., Paris, 156 pp. Viscito E. and Allebach J.P. 1991. The analysis and design of multidimensional FIR perfect reconstruction ﬁlter banks for arbitrary sampling lattices. IEEE Trans. Circ. Syst. 38: 29–41. von Bertalanffy L. 1938. A quantitative theory of organic growth (Inquiries on growth laws. II). Human Biol. 10: 181–243. Walford L.A. 1946. A new graphic method of describing the growth of animals. Biol. Bull. 90: 141–147.

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295 Glossary, acronyms and abbreviations 16-bit image: An image with 16 bit image depth has 65536 colors/gray values (16th power of 2). 8-bit: The number of colors or gray values of a digital image. An image with 8-bit image depth has 256 colors/gray values (8th power of 2). η: Backscattered coefﬁcient. a∗ : see L∗ a∗ b∗ . AC: Alternating current. Accuracy: Describes the correspondence between the real value and the measure deduced from the central tendency. Acquisition software: The interface used to deﬁne capture parameters during digital conversion of an analog image, with a drum, ﬂatbed, or slide scanner. AI: Artiﬁcial Intelligence. ALFA: Automated Light Microscope Fossil Analyzer, acronym for an automated light microscope developed at the ETH Zurich, Switzerland. Algorithm: Computational procedure for solving a problem in a ﬁnite number of steps. Alternating current (AC): An electrical signal in which electron ﬂow and polarity reverses direction at a speciﬁed rate (e.g., 60 times per second (hertz)) obtained from conventional line power, but which may be generated within an electronic device. Amplitude: The absolute value of a given harmonic in a Fourier spectrum. Analysis errors: In image analysis, these are all biases generated by the segmentation and measurement algorithms themselves (impact of variable thresholds, choice of diameter estimators, etc.). ANN: Artiﬁcial Neural Network. Apparent inclination: The visible deviation from the vertical or the horizontal of an object. In X-radiography, the apparent inclination is different than the true inclination if X-ray is not taken parallel to the length of the long axis of clasts. Approximation coefﬁcients: In the wavelet transform, the approximation coefﬁcients result from the convolution of the scaling function with the signal. They correspond to the general trend of a signal observed at a speciﬁc scale. Artiﬁcial Intelligence (AI): The ability of a digital computer or computer controlled robot to perform tasks commonly associated with intelligent beings.

296 Artiﬁcial Neural Network (ANN): Artiﬁcial neural networks are self-learning systems of simple interconnected processing elements (neurons), which mimic the biological nervous system. They are used for a large number of tasks, such as, classiﬁcation and real time control. Aspect ratio: Ratio between a maximum and a minimum diameter of a blob. ASTM: American Society for Testing and Materials. Authigenic quartz: Quartz formed in-situ within a rock, commonly in the form of quartz cement or rims around clastic quartz grains (quartz overgrowths). Autofocus: Function for automated focusing of images. Average: A statistical measure for the central value of a sample or population. The basic form is the arithmetic average, i.e., the sum of a series of values divided by the number of values. Other versions include the weighted average, in which the different values are multiplied by a weighting factor before they are summed, the enumerator is adjusted accordingly. b∗ : see L∗ a∗ b∗ . Background subtraction correction: In image analysis, a method to remove unwanted variations in lighting of a scene by subtraction. Backscattered coefﬁcient (η): A ratio of the number of backscattered electrons to the number of incident electrons. Backscattered electron (BSE): Portion of electrons from a primary beam of electrons that enter a specimen and are elastically scattered back out of the specimen. Bandpass ﬁlter: A ﬁlter characterized by high transmission in the speciﬁed waveband and low transmission outside of the speciﬁed waveband. Bandwidth: Range between two frequencies, wavelengths or wavelet scales. Bedded: A sediment is bedded when sediment layers are thicker >1 cm. Binary image: An image in which pixels values are either black or white. Binary segmentation: Binary segmentation, or thresholding, is the transformation of a gray-scale or color image into a binary image (black and white), in such a way that features of interest are turned into black pixels and everything else into white (or vice versa). Binary: A system in arithmetic, in which only two states are used, 0 and 1, or true and false. In digital images, the two states are black and white. Bit: A contraction of binary digit, with numerical states of 0 and 1. This is the smallest unit of information stored or processed by a computer.

297 Bitmap image: A raster image that deﬁnes the color and space for each pixel in the display. Blob analysis: Computation of geometrical descriptors (size, shape, . . .) for selected geological objects (e.g., size of sand grains, width of fractures, . . .). Blob: Compact and well contrasted object whose spatial arrangement accounts for the image texture. Boolean operators: Logical operators to compare two statements or conditions that are either true or false. For instance, A and B is true only if both A and B are true, A or B is true if either A or B, or both, are true. Boulders: Large clast, diameter greater than 256 mm. Brightness: The dimension of a color ranging from very dark to very bright. In Image analysis, concept of brightness is better represented by the position in the histogram of pixel’s gray scale values along the intensity axis. BSE: Backscattered electron. B-Spline: Polynomial functions built by convolution with the box function B0 (x), with x ∈ [− 21 ; 21 ], and P (x) = 1, following Bp (x) = Bp−1 (x) ∗ B0 (x). B-Splines are usually used for interpolation problems. Bulk sediment density: The speciﬁc density of sediment, generally expressed in g/cm3 . A distinction is usually made between wet bulk density and dry bulk density. Wet bulk density applies to the speciﬁc density of sediment including the water in its pore space. Dry bulk density refers to the density of the sediment itself only, without pore water. The difference between the two densities is a measure for porosity of the sediment. Calcareous Nannofossils: Calcareous remains of unicellular marine gold brown algae belonging to the Haptophyceae (Protists) and the associated nannoliths of unknown provenance. Size range 1 to 30 µm. Calibration curve (or line): A mathematical function describing the relation between two sets of measurements of a property using two different methods. The relation can be linear (line) or non-linear (curve). Usually one of the methods is accurate and precise, but time consuming or expensive, or impossible to use under certain conditions. The other method is an approximation but easier or faster to use. The calibration curve is used to estimate a value from subsequent measurements using the easier of the two methods. Calibration: The process of tuning an instrument, or the output from an instrument, so that readings taken with that instrument are absolute rather than relative. CANADA balsam: Natural, transparent mounting media for microscopic preparations. CANADA balsam is a turpentine of the class of oleoresins.

298 Capture conditions: The parameters that deﬁne the manner in which an image is recorded onto the capture media. In analog photography these would include, the aperture setting, shutter speed, ﬁlm speed or ISO, lighting conditions and focal length and distance to subject. CCD Camera: Cameras with a CCD chip that acquire images into digital form. CCD: Charge coupled device. The most common type of light sensitive array (see diode array) used in digital cameras. CD-ROM: Compact Disc Read-Only Memory. Charging of a sample: In electron microscopy, increased negative charging of a sample due to its insufﬁcient conductivity, and revealed as an increasing brightness of the specimen. Chord length: Cf. intercept length. Chromacity: In most color co-ordinate systems, three variables are required to fully specify a color, for instance the three XY Z tristimulus values. The full range of colors thus occupies a three-dimensional space. A chromacity diagram is a projection of those three dimensions onto a two-dimensional plane. Because some information is lost, a color is no longer fully speciﬁed. However, chromacity diagrams allow illustration (on ﬂat paper) of the spatial relationship between various colors. Chromacity values are the values that a particular color has within this diagram. The chromacities deﬁned by CIE are x, y, and z (x + y + z = 1, so only two of the chromacity values are needed). They are derived from XY Z-tristimulus values, with x = X/(X + Y + Z) and y = Y/(X + Y + Z). CIE: Commission Internationale de l’Éclairage, or International Commission on Illumination, is an organization devoted to international cooperation and exchange of information among its member countries on all matters relating to the science and art of lighting. Amongst other things, CIE provides international standards for deﬁnition of reference colors and color co-ordinate systems. Class: A group of objects or images which are considered to be similar to each other (e.g., several images of the same microfossil species). Classiﬁcation Success: The percentage of images correctly assigned to class X among all images of class X of a testing data set. Classiﬁcation: The process of assigning objects to classes. Clast: Individual constituent, particle, grain or fragment of a sediment. Closing: Basic image processing operation, consisting of dilation followed by erosion. Coccolith: Calcium carbonate plate made by coccolithophores (unicellular marine algae). See Calcareous nannofossils.

299 COGNIS Light: Computer Guided Nannofossil Identiﬁcation System, acronym for an automated light microscope developed at the ETH Zurich, Switzerland. COGNIS: Computer Guided Nannofossil Identiﬁcation System, acronym for an automated SEM developed at the ETH Zurich, Switzerland. Color depth: The number of bits used to characterize a color digitally. A larger number of bits can resolve a greater range of colors (e.g., 48-bit color = 248 colors). Color intensity = Color density (see also intensity). Column: Part of a scanning electron microscope where the electron beam is formed and shaped. Cone of inﬂuence: Region in a wavelet spectrum (“scalogram”) in which edge effects become important. Connectivity: Measure of the number of neighbors relative to a single pixel. Contrast Enhancement: Process of optimizing the contrast on an image. Contrast: The degree of difference between gray values or colors on an image or the dispersion of the histogram of the gray level values along the horizontal axis. Convolution: Convolution between two signals f and+g is a mathematical operation ∞ denoted by the symbol “*” and deﬁned as: f ∗ g = −∞ f (x )g(x − x )dx . In image analysis, the basic idea of convolution is that a window of some ﬁnite size and shape — the support — is scanned across the image. The output pixel value is the weighted sum of the input pixels within the window where the weights are the values of the ﬁlter assigned to every pixel of the window itself. The window with its weights is called the convolution kernel. Convolutional Neural Networks: Special type of anArtiﬁcial Neural Network considered to be especially good at dealing with natural variation in objects, including translation, rotation, and distortion. Coulometry: A geochemical analysis method that measures the concentration of compounds such as CO2 and sulphur by titrating a colorimetric reaction with an electrical current. The amount of the compound present is proportional to the applied voltage. Crossed Polarized Light: In optical microscopy, two polarizing ﬁlters are oriented at right angles so light that is transmitted from one will be intercepted by the other, unless there is an intervening translucent object in between. Cyclothems: Repetitive series of beds deposited during a sedimentary cycle. D65 (2◦ ): A white color standard deﬁned by CIE, which was designed to represent pure white as seen by natural daylight.

300 Data Set File: Data set ﬁle used by COGNIS for training and testing of an Artiﬁcial Neural Network. DC: Direct current. Density proﬁle plot: A plot of the gray values along a selected line or rectangular selection. Density: In image analysis, the pixel value. Syn.: Intensity. Depth of ﬁeld: The range of distance between the closest and farthest objects that are in focus within a photograph. Detail coefﬁcients: In the wavelet transform, the detail or wavelet coefﬁcients, result from wavelet transform of a continuous signal. They correspond to the details of a signal observed at a speciﬁc scale. In the discrete wavelet transform, they are the result of the convolution between the signal and the mother wavelet function. Deviation: Incompressible dispersion of the results inherent to the nature of the analyzed material. Diametric variation: Total projection of a shape in a given direction. Diamicton: Poorly sorted, unstratiﬁed sediment, containing a wide grain size distribution form clay size particles up to pebbles and boulders. Diatoms: Unicellular algae (Protists) placed in Bacillariophyceae. They produce opal skeletons preserved in sediments. Size range 10 to 100 µm. Diffuse illumination: Lighting that is indirect, and as a result, is relatively even across a sample. This type of illumination is usually obtained by reﬂecting primary lighting sources off of a reﬂective surface (see diffusion screen). Diffusion screen: Used to transform illumination from a direct source (e.g., light bulb) into diffuse light (see diffuse illumination). Typically, light is reﬂected off of the screen or other light-colored surface. Digitization: The process of turning a scene, or ﬁgure, or photograph into a digital representation. Digitizing device or Digitizing Unit: Device for the transformation of an analogue signal into digital data (e.g., digitizing an image with a scanner). Dilation: Basic image processing operation used to add a layer of pixels to an object. A pixel is added (set to black) if n or more of its neighbors are black. Dilation connects discontinuous objects and ﬁlls in holes. N is determined by the user. Dinoﬂagellates: Unicellular algae (Protists, mostly photosynthetic, some are parasites). Size up to 2 mm.

301 Diode array: A group of photodiodes used to simultaneously collect image information. Most arrays are composed of photodiodes arranged in a line (linear array) or in a rectangle. Direct current (DC): An electrical signal with a ﬁxed polarity obtained with batteries and ﬁltered line power. Directional illumination: Lighting that is sourced from a particular direction rather than evenly from all directions (see diffuse illumination). Directional lighting is useful for eliminating reﬂections or for highlighting object contrast. Discrete wavelet transform: Discrete wavelet transform is a way to avoid calculation the of coefﬁcients at every possible scale and position and by making the choice of calculations at only scales and positions of 2n . This method is also called a dyadic process. Distortion: An optical phenomenon resulting from the failure of a lens or mirror to produce a good undeformed image. DLL: Dynamic Link Library. DPI: Dots per inch, a measure of pixel density and thus image resolution. DS: An annual accumulation of organic matter. DSDP: Deep Sea Drilling Program. Dyadic: See discrete wavelet transform. Dynamic Link Library (DLL): Collection of small programs, which can be called upon when needed by the program that is running. Edge detection: see Edge-ﬁnding ﬁlter. Edge effect: In time-series analysis, reduced signiﬁcance of wavelet coefﬁcients due to incomplete covering of the analysis window by the data set at the ends of the timeseries. Edge-ﬁnding ﬁlter: A ﬁlter that reveal the boundary between objects or two ROI. Sobel, Laplacian and Kirsch operator are common edge detection ﬁlters. EDM: Euclidean Distance Map. Electron gun alignment: Moving the ﬁlament tip in order to maximize the resulting signal. Gun alignment is done either mechanically or through the use of electromagnets. Electron gun tilt: Angle between the primary electron beam and the sample. This angle can be changed to enhance the quality of the signal.

302 Electro-osmotic knife: A ﬂat negatively charged metal blade, which is used to smooth wet and soft sediment surfaces. The electric charge promotes alignment of the sediment particles. Equivalent disk diameter: Diameter of a disk having the same surface area as the blob under investigation = Surface diameter. Equivalent inertia diameters: Diameters of an ellipse having identical inertia moments as the object under study. Erosion: Basic image processing operation used to peel off the outer layer of pixels of an object. A pixel is removed (set to white) if n or more of its neighbors are white. N is determined by the user. Error Rate: The percentage of images incorrectly assigned to class X among all images assigned to class X is called the error rate. Error: Dispersion of measurements due to the methodology used for analysis. Ethernet: Interface standard (IEEE 802.3) for communication between computers. Ethernet is currently the most widely installed local area network technology. Euclidean Distance Map (EDM): In a binary image, each foreground (black) pixel in the binary image is replaced with a gray value equal to that pixel’s distance from the nearest background (white) pixel. Fabric: Preferred orientation (or lack of it) of the long axes of clasts. Faraday cup: The Faraday cup measures the ion or electron beam current. Fast Fourier Transform (FFT): An algorithm for computing the Fourier transform. Feature extraction: Measuring, or otherwise extracting, useful aspects of a signal or image. In ANN, often performed before a classiﬁcation stage as careful selection of the features to measure can improve classiﬁcation performance. Feret diameter: Length of the segment deﬁned by the projection of an object onto a line. FFT: Fast Fourier Transform. Fiber optics: Optics made of ﬁberglass. Field: Is the spatial extension within which measures are taken (e.g., ﬁeld of view). Filament Saturation: Point of the highest amount of electron emitted by a ﬁlament. Filter: A ﬁlter splits something into two parts, by retaining one part and allowing the other part to pass through the ﬁlter. In digital images, ﬁlters are mathematical operations that are performed on the pixel values, to remove some unwanted aspect of the data (noise, for instance) to make the remaining data easier to analyze.

303 Filtering: Process of ﬁltering a sediment suspension onto a ﬁlter membrane. Filtering: The processing of an image using a ﬁlter. Final Lens: Electronic lens on a SEM for focusing. FireWire or IEEE 1394: is a interface standard for fast communication between computer equipment, especially multi media devices, conceived by Apple Computer and then developed by the IEEE 1394 working group (Institute of Electrical and Electronic Engineers). Focal spot size: In radiography, the size of the region from which the X-rays emanate within a tube anode. Focus: To adjust the optics of a lens to sharply deﬁne a subject. Foraminifera: Diverse group of unicellular shell-bearing protozoans with benthic and planktic families belonging to Rhizopoda. Up to 16 mm in size. Fourier spectrum: Decomposition of any signal into a series of periodical signals (harmonic). Fourier transform: This function allows the transformation of a complex signal into the sum of elementary signals, called harmonics, of given amplitudes. This operation leads to a graph or spectrum, in which each harmonic is plotted in function of its amplitude value. Fractal: Mathematical theory to address the problem of autohomothetic objects and shapes with non-integer dimensions. Frequency localization: In time (or space)-frequency tiling, the frequency localization corresponds to the position of the frequency in the frame. In other words, it corresponds to the place or time at which this frequency occurs in the signal. Frequency: Number (“repetitions”) of waveforms (“cycles”) within a unit of length, or time. Gabor transform: This transform was the ﬁrst attempt to obtain information in terms of space and frequency of a raw signal. It led to the concept of Windowed Fourier Transform (WFT), or Short Time Fourier Transform (STFT). In this case, a moving window is applied to the signal and the Fourier transform is applied to the signal within the window as the window is moved. Gain: Increase in signal or ampliﬁcation of a signal. Gamma correction: In display devices like televisions and computer screens, the relationship between input energy of a light signal (I ) and the resulting brightness of the output on the screen (O) is non-linear. O = I b , with b, or gamma, around 2.5 for most computer screens. Because I and O are scaled between 0 and 1, low input energies result in colors that are too dark, if not corrected for. A (usually partial)

304 gamma-correction is therefore applied to the input signal, to improve contrast and brightness of the display on the computer screen; different types of computers use different corrections. Gamma: In terms of analog photography, this is the slope of the linear portion of the grayscale dynamic or characteristic functionality that relates scene luminance to the optical density of the analog recording media. Gamut: The entire range or extent of something. In this book, the range of colors that can be expressed in a given color co-ordinate system. Gaussian: The well-known normal distribution given by f (x) =

− 1 e (2π σ 2 )1/2

(x−µ)2 2σ 2

.

Gaussian Blur: Filter that convolve the image with a kernel having a Gaussian distribution. Glacial marine sediments: Sediments released from glacier ice or an ice shelf into the marine environment through a water column. Glacioeustasy: Changes in sea level caused by changes in ice volume. Glare: The specular component of light reﬂected off a surface. GRAPE density: Bulk density of sediments and rocks can be estimated from the measurement of gamma-ray attenuation. GRAPE is referring to an early application of the method to compute porosity using an assumed grain density. GRAPE: Gamma-Ray Attenuation Porosity Evaluator. Gravity ﬂow: Movement of sediment downslope due to the force of gravity. Grayscale: A numerical scale that represents optical density (shades of gray), with 256 steps ranging from 0 to 255 for 8-bits images, without further speciﬁcation how the gray-scale is generated. Commonly, 0 = black and 255 = white, but the inverse scale can be used also (255 = black). Haralick ﬁlter: An algorithm that enhance textural features by the measure of homogeneity of the image. For further explanation: Haralick R., Shanmugam K. and Dinstein I. 1973. Textural Features for Image Classiﬁcation. IEEE Trans. Syst. Man Cybern. 610–621. Hardware noise: see noise. Harmonic: A synonymous term for frequency in Fourier analysis of a signal. The ﬁrst harmonic is also called the fundamental harmonic. High Tension: Voltage (in KV) between anode and cathode (Filament/Gun) of a Scanning Electron Microscope.

305 Histogram: A statistical term for a bar or line diagram that depicts the distribution of a series of measurements. The horizontal axis represents a numerical scale for some property that was measured on a sample consisting of a number of elements. The horizontal axis is divided into classes with a certain width. The vertical axis gives the frequency, i.e., the number of elements, in each class. Homoscedasticity: Applies to groups / populations having identical variances. Hue: or tint. Hue corresponds to the common deﬁnition of color, e.g., “red”, “orange”, “violet” etc. In the HSB color model that determines the frequency of light or the position in the spectrum or the relative amounts of red, green and blue. HSB: Hue, Saturation, and Brightness. HSB is a color model. Hybrid-median: Recombination of several median values estimated for various subgroups in a sample into a new measure for the midpoint (see median). Hz: Hertz, frequency of image repetition. Iceberg Rafted Debris: Sediment particles released from icebergs through a water column. Icehouse: A time of Earth history in which signiﬁcant glacial ice is present. IEEE: Institute of Electrical and Electronic Engineers. Illumination: The type and character of light used for image acquisition. Illumination sources vary by both spectrum and source geometry. Most illumination sources are in the visible spectrum, however, some may be in the infrared (IR), ultraviolet (UV) or X-ray bands. Image analysis: Extraction of quantitative information from images captured in digital form. Image compression: The reduction of an image ﬁle’s storage requirements through lossy or lossless compression methods. Image enhancement: Highlighting of some portions or components of an image through modiﬁcation of pixel values, with the aim to make the image easier to interpret visually and (or) to prepare it for subsequent analysis. Image lifecycle: A conceptualization of the various steps inﬂuencing the capture of information during the photographic processes that includes the acquisition, analysis, and archiving conditions associated with the image. Image pre-processing: Pre-processing is used in this book to describe those steps in image analysis after acquisition of the image, which are necessary for further analysis, but which are not part of the actual processing of the image.

306 Image processing: Modiﬁcation of an image, to allow subsequent retrieval of the required numerical data. Image registration (or indexing): Aligning two or more overlapping images to produce a larger image. Registration may be accomplished using ﬁducial marks acquired with each image. Image resolution: The density of pixels in an image, and thus a measure of the precision with which objects within a photograph can be differentiated. Incident Light Microscope: Microscope that magniﬁes objects under reﬂected light. Infrared light: Radiation in the 750–1200 nm wavelength band. Input device: An instrument used to capture an image such as a ﬁlm-based camera, scanner, or digital camera. Integration errors: Errors linked to the number, density and location of discrete pixels used to build the digital image. In practice this is essentially linked to magniﬁcation and CCD resolution. Intensity analysis: Statistical computations of parameters from pixel intensities (e.g., average color within an image, variance of light transmittance within a single crystal, . . .). Intensity: General term to designate the gray level value of a pixel. Interaction volume: In SEMs, the region of a sample in which all electron interactions occur as a primary beam is directed onto a sample. Intercept: Segment deﬁned by the intersection between a geometrical body and a random line. Interpolation algorithm: The program used to ﬁll in missing pixel information in an image. Many acquisition and scanning devices use an interpolation algorithm to increase image resolution beyond the resolution of the sensor system (see optical resolution). Interpolated Resolution: Is the resolution that the device can yield through interpolation — the process of generating intermediate values based on known values. IR: See infrared light. IRD: Iceberg Rafted Debris or Detritus. ITU-R: International Telecommunication Union - Radiocommunication Sector. JPEG: Joint Photographic Experts Group. JPG, JPEG ﬁle format: An efﬁcient image storage format that achieves high image compression ratios by a two dimensional FFT transform of the raw image, followed by the truncation of high frequency information. Information lost in this way cannot be recovered. This method is thus a lossy compression method.

307 Kernel: see convolution and convolution kernel. K-means algorithm: A set of algorithms used to assign data points to a ﬁxed number of classes. Each class is assigned a center. The algorithm attempts to move the centers so that: (1) each data point is assigned to the class whose center it is closest to; (2) each center is the mean of the data points assigned to its class. KV: Kilovolts. L∗ : see L∗ a∗ b∗ . L∗ a∗ b∗ : A three-dimensional color co-ordinate system deﬁned by CIE, intended to linearize the perception of color by the human eye. L∗ describes lightness, its values can range between 0 (black) to 100 (white). The other two variables describe the actual color, with a∗ representing green (negative values) or red (positive) and b∗ representing blue (negative) or yellow (positive values). Lamina: The ﬁnest recognizable unit layer or bedding, differing from other layers by colors, composition, or particle size. Laminae are thinner than 1 cm. Laminated sediments: Sediments that consist of laminae or that can be splitted into thin layers. Lens aberration: A defect caused by optical rays (or electron beams) passing through the outer region of the lens focusing on a different plane than optical rays (electron beams) passing through the center of the lens. It produces a defect of focus, such as blurring in an image. Light distribution: An informal phrase used to denote that part of the variation in color or gray-scale in an image that is due to non-uniform illumination during acquisition. Light intensity: Amount of light shed on a sample. Light sources: Devices to light up objects on different microscopes. Lightness: A measure for light intensity reﬂected by an object. Lightness corresponds to L∗ in the L∗ a∗ b∗ color co-ordinate system, and is a non-linear transform of Luminance. Line scan: A scan of some property along a thin, narrow line. Line scan cameras build a digital image from a large number of consecutive lines that are a single pixel wide. In chapter 6, line scan refers to sediment color data that are read from a digital image along a line (or narrow bar) across an image. Line time: Time needed to move the electron beam of a Scanning Electron Microscope along a scanning single line. Linear RGB: see RGB. LM: Light Microscope.

308 Loessite: Lithiﬁed loess, or lithiﬁed eolian siltstone. Longpass ﬁlter: A ﬁlter characterized by high transmission of longwave (typically >700 nm) radiation. Longpass ﬁlters are often used to reduce transmission of ultraviolet (UV) or blue radiation. Lossless compression: A data compression method such as LZW encoding that decreases an image ﬁle size without the loss of information by recoding redundant strings with less a less storage intensive representation. Information in not permanently lost using lossless compression. Lossy compression: A data compression method such as JPEG that decreases an image ﬁle size dramatically through numerical transformations such as FFT or wavelet convolution which result in the loss of high frequency information. Information lost in this way cannot be recovered. Lowpass ﬁlter: A ﬁlter that removes the high-frequency content of a signal (or image) leaving only the low frequency information. LS: Annual accumulation of mineral matter. Luminance factor: The ratio of the amount of light reﬂected or emitted from a photographic scene to that diffusely reﬂected from a white surface under the same lighting and viewing conditions. Luminance: A measure for light intensity reﬂected by an object, it corresponds to Y in XY Z tristimulus values. See XY Z. LUT: LUT stands for look-up-table, which refers to an interactive window that displays the color code in use in image analysis software such as NIH-Image. LZW: Lempel-Ziv-Welch, lossless compression algorithm. Magniﬁcation: The ratio of image to sample size (e.g., 100× original) produced through a combination of optical elements and/or image processing. Major annulus: Major growth increment, often observed as a local bump, on clam shells. Mathematical morphology: Image processing language using geometrical neighborhoods (structuring elements) to interrogate the content of an image by hit or miss. Matrix: The material within a clastic rock or sediment that is relatively much ﬁner than the average particle size (clasts). Median ﬁlter: A noise-reducing ﬁlter that works by changing the value of a pixel to the median value of the surrounding pixels.

309 Median: A statistical measure for the midpoint of a sample or population (compare average). The median is the middle value of a series of measurements that have been ranked if the number of measurements is odd; and it is the average of the two middle values if the number of measurements is even. Compared to the average, the median is less sensitive to outliers, i.e., the occasional extremely high or low measurement. Metadata: Any information that deﬁnes the operational parameters and conditions during acquisition and processing of an image. Microfossils: Fossilized microorganisms too small to be studied without the aid of a microscope. Micrometer: A glass slide into which a ﬁne metric grid is etched, which is used to calibrate the magniﬁcation of a microscope. Microprobe rounds: Samples that are encased in epoxy within a cylinder-shaped mould and then polished, typically for analysis in microprobe instruments. Milankovitch cycles: The ofﬁcial name is orbital cycles. Milankovitch cycles is an informal term, named after the Yugoslavian scientist who ﬁrst described them. Orbital cycles are quasi-periodic changes in the earth orbit due to gravitational forces between the planets. Modal analysis: Or composition analysis, or phase analysis. In image analysis, it is the measure of the number of pixels that belong to a single phase (usually having a distinct mode in the histogram of gray level values) compared to the total number of pixel in the ﬁeld of view. Morlet wavelet: Type of complex wavelet (“mother”) function, consisting of a plane wave modulated by a Gaussian envelope. Morphometric Data: Numerical data concerning the morphology of an object (e.g., length, width or roundness). Mother wavelet: The fundamental expression of the wavelet (a function) from which dilated and translated forms are used in the wavelet transform. Motorized Stage: Microscope stage with motorized X, Y and Z axis. Multi-layer perceptron: A common type of neural network consisting of a number of fully connected layers. This type of network usually requires a supervised training method, where each item in the training set has a correct answer assigned to it by the operator. Multiresolution: The concept is similar to a mathematical microscope. If at a given scale, we add the detail and the approximation coefﬁcients, we obtained the signal approximation at a smaller scale.

310 Munsell color chart: The Munsell color notation is a non-numerical color system used for visual classiﬁcation. The color of an object is determined by comparing it to a Munsell color chart, that is a suite of chips with different colors, and ﬁnding the color that is the most similar. A Munsell soil chart, which contains a selection of colors that occur in soils, is used extensively for visual description of colors in sedimentary sections. Neighbour: For any type of maps, including digital images, a term used to denote data points, or pixels, near the point under consideration. Neural network: see Artiﬁcial neural network. Neuron: A processing element within a neural network. Usually has a number of inputs and a single output. Neutral density ﬁlter: A ﬁlter that uniformly reduces radiation transmission across the ultraviolet (UV), visible and infrared (IR) wavelengths. Can also be referred to as gray density ﬁlters. Neutral gray: Color deﬁned by 18% gray photographic standard gray matte cards. Nicols: Nicol prism. This prism produces a plain-polarized beam from ordinary light by transmitting waves vibrating in only one direction. NIH-image: Freeware image analysis software package developed by the US National Institutes of Health. Noise: The term noise is derived from radio technology and represents random ﬂuctuations that are unrelated to the actual signal. In digital images it describes random ﬂuctuations in color or gray scale values, which are unrelated to the actual scene in the image (signal). Hardware noise, or shot noise, is that part of the noise in an image that is produced by the camera. For example, a digital image of a uniform gray surface will show a certain amount of scatter in color values around some average gray value; the amount of scatter is a measure for the quality of the camera. Nominal grayscale value: The expected grayscale value for a grayscale zone in a standard such as the Kodak Q-13 grayscale zone card. Non-functional pixels: Individual photodiodes in an imaging sensor (see diode array) that do not operate to speciﬁcation. These sensors result in images with consistently missing or incorrect pixel values. Non-linear R G B : see RGB. Non-uniform illumination: The amount of light reaching the specimen is not equally distributed in the ﬁeld of view. NTSC: TV norm with a power/image frequency of 60 Hz and 30 frames per second developed by National Television Standards Committee (USA).

311 Nyquist frequency: Maximum frequency or small wavelength that can be resolved by spectral or wavelet analysis, the wavelength of the Nyquist frequency is equal to 2 times the average data interval. Ocean Drilling Program (ODP): International partnership of scientists and research institutions organized to explore the evolution and structure of Earth and its oceans. It drills sediments in the deep sea with the drill ship Joides Resolution. ODP started in 1985 and is due to terminate in 2003. Its predecessor was the Deep Sea Drilling Program (DSDP); its successor will be the International ODP, or IODP. ODP: Ocean Drilling Program. Offset: Adjustment of the base line of a signal (e.g., the black level of video signal). Opening: Basic image processing operation consisting of erosion followed by dilation. Optical density: A measure of the opacity of a negative, slide, or print that relates to the amount of light that will be reﬂected. Optical resolution: The resolution at which a speciﬁc acquisition system can capture an image using only the hardware (optical) elements (see photodiode) in the system (as opposed to interpolated resolution). Optics: Optical instrumentation, for example, objectives or eye pieces of a light microscope. Output media: Any material capable of presenting image information in a hard copy format, for example, a photographic print, slide or transparency. PAL: Phase Alternate Line, TV norm mainly used in countries with a power frequency of 50 Hz and 25 frames per second. Parallax effects: The term parallax was deﬁned in astronomy originally, and describes the apparent change in the position of an object, caused by an actual change of the position of the observation point. In the context of photography as used in this book, the term refers an apparent change in the geometry of objects relative to each other in a photograph, due to difference in angle with and distance to the camera. Particle Separation: Physical separation of particles for optimized detection (e.g., diluting a sample). Pebbles: Clast or rock fragment larger than a granule and smaller than a cobble (between 4–64 mm); in this volume used as a general term to refer to clasts >2 mm and smaller than boulders. Periodicity: Length of an interval through which a signal repeats itself. Periodogram: Raw (non-smoothed) power (or variance) spectrum from Fourier analysis.

312 Periostracum: Primarily proteinaceous layer that covers the outside surface of mature shells. Phase analysis: see modal analysis. Phase: A discrete homogeneous part of a material system that is separable from the rest. Photodiode: A light-sensitive semiconductor device that generates electrical current proportional to incident light. Photodiodes are the main constituent in electronic imaging and scanning devices. Photospectrometer: An instrument to measure the spectral reﬂectance of a surface, by illuminating the surface with a diffuse light/energy source and measuring the reﬂected light in narrow bands (typically 10 or 20 nm wide) across a range of wavelengths. Photospectrometry can be conﬁned to the range of visible light (400 to 700 nm) or may include the near-ultraviolet (250–400 nm) or near-infrared (700–850 nm). Spectral data for visible light can be integrated subsequently and translated into L∗ a∗ b∗ coordinates or other color coordinate systems. Pixel: A contraction for picture element, the smallest unit of visual information recorded in a digital image, characterized by its position (x, y) and intensity. Pixel Ratio: or pixel aspect ratio is computed by dividing the width by the height of the pixel. Estimation of the pixel ratio is necessary when the photodiodes used for image acquisition are not perfectly square. This information is needed to ensure accurate spatial calibration. Pixel Resolution: Number of pixel in X and Y direction of an images or a memory array of a digitizing device. Plan Apochromat: Special type of objective, optimized for low image distortion. Planktic Foraminifera: Unicellular heterotrophic planktic microorganisms which tests are preserved in sediments (size up to 2 mm). See foraminifera. Plug-ins: Small software packages that are written to work with another program, usually to perform a speciﬁc process or task. Poisson: Probability density function adequate for describing rare events. Population: Is the set of all possible measures within the universe under study. Precision: Describes a small dispersion of measures with respect to a central tendency. Preparation errors: Errors involved in the image acquisition procedure that affect the quality of representation of objects in a scene (saturation, shadowing, etc.). Prismatic layer: The outer layer in shells, which is composed of prisms of calcium carbonate crystals and is covered by the periostracum.

313 Pseudo-resolution: Artiﬁcial domains, or connections between originally discrete regions produce artiﬁcially during image processing. Random electronic instrument noise: Variations in the intensity values acquired caused by the ﬂuctuations within the acquisition system itself. Range image: An image in which the pixel color is related to a “z” or altitude. Therefore, a range image is a matrix of pixel positions and altitudes, i.e., a pseudo-3D image. Reﬂectance: The proportion of the amount of light received by an object or surface and the amount that is reﬂected. Reﬂectance is low for a matte black object, high for a reﬂective white object. Refracted light: Light that has been bent from its incident path as it travels between media with differing indices of refraction. Region of interest (ROI): A speciﬁc area of a sample that is of interest. Registration: Storage of X-ray data on a receiver placed behind an object. See also Image registration. Remote Control: Control of apparatus (e.g., a microscope) from a distance. Resolution: An expression of a number of pixels contained in an image. In the context of digital images, the word resolution usually refers to how frequently an object was sampled. The resolution of a digital image is usually speciﬁed as the number of dots per inch (dpi). For the purpose of size and shape measurements from a digital image, the resolution is expressed relative to the true size of an object depicted in that image. RGB: Red, Green, Blue (tristimulus) color space. The RGB color coordinate system(s) uses the additive primary colors red, green, and blue to renders colors for television, computer screens and digital images. In linear RGB, the color values have a linear relation with XY Z tristimulus values. In non-linear R G B , R = Rmax(R/Rmax)b , in which b is a constant, and Rmax is the maximum value that R can have (usually 255). G and B are similarly deﬁned. Different manufacturers use different values for the constant b. Robustness: The property of measurements of staying similar towards slight modiﬁcations of operating conditions, such as gentle rotation of the ﬁeld of view. Rotation: Different orientation of an object on different images. Roughness: Relative amount of pixels extending outside a smooth inscribed reference shape. Roundness: Geometrical estimate of the time of residence of a particle in an abrasion process (wear index).

314 RS232: Common interface standard for communication between computer equipment (e.g., between a motorized stage and a PC) developed by the Electronic Industries Association. Sample geometry: Shape and thickness characteristics of a sedimentary sample that may inﬂuence the acquisition of image information. For example, samples with uneven thickness will result in X-radiographs with variable exposure across the sample. Sample: The single measure performed on the support (e.g., measure of intensity). Scaling function: It is used with dyadic discrete wavelets. The scaling function is associated with the smoothing of the signal and its convolution with the signal produces the approximation coefﬁcients. Scalogram: Two-dimensional graphic that displays color or gray of wavelet coefﬁcient variation according to time (or depth) in x-axis, and according to scale (or wavelength) in y-axis. Scanning Electron Microscope (SEM): An electron microscope from which an image of a sample is produced by scanning an electron beam in a television-like raster over the sample and displaying the resultant signal from an electron detector on a screen or as an image ﬁle. Scene luminance: A measure of the amount of light reﬂected or emitted by the subjects within a photographic scene. Scene: The subject or subjects of an image and any background captured during the imaging process. Syn.: view. Scheffe Test: Statistical test that shows the differences between each pair of means, used with an analysis of variance. Schottky Field Emitter: Special type of electron source in a scanning electron microscope. SCOPIX: Digital X-radiography system for sediment cores developed by the French company SEGETEL and used at the Université Bordeaux 1, France. SECAM: Sequential Color Avec Memory, TV norm with a power/image frequency of 50 Hz and 25 frames per second developed by France. Sediment image color: Color-value or gray-value that is extracted from a digital bitmap image bandwidth, color or gray value that do not necessarily reﬂect the visual appearance of the sediment. Sedimentation rate: The amount of sediment accumulated over a given period of time, usually expressed as thickness of accumulation per unit time.

315 Segmentation: The process of breaking an image up into different regions, that corresponds to structural units in the scene or to objects of interest. Thresholding is one among segmentation techniques. SEM: Scanning Electron Microscope. Sensitivity: Ability to differentiate a signiﬁcant difference between different samples. In Image analysis, a measure of the responsiveness of an imaging system to variations in scene luminance. Shape: Geometric description of the spatial distribution of pixels forming a given object. In Image analysis, often used a synonym of aspect ratio. Sharpness: The degree of focus. Shortpass ﬁlter: A ﬁlter characterized by high transmission of shortwave (typically <800 nm) radiation. Shortpass ﬁlters are often used to reduce transmission of infrared (IR) or red wavelengths. Shot noise: see noise. Sigmoidal response: An s-shaped relationship between two variables, arising from threshold responses and differential sensitivity throughout the dynamic measurement range. Signal-to-noise ratio: Relation between value (e.g., gray scale) of a deterministic process (e.g., solar cycle) and random variability. Single lens reﬂex camera: A camera where both viewﬁnder and imaging sensor use a common set of optical elements (or lenses). The principal advantage is precise framing of the image and optical element quality. Slab: A cut sample of rock that is typically polished on one side. SLR camera: see single lens reﬂex camera. SMPTE: Society of Motion Picture and Television Engineers. Solar irradiance: Entire spectrum of energy waves emitted by the sun, ranging from high-velocity gamma-and X-rays, visual light, low velocity infrared radiation, to corpuscular (sun matter). Spatial calibration: Calibration of size measurements in two (or three) dimensions (space). Spatial localization: In time (or space)-frequency tiling, the spatial localization corresponds to a given position in the signal. In other words, it corresponds to the place or time, at which a sum of given frequencies occurs in the signal. Spectral analysis: Partitioning of the variation in a time series into components according to the duration, or length, of the intervals within which a variation occurs.

316 Spot size: In SEMs, the size of the beam of primary electrons that is directed on a target (sample). Stereology: Discipline of the mathematical sciences aiming to estimate properties in an n-dimensional space from measurements in sub-spaces of lower dimensionality. STFT: Short Time Fourier Transform. Stray marks: Extra marks on the image and/or radiograph; unnatural and fabricated during the scanning or X-raying process. Structural analysis: Computation of spatial relationships between geological objects (e.g., preferential orientation of grains in a sediment, average distance between pores, . . .). Support: Is the spatial extension (area in 2-D) on which a measure is performed. SYRACO: Système de Reconnaissance Automatique de Coccolithes, acronym for an automated light microscope system developed by L. Beaufort and D. Dollfus at the Université d’Aix-Marseille, France. Taxa: Different taxonomic units/groups of organisms (e.g., different species of planktic foraminifera). Testing Data Set: Set of data (e.g., images) used for testing of anArtiﬁcial Neural Network. Texton: Elementary pattern that can be isolated and whose spatial arrangement accounts for the image texture. Textural analysis: Computation of spatial relationships within geological objects (e.g., characterization of gray level patterns within spores, identiﬁcation of zonation patterns within grains, . . .). Texture: Generic term to describe the spatial arrangement of primitives (pixels, blobs, textons, . . .). Threshold response: A lack of sensitivity in a recording media such as silver halide ﬁlm which limits the response of the media above and below some critical value. Threshold: A criterion value (sometimes arbitrarily established) that is used to determine if particular conditions are met. In time-series used to determine a physical or arbitrary boundary between two stages (high value/low values) there can be more than one threshold. Thresholding: The processes of segregating an image into two domains of differing intensities (usually black versus white) in which the phase of interest is of a different intensity relative to the background. TIFF: Tagged Image File Format.

317 Till: Unconsolidated sediments deposited by glacial ice. Time series: Sequence of measurements, typically taken at successive points in time. Tint: See Hue. Tomography: Techniques for making detailed X-radiography of a predetermined plane section of a solid object while blurring out the images of other planes. Training Data Set: Set of data (e.g., images) used for training of an Artiﬁcial Neural Network. Translation: Different position/location of an object on different images. Transmitted Light Microscope: Microscope that magniﬁes objects under transmitted light. Tree rings: Annual quasi-concentric growth layers in trees, usually alternation of bright (spring/summer) and dark (winter) layers. Tristimulus values: Tristimulus values are the amounts of three primaries that together specify a color. CIE deﬁned tristimulus values under the name X, Y , and Z (see XY Z). TV Cameras: Cameras operating in TV mode (50/60 Hz image frequency) with a video output signal. Ultimate eroded set: Ultimate set of pixels remaining after a series of successive erosions. Ultraviolet light: Radiation in the 1–400 nm wavelength band. Umbo: The raised, knob-like section of some clam and mussel shells. Universe: Is the source of all possible measures within the ﬁeld of study. UV: UltraViolet. Variance: Measure of dispersion of a value around its mean. Varves: Varves are sequences of sedimentary laminations deposited within a single year. Clastic-organic varves: Varves that are composed of 2 laminae: lighter mineral lamina that is detrital origin and a darker organic lamina that is from autochthonous primary production. Video Framer Grabber: Digitizing device in a computer that converts a video analogue signal (50/60 Hz) into a digital signal. Viewing components: Any component of the image analysis system, used to visualize image data, such as a monitor, printer, or plotter.

318 Voronoï: Polygonal partitioning of the space based on the notion of nearest neighbor. Warm Field Emission Gun: Special type of electron source in a scanning electron microscope. Water-acetone-epoxy exchange: A method to impregnate soft sediment samples with rich water content. Watershed segmentation: A method to separate touching objects or blobs in images. Wavelength: Distance from a point on one wave form to the equivalent point on the next wave form. Wavelength is the reciprocal of frequency. Wavelet coefﬁcient: Modulus of the complex number that results from the decomposition of a signal in time and frequency space. Wavelet transform: A wavelet is a wavelike function used to investigate a signal or an image. The transformation of the initial signal by the wavelet is a wavelet transform, which is a convolution of wavelet function with the original signal. WFT: Windowed Fourier Transform. White noise: Spectral power (= variance) that can arise from purely randomly distributed data. In time-series analysis used as one way to determine background spectrum for conﬁdence levels of spectral estimates. White point calibration: White point calibration is performed on a camera to ensure correct color representation. The camera measures the light reﬂected from a pure white standard target and equates these values with the maximum white that can be measured by the camera (255, 255, 255 in RGB space). Working Distance: Distance between an object and the ﬁnal lens on a SEM. X-radiograph: Image obtained by sending X-rays through an object onto a negative ﬁlm. The amount of X-Rays absorbed by the specimen is proportional to variations in density, thickness, and composition. On negative plates, high-density specimens appear brighter compared to low-density ones. X-ray densitometry: A method that identiﬁes spatial density differences based on the penetration of X-rays. X-ray: Roentgen-radiation. High-energy radiation in the ∼0.01 to 10 nm wavelength band. X-Y center: Center of a blob in the image in an orthogonal reference system. Often estimated computing the moment of inertia of the blob. XYZ: The tristimulus color co-ordinate system deﬁned by CIE. Y represents Luminance, and is (linearly) proportional to the total amount of light (energy) reﬂected from a surface, but weighted for the various wavelengths to account for sensitivity of human vision to different wavelengths. Y is scaled from 0 (black) to 100 (white). The other coordinates, X and Z, express the actual color.

INDEX

14 C see radiocarbon

η backscattered coefﬁcient a* 43, 45, 46, 50, 66, 117–119 absorption band 18 AC see alternating current accuracy 15, 36, 38, 39, 61, 88, 89, 163, 166, 209, 269, 270, 277 acetone 190 acquisition 3–5, 11, 13, 15–17, 21, 22, 24, 27, 28, 31, 32, 40, 41, 91, 122, 129, 138, 166, 168, 171, 181, 189, 209, 223, 238 acquisition condition 5, 6, 12, 15, 38, 88, 90, 92–93, 116, 129, 169, 221, 223 acquisition methods 1, 12, 15, 21–32 acquisition of microscopic images 254–262 acquisition settings or parameters 24, 92, 93, 204, 207, 216, 217, 223 acquisition software 129 acquisition system or device 5, 12, 16, 18, 28, 91, 207, 209, 223, 230 adaptive resonance theory 264 addition 52, 93 AI see artiﬁcial intelligence ALFA (Automated Light Microscope Fossil Analyzer) 230, 244–247 algorithm 4, 6, 41, 55, 56, 77, 90, 91, 101, 149, 172, 222, 232, 239, 240, 257, 261, 283 interpolation algorithm 27, 151, 152, 156, 163 K-means algorithm 257 Mallat’s algorithm 280, 281, 283, 290 alignment 6, 15, 16, 82, 161, 208, 209 alternating current (AC) 31, 32, 208 amplitude 111, 118, 152, 154, 156, 157, 159, 161, 199, 208, 274–277, 291 analog 4, 11, 14–16, 24–26, 27, 127–131, 133, 236 analysis 4, 12, 18, 26 blob analysis 62, 67–78, 80 color or intensity analysis 21, 62, 63–66, 105– 124 composition analysis 92, 126, 138, 203 grayscale analysis 126, 128–134 modal analysis 78–79, 87–89, 93–95, 98, 204 morphometric analysis 54, 229 particle analysis 229–251

phase analysis see modal analysis size analysis 87, 93, 95–96, 98, 100, 165, 214, 215, 217, 220 shape analysis 87, 88, 93, 96–97 spectral analysis 147, 156, 158, 273–276, 284, 285, 289, 290, 291 structural analysis 59, 62, 77–85 textural analysis 59, 62, 63, 85, 203 andesite 169 ANN see artiﬁcial neural network Anodonta Cygnae 283, 284, 286, 288 aperture 24, 46, 108, 208, 239 apparent inclination 175 area 14, 15, 18, 19, 25, 27, 37, 40, 42, 54, 65, 67, 70, 71, 76, 79, 80, 84, 85, 89, 90, 94, 101, 107–110, 114, 131, 139, 166, 168, 172, 174, 177, 178, 181–183, 193, 197, 206–208, 217, 219, 220, 221, 230, 235, 237–240, 245, 246, 248, 255, 256, 262, 265, 286 arsenopyrite 91, 98 artifact 16, 18, 32, 56, 106, 107, 148 artiﬁcial intelligence (AI) 240, 244 artiﬁcial neural network (ANN) see neural network aspect ratio 74–75, 96, 97, 101 assemblage 229, 246 ASTM 37, 38 authigenic quartz 217 autofocus 92, 232, 233, 238, 239–240, 244, 246, 253, 254 automation 14, 31, 32, 77, 106, 223, 240, 244, 253, 262, 263, 318 automated classiﬁcation 240–244 automated image acquisition 31, 230–240, 246, 262 automated microscopy 229 automated particle analysis 229–251 automated recognition 4, 232, 253–271 automated varve counting 192–193 autumn see fall average 37, 40, 41, 45, 47–49, 62, 63, 76, 78, 80, 82, 92, 93, 108, 109, 111, 112, 114–118, 120, 136, 140, 144, 145, 152, 154, 191, 193, 196, 197, 199, 210, 211, 217, 219, 220, 223, 243, 259, 278, 283, 286 average light curve 110–112

320 average mean atomic number 205 axis 38, 41, 49, 63, 64, 66, 109, 110, 112, 117, 122, 133, 135, 143, 155, 205, 207, 232, 239, 240, 244, 274 long or major axis 72, 81, 168, 173, 174, 175, 177, 178, 183, 206 short or minor axis 72, 168, 174, 175, 178, 183 b* 43, 45, 46, 50 B-Spline 281, 284, 290 back-propagation 264 background 5, 40, 41, 52, 54, 56, 69, 76, 85, 131, 135, 136, 144, 149, 159, 169, 171, 183, 212, 233–235, 254–258, 270 background correction 131, 132, 133, 134, 135, 137 background subtraction 41, 131, 134 backscattered coefﬁcient (η) 204, 205 backscattered electron (BSE) 23, 29, 30, 37, 38, 54, 63, 94, 95, 98, 99, 149, 203–225 Baldeggersee, Switzerland 20, 94, 95, 102 bandwidth 16, 18, 91, 144, 147–149, 151, 154–156, 159, 160 basal 176, 178 beamsplitter 17 bias 68, 70, 78, 80, 88, 89, 90, 96, 97, 101, 129, 131, 132, 133, 134, 135, 138, 166, 170, 176, 177, 178 binary 126, 156, 172, 183 binary covariance function 82, 83 binary segmentation 52 biogenic silica 205 biomineralization 283, 288, 289 bit 20, 27, 41, 52, 128, 209, 236, 238, 246, 247, 248, 249 bitmap image 149, 191, 192 black 21, 28, 42, 43, 45, 49, 52, 54, 55, 56, 60, 76, 83, 102, 111, 113, 114, 115, 128–131, 139, 140, 149, 151, 155, 158, 159, 160, 161, 172, 173, 183, 193, 210–213, 217, 231, 235, 236, 238, 246, 258, 286 black body temperature 16 blob 62, 67–77, 78–85 blue 18, 19, 28, 43, 45, 46, 64, 65, 91, 92, 105, 114 blur 25, 47, 48, 49, 53, 209, 210, 211, 259 boolean operators 52, 217, 219 boulders 176 brightness 6, 20, 24, 28, 35, 40–43, 44, 46, 47, 48, 49, 108, 126, 134, 137, 138, 170, 171, 181, 182–183, 192, 205, 207, 208, 212, 222, 232 BSE see backscattered electron bulk density 199, 200 C-program or C-programming language 238, 246, 248 calcareous fossils 229–250 calcite 79, 94, 95, 208, 237, 242

calibration 3, 6, 12, 35–56, 38, 209, 285–289 calibration curve (or line) 39 calibration grid 30, 92, 209 calibration standards 5, 21, 36, 39, 57, 134, 176, 208 color or intensity or density calibration 21, 36, 39–40, 43–47, 57, 105, 108, 116–117, 149 grayscale calibration 125–140, 131–134, 169, 176, 191–192 spatial calibration 36, 172, 209 camera analog camera 16, 26, 28 camera set-up 106–107, 110, 112, 254 CCD camera 28, 61, 91, 170, 188, 231, 232, 236, 246, 247, 248, 256 digital camera 14, 16, 28, 40, 92, 105, 106, 128, 170 line scan camera 28, 49, 114, 115, 192 single lens reﬂex camera 24 still camera 105, 109–114, 121, 128 Canada balsam 233, 234 capture conditions see acquisition carbonate 20, 32, 60, 119, 122, 126, 134, 136, 137, 138, 205, 222, 274, 286 Cariaco basin 115, 126 Cauchy-Crofton 76–77 CCD 28, 60, 128, 139, 236, 238, 244 CD-ROM 230, 245 center of gravity 64, 71, 81 central tendency 88, 89, 90 chalcopyrite 91, 98 chalk 62, 63 charcoal 17, 258 chemical, chemistry 2, 24, 25, 88, 89, 105, 117, 119, 135, 163, 215, 216 chequerboard 36, 37, 38, 39 Chinese Loess Plateau 214, 215, 222 chord length 73 chromacity 44 CIE 3, 43, 44, 45, 57, 105, 119 class 42, 80, 241, 242, 243, 244, 253, 257, 264, 266, 267, 268, 269, 270 classiﬁcation 1, 3, 36, 43, 54, 78, 87, 98, 222, 230, 241–246, 249, 250, 253, 254, 262, 263, 265, 266, 267, 271 classiﬁcation success 241, 245 classiﬁer 53, 230, 238, 246, 249, 262, 263, 268 clast 166, 170, 171, 172, 174, 175, 180, 182, 183 closing 54 cloth tape measure 107, 114, 115 CNN see convolutional neural network coating 19, 22, 207, 221 coccolith 2, 234, 236, 237, 239, 240, 241, 242, 243, 247, 249 coefﬁcient 52, 53, 112, 275 approximation coefﬁcient 280, 281, 282, 284, 285, 287, 288, 291

321 backscattered coefﬁcient 204, 205 detail coefﬁcient 282, 283, 284, 285, 287, 288, 289, 290, 291 wavelet coefﬁcient 147, 148, 149, 151, 154, 160, 161, 279, 282, COGNIS (computer guided nannofossils identiﬁcation system) 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250 color (colour) 11–33, 39–52, 43–47, 57, 59, 63–66, 105–123, 108–109, 143–163 additive color 19 color chart or standard 5, 18, 44, 57, 92, 108, 208, 299 color conversion 44–46, 116–117 color depth 27 color intensity 40, 110, 114 color separation guides 108, 139 primary color 19 subtractive color 19 compacity 53, 93 compression 6, 26, 27, 28, 32, 129, 133, 147, 149 lossless compression 129, 130 lossy compression 6, 129, 130 concave 74, 96 cone of inﬂuence 149, 155 connectivity 67, 69–70, 76, 249 four connectivity 76 height connectivity 76 contrast 6, 12, 16, 18–21, 24, 28, 29, 35, 40–43, 44, 53, 66, 108, 112, 129, 130, 144, 145, 151, 152, 157, 159, 170, 183, 188, 191, 192, 205, 207, 208, 222, 232, 234–237 contrast enhancement 20, 40–41, 47, 48, 49, 55, 94, 108, 149, 171, 198, 216 spurious contrast 207 convex 55, 56, 72, 77 convolution 53, 147, 259, 281, 282 core 2, 15, 26, 42, 50, 55, 61, 106, 107, 109, 110, 112, 120, 123, 125–140, 149, 159–163, 165–183, 203, 208, 214, 221 split core 21, 114, 115, 122, 126, 169, 174, 177 whole core 21, 169 correlation 66, 77, 78, 82, 113, 114, 116, 117, 119, 120, 126, 134, 136, 137, 150, 161, 199 auto-correlation 30, 84 pearson’s correlation coefﬁcient 113, 114, 197 coulometry 136 covariance 64, 65, 71, 82, 83, 84 cover slip 232, 233, 234, 247 crossed polarized light (XPL) 20, 21, 55, 236 crystal 21, 24, 29, 30, 38, 62, 74, 79, 94 Cu sulﬁdes 89 Cumberland sound, SE Bafﬁn Island, Nunavut, Canada 166, 176, 181, 182 current 5, 25, 32, 168, 177, 207, 215, 216, 221, 222, 232, 239, 240, 244 alternating current (AC) 31, 32, 208 direct current (DC) 32, 208

cyan 19 cycles 122, 154, 156, 158, 159, 160, 161, 266, 290 climate cycle 2, 126, 154 orbital cycle 143, 144 solar cycle 143, 144, 161 cyclicity 126, 144, 152, 158, 161, 163, 284, 289 cyclothems 215 D65 44, 45, 57 DC see direct current DendroScan 145, 193, 194, 196, 197 density 18, 21, 25, 27, 35, 70, 78, 90, 98, 119, 120, 121, 122, 128, 129, 168–171, 177, 183, 188–189, 192–193, 196–200, 205, 247 density proﬁle plot 192, 193 density wedge 5, 26, 39, 208 Deep Sea Drilling Program (DSP) 4, 125, 126, 128, 131 deposition 143, 144, 159, 165, 166, 176–178, 181, 197, 198, 199, 215, 284 depth scale 144–163 depth of ﬁeld 5, 24, 27, 125, 139, 253 detector 30, 51, 52, 128, 205–209, 211, 213, 216, 223, 236 detector efﬁciency 208 detrital (input) 98, 195, 197, 198, 199 deviation 88, 109, 197 diameter 37, 39, 59, 70–74, 80, 90, 99, 179, 246 circumscribed disk diameter 73–74, 75 equivalent disk diameter 71, 96, 98, 206 equivalent inertia diameters 71–72 feret diameter 72, 73, 74, 75, 81, 96 inscribed disk diameter 73–74 diametric variation 73, 76, 77, 82 diamicton 21, 165–183 diatom 20, 111, 119, 122, 150, 159, 205, 239 dichroic 19 diffuse backlighting source 17 diffusion screen 17 digital imaging 2–6, 24, 30, 36–38, 43, 56, 59–61, 62–63, 67, 69, 77, 78, 90, 92, 101, 105, 110, 130, 139, 166, 188, 189, 192–193, 198, 203, 209, 216, 222, 232–234, 238–239, 245 digitization 15, 30, 60, 209, 236–238 digitizing device or digitizing unit 230, 234, 246 dilation 54–55, 84–85, 98 dinoﬂagellates 244 diode array 26 discrimination 65, 91, 92, 318 dispersion 41, 62, 63, 64, 82, 85, 88, 89, 93, 94, 97 distribution 85 asymmetric distribution 64, 94 Gaussian distribution 64, 94 normal distribution 64 Poisson distribution 85 skewed distribution 64, 177 Student distribution 65

322 division 52 DLL see dynamic link library dolomite 213–214 DPI or dot per inch 12–14, 20, 27, 139, 140, 170, 191 DS (organic annual ﬂux) 197–199 DSDP see Deep Sea Drilling Program 125, 126, 128, 131 dyadic see discrete wavelet transform dynamic link library (DLL) 238, 248, 249 Eagle Basin, Colorado, USA 215, 216 edge 17, 53, 107, 144, 211, 262, 265 edge detection 6, 35, 51–52, 56 edge effect 148–149, 155, 157, 159 EDM see euclidean distance map EDS see energy dispersive dpectroscopy Efﬁngham inlet, British Columbia 150, 159 electromagnetic spectrum 11, 18, 19, 25 electron gun 31, 204, 236, 249 electron gun alignment 208 electron gun tilt 31 electro-osmotic knife 21, 107 ellipse 6, 71, 75 ellipse of equivalent inertia 71, 72, 73, 74, 96 best ﬁtting ellipse 6, 95, 174, 206 elongation 72, 74, 75, 81, 97 energy dispersive spectroscopy (EDS) 2, 213 enlargement 27, 93, 94, 170 entropy 53, 93 environment 1–4, 11, 12, 21, 43, 46, 59, 87, 100, 116, 126, 144, 151, 161, 163, 187–188, 193, 197, 203, 204, 211, 222, 244, 245, 273, 274, 283, 284, 290 epoxy 21, 29, 188, 190, 191, 205 equidistant 145–147, 151, 152, 154 erosion 54, 55, 73, 74, 80, 98, 159 error 36–40, 87–102, 106, 126, 129, 136, 138, 140, 143, 148, 149, 154, 159, 163, 170, 172, 183, 195, 205, 211, 259, 264, 268 analysis error 88, 90, 98–100, 101 error Rate 241, 242, 243, 244, 263 integration error 88, 90, 93–97, 101 preparation error 88, 90, 91–93 sampling error 88, 93–97 systematic error 88, 89, 90, 92 estimator 67–73, 77, 90 Ethernet 238 euclidean distance 66 euclidean distance map (EDM) 54 euclidean geometry 67, 77, 84, 89 exposure 12, 13, 15, 16, 21, 24–28, 129, 137, 139, 168, 177, 189, 190, 236, 238, 244, fabric 1, 2, 174, 177–179, 182, 214 factorization 53, 93 fall 188, 189, 197

Faraday cup 216, 222 fayalite 89 feature extraction 254, 262 Feature extraction layer 264, 265, 266 feature of interest 5, 41, 42, 47, 49, 52–54, 98, 107, 169, 170, 192, 205, 236–237, 259 FFT see Fourier ﬁber optics 235, 246 ﬁeld 37–39, 60, 63, 78–79 ﬁeld of view 5, 12, 15, 28, 37, 40, 41, 52, 53, 61, 93, 95, 108, 209, 210, 222, 234, 235, 239, 240, 244 ﬁlament 5, 29, 31, 232, 236 aging ﬁlament 31 ﬁlament Saturation 236 LaB6 ﬁlament 30, 31, 32, 37, 223, 248, 249 microscope ﬁlament 5 tungsten ﬁlament 16, 31 ﬁlm 13–16, 18, 19, 21, 24–27, 126, 128–131, 133, 139, 168, 177, 188, 189 ﬁlter 6, 18, 47, 56, 91, 92, 129, 169, 172, 192, 210, 211, 213, 217, 219, 223, 259, 266, 280, 281, 290 additive ﬁlter 19 averaging ﬁlter 47, 48, 52, 53, 255 bandpass ﬁlter 18, 24 Chei ﬁlter 211 color ﬁlter 19, 64, 91, 92 cross-polarized ﬁlter 21 edge-ﬁnding ﬁlter 211, 212, 214, 217 Gabor ﬁlter 265 Gaussian blur 49, 53, 210, 259 Haralick ﬁlter 214, 217, 219 hybrid-median ﬁlter 48, 214, 216, 217, 219 interference ﬁlter 18, 91 Kirsch operator 52, 53, 211, 212 Laplacian ﬁlter 51, 53, 216, 219 longpass ﬁlter 18 lowpass ﬁlter 18, 259, 280 median ﬁlter 48, 49, 52, 172, 173, 211 neutral density ﬁlter 18, 21 noise ﬁlter 6, 47, 172, 255 polarizing ﬁlter 18, 19, 20, 21, 236, 237, 247, 248 shortpass ﬁlter 18 smoothing ﬁlter 49 Sobel edge detector / ﬁlter 51, 53, 56, 211, 212, 214, 219 subtractive ﬁlter 19 ﬁltering 3, 11, 18–21, 35–57, 98–100, 147, 209– 211, 219 ﬂuorescence 16 focal depth 258 focal length 93, 125, 189 focal plane 233, 234, 239, 258, 259 focal spot size 189 focus 24, 37, 92, 93, 189, 204, 232, 239–240, 244, 258–262

323 focus value or function 239, 240, 244, 258, 259, 261 foraminifera 176, 181, 229, 230, 232, 238, 244–246 foreground 234, 254, 255, 258, 270 Ford-Walford plot 286–288 Fourier 77, 273, 274–276, 277, 285 fast Fourier transform (FFT) 130 Fourier spectrum 275 Fourier transform 147, 276, 277, 278, 280, 282, 291 short time Fourier transform 277, 278 windowed Fourier transform 277 fractal 75, 77, 262 fracture 62 frame grabber 25, 209, 231, 232, 236, 240, 246, 247, 248 freeze-drying 21, 29 frequency 30, 31, 78, 81, 147, 151, 275, 277, 278, 279, 286, 290, 291 frequency localization 273 high frequency information 119, 126, 129, 130, 144, 145, 149, 212, 213, 219, 258–260 fresh water 273, 283, 286, 288 gain 92, 236 galena 98 gamma 43, 44, 51, 119, 129, 131, 132, 139, 140 gamut 42, 46, 53, 117, 129 Gaussian 64, 94, 147 GEOTEK 114, 115, 122 GISP2 126 glacial period 119, 215, 220, 282 glacial marine sediments 165–182 glaciation 215 glacioeustasy 215 glare 16–19, 24, 126, 131, 140 glass 89, 190, 191, 192, 207, 208, 222, 232 Gondwana 215 grain 14, 17, 29, 38, 47, 51, 54, 55, 56, 62, 77, 79, 85, 93–101, 193, 203–223 grain boundary 47, 48, 49, 55, 54, 100, 205, 211, 212, 216, 217, 219, 223, 246 grain-size 2, 174, 175, 176, 177, 179, 180, 182, 199, 203, 213–223, 246 grain-size analysis see granulometry grain-supported facies 98 granular material 90 granulometry 95, 100, 165, 166, 168, 173 GRAPE 119, 120 gravity ﬂow 176 gray (grey) 43, 50, 69, 110, 113, 151, 191, 210, 216 18% gray sheet or card 5, 108, 110, 113, 114, 139 graycard light correction 112 gray chart 27, 131, 132, 134, 135, 137, 138 gray level & gray scale & gray value 3, 13, 20, 21, 35, 39, 41–45, 48–50, 52, 53, 55,

59, 62, 63, 65, 66, 85, 92, 98, 99, 106, 110, 111, 113, 116, 121, 125–140, 139, 140, 144, 145–147, 150, 152, 153–155, 157, 159–161, 166, 169, 170, 176, 177, 182, 183, 188–193, 197, 198, 199, 200, 207, 209, 210, 211–213, 214, 216, 217, 219, 234, 235, 239–241, 246, 248, 255, 256, 284, 285 neutral gray 108, 109, 112, 113 nominal grayscale 132 green 28, 43, 45, 46, 64–66, 91, 105, 114, 115 Greenland shelf 126, 166, 176, 182 grid 5, 15, 30, 37, 68, 70, 73, 74, 78, 92, 209, 258 growth increments 143, 144, 273, 283–287, 289, 291 Haar scaling function 279, 282 hardware 3, 5, 6, 12–14, 26, 27, 32, 91, 92, 108, 125, 128, 166 harmonic 126, 274–276, 290 hematite 79 hercynite 89 heterogeneity 96, 136 high-resolution 2, 3, 26, 28, 32, 95, 105, 106, 126, 143, 149, 161, 163, 172, 191–193, 213, 214, 216, 222 high tension (HT) 37, 232 histogram 41–43, 53, 63, 65, 79, 80, 98–101, 177, 179, 211, 213, 217, 219, 234 minimum histogram 93 Holocene 119, 143, 147, 206, 242, 283 homogeneity 2, 51, 53, 66, 89, 204 homoscedasticity 66 holodisc distance 74 hue 43, 119 ice-proximal 176 iceberg rafted debris (IRD) 165, 166, 174, 175, 179 icehouse 215 Iceland and Icelandic shelf 165, 166, 175, 176, 181, 182 IEEE or Institute of Electrical and Electronic Engineers 13, 238 illumination 5, 6, 16, 17, 18, 26, 31, 40, 139, 233, 235–236, 246 backlight illumination 17 brightﬁeld illumination 17 diffuse illumination 16, 17 directional illumination 16, 17 illumination source 16, 18 uniform or even or regular illumination 17, 40, 109, 139, 234 non-uniform or uneven or irregular illumination 4, 13, 16, 17, 18, 40, 41, 56, 106, 209, 210, 234, 235, 254, 255 ilmenite 79

324 image binary image 6, 52, 56, 54–56, 69, 82, 100, 171, 172, 173, 205, 206, 219, 257 black & white image 52, 92, 99, 128–130, 139 image acquisition 1, 3, 4, 5, 6, 11–33, 36, 37, 40, 59, 85, 91, 92, 149, 166–170, 174, 181, 204–209, 221, 222, 230, 236, 238, 244, 254 image calibration 6, 11, 15, 21, 27, 35–57, 199, 209 image classiﬁcation 3, 36, 54, 78, 87, 98, 222, 240, 241, 250 image compression 6, 28 image depth 92 image distortion 15, 32, 36, 37, 38, 106, 125, 166, 169, 170, 190, 209, 241 image enhancement 3, 6, 11, 12, 19, 36, 40–43, 47, 56, 192, 234, 236 image exposure 15 image intensity 207–208 image lifecycle 125, 129–130 image math 52, 36 image measurement 6, 36, 38, 59–85, 172–174, 183, 213–214, 223 image overlap 13, 15, 107, 112–114, 117, 177 image pre-processing 3, 35, 36–43 image processing 1–6, 11, 12, 16, 27, 47–56, 59, 95, 101, 119, 146, 147, 149–151, 170–172, 182–183, 191–192, 209– 213, 217, 263 image quality 5, 11, 12, 14–16, 26, 30, 31, 32, 37, 87, 91, 92, 107, 122, 129, 130, 131, 152, 169, 177, 189, 191, 200, 205, 207, 208, 209, 216, 230, 245, 262 image registration 15–16, 26, 30, 106 image representativity 5, 6, 59, 61, 111, 112, 214 image resolution 12, 14, 32, 37, 96, 129, 150, 152, 170, 206, 210, 222, 238 image scale or size 12, 14, 129, 170, 182 image segmentation 6, 12, 36, 56, 52–54, 78, 90, 98, 171, 183, 209, 211–213, 216, 223, 233–236, 246, 248, 255 overview image 38, 230, 244, 245, 248, 249, 265 range image 284–290 IMAGES, International Marine Past Global Change Study 2, 4, 182 inclination 166, 173, 174, 175, 177, 179, 181, 182 input 43, 44, 52, 130, 161, 262–266 input device 129 input layer 263, 264 input signal 44 integration time 92 intensity, see pixel or light or image interaction volume 205, 213, 223 interglacial period 126, 215, 220 intersection 67, 68, 73, 82, 83

intercept 68, 69, 73, 77 IR see infrared light IRD see iceberg rafted debris or detritus iron oxides and iron sulﬁdes 204, 208, 222 isotropic 82, 169 ITU-R 45 JOIDES Resolution 125, 131, 139 JPEG or JPG 6, 27, 28, 130 Jura Montains, France 282 Kangerlussuaq, East Greenland 176, 185 kernel 47, 51–54, 56, 299 Kodak Q-13 card 131, 132, 134, 137, 139, 140 Krumbein 1, 77, 78, 213 KV 25, 37–38, 177, 189, 205, 215, 222, 223 L* 46, 110, 115, 117, 118, 119, 120 L* a* b* 3, 6, 27, 43–45, 50, 66, 105, 115, 116, 117, 119 LaB6 see ﬁlament Laguna del Hornillo, Central Spain 99, 206 Lake Baikal, Siberia 96, 102, 184, 224 Lake El’gygytgyn, Siberia 94, 102 Lake Nautajärvi, Finland 187, 188, 190–193, 195– 202 Lake Saint-Cierges, France 286, 288 Lake Vico, Central Italy 55, 100, 101 lamina or lamination 2, 20, 47–49, 60, 98, 105, 119, 122, 143, 144, 147, 149–151, 154, 159, 163, 189, 201 Laplacian operator 51, 53, 216, 219 lead (Pb) 169, 177 LED see light emitting diode 17 lens 12, 13, 15, 17, 21, 28, 37, 105, 107, 139, 204, 239, 240 ﬁnal lens 232, 240, 244 lens aberration 15, 208 macro lens 24 light 16, 18, 19, 24, 27, 28, 42, 43, 62, 95, 106, 109, 110, 114, 131, 139, 232 coaxial light 17 cold light source 235, 246 cross-polarized light (XPL) 235, 236, 238, 299 day light 44, 106, 139 diffuse light 17, 24 ﬂood light 16 infrared light (IR) 2, 11, 16, 18 near-infrared 11, 16, 105 light correction 105, 107, 109, 109–116, 117, 122, 131 light curve standard deviation 110–112 light distribution 40, 41, 42, 109, 110, 111, 112, 113, 114, 210 uneven light distribution 40, 41, 106, 107, 109, 110, 111, 112, 114, 117, 122

325 uniform light distribution 109 light intensity 5, 37, 40, 43, 45, 92, 106, 107, 108, 109, 110, 112, 234, 235, 236 light sources 16, 17, 18, 19, 27, 40, 46, 107, 108, 110, 114, 115, 122, 131, 170, 234, 246 reﬂected light 15, 18, 26, 27, 61, 106, 235 refracted light 140 transmitted light 15, 17, 20, 21, 22, 27, 61, 205 ultraviolet light 11, 16, 18, 234 visible light 105 light emitting diode (LED) 17 light ﬁltering 11, 18–21 lighting 12, 15, 16–18, 24, 27, 52, 106, 126, 128, 131, 133, 134, 139, 140, 255 lightness 43, 44, 110, 115, 117, 119, 191 LM see light microscope lithofacies 166, 175 lithology (lithologic) 105, 128, 129, 135, 138, 181 loess 126, 214, 215, 219 loessite 203, 214–216, 219–223 luminance 44, 45, 117, 129, 130, 131, 133 luminance factor 129 LUT 55, 182, 183 LS (annual minerogenic ﬂux) 197, 199 LZW 130 macro or script 49 magenta 19 magnetic susceptibility 126, 181, 225 magniﬁcation 5, 6, 12, 14, 15, 22, 24, 29, 36, 60, 61, 79, 90, 94–96, 190, 208, 209, 216, 221–223, 232, 236, 240, 249, 255 Mahalanobis distance 65, 66, 92 major annulus 288 Mallat’s dyadic algorithm 280, 281, 283 marine oxygen isotope stages 126, 140 marine stratigraphy 125 Marion Dufresnes 182 mathematical microscope 273, 280, 291 mathematical morphology 59, 74, 77, 82, 85 mathematical operations 36, 52 matrix 46, 65, 71, 117, 149 maximum likelihood 53 mean 29, 39, 52, 53, 63–66, 94, 99, 112, 116, 135, 140, 145, 150, 154, 159, 178, 196, 197, 199, 200, 204–206, 246, 257, 288 arithmetic mean 64 geometric mean 64 measurements 1–6, 36–39, 59–85, 87–90, 93, 93– 101, 172–175, 178, 179, 183–184, 213–214 median 48, 64, 93, 96, 98, 100, 115, 178, 180, 181, 197, 199, 206, 219, 220, 221 memory 28, 171, 182, 236 mesh 79 metadata 5, 6, 35, 55, 126, 129–131, 139, 171–173, 182, 208, 223

microfossils 2, 4, 38, 229–250, 253, 262–265 micrometer 37 microprobe 204, 207, 213, 222 microscope 16, 20, 21, 28, 92, 229, 230, 243, 254 binocular microscope 1, 205 microscope’s column 31, 208, 233, 236 environmental scanning electron microscope (ESEM) 22, 204, 205, 207 incident light microscope 235 light microscope (LM) 36, 37, 57, 230–239, 244–248, 250, 259, 262, 263 petrographic microscope 55, 96, 251 scanning electron microscope (SEM) 4, 5, 11, 22, 28, 29, 30, 31, 32, 36–39, 67, 92, 95, 96, 149, 150, 199, 204, 205, 207– 209, 214, 222, 223, 230, 231, 232, 233, 234, 236, 238, 240, 242–246, 248, 249, 262, 263, 286 stereomicroscope 193, 235, 246 transmitted light microscope 15, 22, 205, 230, 232, 235–236, 238, 239, 244, 246, 248 microtopography 284, 286 Milankovitch 119, 126, 144, 274 Miles-Lantuejoul 96, 80 mineral or mineralogy 2, 18, 19, 25, 39, 53, 63, 91, 92, 98, 143, 159, 161, 163, 176, 181, 188, 189, 193, 195, 197, 198, 199, 204, 211, 217, 229 minerogenic sum 196–198 mispickel 91, 92 monochromatic 28, 125, 126, 137 monospectral 92 monsoon 215 morphology see mathematical morphology morphometry 2, 229, 230, 245, 246 morphometric data 96–98, 230, 245 mosaicking 117 multi-layer perceptron (MLP) 263–264 multiresolution 273–291 multispectral imaging 91–92, 98, 102 Munsell color chart 44, 51, 108 nannofossils see calcareous fossils National Sciences Foundation-US (NSF) 2, 4, 122, 139, 182 neighbor (neighbour) 36, 47–49, 51, 54, 62–63, 69, 74, 76–77, 112 neural network 229–250, 253–271 artiﬁcial neural network (ANN) 238, 240, 241, 244, 245, 249, 250, convolutional neural network (CNN) 241–245, 249–250 fat neural network 241 fully connected network 263, 264 neural network classiﬁer 230, 238, 246, 249 paradise neural network 254, 264–267, 269, 270

326 supervised network 264 unsupervised network 264 neuron 263–266 neuron planes 265 nickel 91 Nicolay Lake, Nunavut, Canada 14 Nicols 236, 238 NIH-Image 41, 42, 45, 50, 55, 139, 140, 149, 170– 174, 182–185, 192, 198, 217 noise 18, 31, 47–51, 92, 93, 147, 155, 158, 170, 172, 173, 205, 209–211, 289 hardware noise 42, 47, 48, 49, 92, 209, 211 high frequency noise see white noise noise reduction 38, 47, 58, 102, 172, 192, 255, 258 random noise 47, 152 random electronic noise 209 shot noise 48 white noise 145, 151 non-destructive techniques 25, 105, 182, 187, 199 non-invasive sampling 125, 126, 161 nonlinear (non-linear) 26, 37, 38, 43, 44, 51, 116, 117, 125–140 North Atlantic 134, 137, 176 NSF see National Science Foundation NTSC 31 ODP or Ocean Drilling Program 55, 105, 106, 111, 113, 115, 117–123, 125–128, 131, 132, 134, 137–140 offset 92, 236 Olivetti research laboratory database 241, 242 ontogenesis 284, 286 opaque 17, 26 opening 54, 73, 77–78, 100, 101, 217, 219 optical density 128–129, 131, 133, 140 optical resolution 12, 13, 191 optics 28, 27, 234, 235 organic (input) 98 organic annual ﬂux (DS) 197, 198, 199 organic matter 66, 119, 122, 188, 195, 197, 198, 205, 258, 285 orientation 6, 52, 59, 62, 71–74, 81–82, 85, 100, 101, 166, 174, 176, 178, 180, 181, 209, 236, 237, 244, 253, 265 outliers 154, 156, 159, 178–180 output 130, 151, 154, 160, 161, 193, 194, 197, 209, 223, 241, 257, 263, 264–266 output layer 263 output media 31, 40, 43, 52, 129, 150 overlap 13, 15, 16, 107, 112, 113, 116, 117, 169, 175, 177, 178, 181, 190, 203, 205, 232, 243, 254 PAL 31 paleoclimate 2, 4, 5, 126, 128, 129, 143, 203, 204, 211, 214, 215, 220, 222

paleoenvironment (past environments) 21, 87, 163, 187, 203, 274 paleoenvironmental reconstruction 11, 193, 204 paleoenvironment research 12, 59, 100, 211, 222 Paleozoic 214, 215, 222 Palmer deep, Western Antarctica 113, 119, 120 Pangea 215 Paradox basin, Utah, USA 220 parallax 6, 25, 107, 117 particle 37–39, 68, 71–74, 77, 79–85, 95, 97, 172– 174, 176, 179, 183, 214, 222, 229–250, 253 pattern detection layer 265 pattern detection module 265, 266 pebbles 166, 170, 175, 176 pedogenesis 220 pentlandite 91, 92 perceptron 263–264 perimeter 6, 63, 67, 73, 75–77, 84, 85, 89, 168, 173– 175, 177–180, 182, 183, 217, 223, 246, 262 inner perimeter 76 outer perimeter 76 period 147, 158, 161, 274, 290 periodicity 144, 163, 289 periodogram 158 periostracum 284, 286 Permian 215 phase 1, 4, 18, 40, 41, 47, 49, 51, 54, 78, 79, 82, 87, 91–95, 98, 100, 156, 157, 163, 189, 203, 206, 207, 210–214, 217, 222, 236, 237, 248, 274, 275, 277, 289 phase ratio 93, 94 photodiode 26 photography 11, 16, 17, 21, 22, 108, 131, 139, 140 analog photography 4, 11, 24–28 digital photography 4, 11, 28, 32 photographic stand 106 photomicroscopy 16, 17, 22 sediment core photography 125, 126, 131, 137, 208 photospectrometer 105, 119, 120, 122 pixel 3, 6, 12, 13, 14, 27, 28, 36, 38–43, 46–56, 59– 66, 69–70, 73, 75–78, 82–83, 87–90, 92, 94–98, 100, 101, 108–110, 112, 117, 140, 145–147, 150–152, 159, 163, 168, 170– 174, 183, 191, 193, 206, 209–214, 216, 217, 219, 222, 223, 236, 238, 242, 246, 255– 260, 284, 285, 287, 289, 290 non-functional or dead pixels 28 pixel ratio or shape 6, 36 pixel resolution 89, 94, 236, 238 pixel size 12, 14, 36, 38, 95, 101, 147, 151, 238 pixelization 14, 89 pixel density or intensity 4, 12, 39, 51, 56, 62, 63, 170 neighboring or adjacent pixel 36, 47, 51, 54, 62, 69, 77

327 plan apochromat objectives 235, 246 plane 19, 67, 68, 233, 234, 239, 258, 259, 265, 284, 289 Pleistocene 55, 140, 184, 214, 220 Pliocene 119 plug-ins 211 point 67–69, 74 polish 205, 211, 214 polished samples 22, 23, 29, 88, 107, 193, 205–207, 209, 213, 215, 221–223 polishing grit 23, 207, 215 pollen 4, 244, 253–271 polynomial 66, 110–112, 131, 133, 135 population 41, 53, 61, 65, 78, 80, 81, 286 porosity 54, 122, 205 power spectrum 116, 273, 289 precision 38, 70, 88, 89, 93, 94, 119, 236, 238 prismatic layer 284, 286 probe 67, 68, 69 productivity 27, 122, 144 pumice 169 pyrite 91, 92, 98, 119 pyrrhotite 89, 98 quality control 1, 3, 21, 87, 101, 125, 229, 230 quantiﬁcation 1, 4, 7, 11, 12, 14–17, 24, 28, 32, 36, 39, 66, 67, 75, 85, 87–102, 105, 125, 128, 188, 197, 200, 219, 229 quartz 81, 205, 208, 212–222 Quaternary 123, 163, 215, 222 radiocarbon 143, 144, 163 random 67, 68, 78, 79, 80, 85, 108, 152, 220, 243, 289 rank leveling 40 recognition 4, 229, 230, 245 particle recognition 230, 232, 244, 245, 253– 271 pattern recognition 265 recommendations 1, 5, 221 red 18, 19, 43, 45, 64, 66, 114, 183 reﬂectance 61, 64, 105, 123, 126, 140, 235, 246 reﬂectivity 40, 110 region of interest (ROI) 205 registration 15, 16, 26, 30, 106, 188 rejection rate 268 representativity 5, 6, 40, 41, 59, 61, 87, 92, 107, 108, 109, 111, 112. 169, 176, 214, 222 reproducibility 6, 7, 36, 38, 39, 55, 88, 118, 129, 229, 245 resolution 5, 6, 11–14, 22, 24, 26–28, 32, 36–38, 55, 60, 70, 77, 78, 89, 90, 94–96, 105, 119, 121, 129, 130, 133, 140, 147, 150, 152, 159, 170, 172, 174, 176, 183, 189–192, 199, 206, 207, 209, 210, 222, 223, 236, 238, 281, 284 color or gray level resolution 26, 27, 92, 247, 248

interpolated resolution 12, 27 optical resolution 12, 13, 191 pseudo-resolution 47 spatial resolution 26, 27, 30, 32 reticule grid 37 RGB 3, 5, 20, 43–47, 50, 51, 64, 65, 91, 92, 98, 109, 114–117 linear RGB 44, 46 non-linear RGB 43, 117 rhyolite 169 robot 229, 230, 234, 245, 246 robustness (robust) 31, 70, 73, 77, 87–89, 92, 98, 147, 174, 179, 188 ROI see region of interest rose diagram 82 rotation 70, 74, 76, 232, 238 roughness 77, 89, 101, 262 roundness 7, 59, 77, 78, 81, 86, 177, 246 RS232 238, 246, 247, 248 ruler 5, 15, 107, 110, 117, 127, 131, 139 Saanich inlet, British Columbia 111, 122 safety 16, 25 sample 61 sample geometry 15, 106 sample preparation 21–23, 174, 188, 205–207, 215, 232–234 sample shape 15, 26, 32 sampling 6, 18, 21, 59, 61, 67, 68, 75, 76, 78, 87, 88, 90, 93, 101, 102, 145, 166, 168, 174, 176, 177, 199, 214, 221 nested sampling 61 sampling theory 59, 85 subsampling 21, 23, 25, 26 Sanagak lake, Nunavut, Canada 13 sand 14, 29, 62, 77, 81, 97, 107, 165, 175, 214, 232 Santa Barbara basin, off California 121–124 saturation 236 Sawtooth lake, Nunavut, Canada 29 scale 11, 12, 14, 62, 75, 77, 90, 107, 143–163, 166, 170, 172, 183, 280–285, 287, 289, 290, 291 scale factor 96, 147, 278 scaling function 279–282, 291 scalogram 149, 151, 155, 157, 159, 162 scan 14, 24, 92, 172 linescan 28, 37, 49, 108–117, 121, 122, 143– 147, 149–151, 155, 192 scan speed or time 37, 93, 223 slow scan 30, 31, 38, 208, 232, 236, 238, 248, 249 scanner 12–16, 20, 21, 27, 28, 114, 122, 139, 169, 170, 171, 176, 183, 191, 205 3D scanner 284, 285, 286 scanning 13, 20, 24, 26–28, 67, 69, 108, 109, 128, 129, 140, 149, 171, 177, 183, 184, 239 scanning interface unit (SIU) 209 scene 59, 60, 62, 73, 90–92, 95, 125, 129–131, 133– 135, 139–140

328 Scheffe test 178 Schottky ﬁeld emitter 31, 236 SCOPIX 188, 191 scraping 21, 107, 121 scratch 107, 109 script see macro season 122, 145, 152, 188, 191, 192, 195, 197, 198, 200, 215, 250, 286, 291 seasonal resolution 192, 200 seasonality 215 SECAM 314 secondary electron 29, 30 sediment anoxic sediments 147 bedded sediment 106, 119 clastic sediment 21 clay-rich sediment 21, 119, 126 deep-sea sediments 125, 126 eolian sediment 126, 140 glacial marine sediments 165, 176–178, 180, 181 impregnated sediment 190, 193, 203 marine sediment 3, 125, 126, 128, 144, 147, 159, 165, 166, 174, 187, 214, 222 lacustrine sediment 2, 3, 5, 144, 165, 187, 188, 193, 214, 222 laminated sediment 4, 13, 14, 20, 29, 41, 48, 49, 106, 112, 117, 119–122, 143, 146– 148, 159, 161, 163, 166, 187, 188, 193 sediment bed 111, 112, 119, 144, 273 sediment core 2–5, 16, 21, 24–26, 87, 100, 106, 107, 109, 110, 125, 126, 138, 139, 145, 165–183, 190, 191, 214 sediment gravity ﬂows 176 sediment matrix 51, 84, 98, 165, 172, 176, 205, 211–213, 216, 217, 219, 284 sedimentary event 111, 112, 204 sedimentary sequence 60, 98, 191, 199 sedimentary structure 3, 21, 25, 187, 199 terrigeneous sediments 184 unconsolidated sediment 176, 198 varved sediment 2, 106, 111, 121, 168, 189, 192, 214, 282 sedimentation 122, 143, 163, 187, 198 sedimentation rate 126, 144–147, 151–160, 163 segmentation 6, 12, 35, 36, 52–56, 78, 90, 98, 171, 172, 181, 183, 209, 211–213, 216, 219, 223, 233–236, 246, 248, 255 behavioral segmentation 98 convex Hull segmentation 98 multigaussian segmentation 98 SEM see microscope sensitivity 28, 89, 129, 132–134, 208, 236, 238, 244 sensor 13–16, 18, 21, 26–28, 284 shadow (shadowing) 16, 17, 18, 84, 90, 107, 138, 189, 190, 206, 235

shape 15, 26, 32, 36, 54, 64, 70–74, 77, 80, 85–90, 93, 96–97, 99, 107, 111–114, 132, 170, 174, 175, 178–181, 206, 207, 211, 212, 222, 223, 240, 262, 263 sharpness 158, 190, 235 shell growth 273–292 SI (units) 36 sieve 79, 224 signal-to-noise ratio 28, 30, 144, 151, 207, 209 silt 14, 29, 121, 122, 165, 175, 214, 215, 220 siltstone 187, 212, 213 single lens reﬂex camera 24 size distribution 54, 79, 80, 85, 86, 176, 177, 219 skewness 64, 177, 180, 197 SKIZ (skeleton by zone of inﬂuence) 85 slab 3, 4, 15, 21, 107, 114, 159, 160, 168, 169, 191, 207 SLR camera: see single lens reﬂex camera smear slides 232, 233, 258 SMPTE or Society of Motion Picture and Television Engineers 44, 315 software 3–6, 13, 27, 36, 40, 45, 48, 51, 74, 89, 106, 125, 128, 129, 149, 166, 171, 182, 183, 193, 198, 211, 230–233, 236, 238, 244–249, 253–271, 291 solar irradiance 144 spatial localization 277 spectral analysis 147, 156, 158, 273, 274, 284, 285, 289, 290, 291 spectroscopy 18, 119 spectrum 11, 18, 24, 25, 64, 77, 105, 116, 119, 126, 151, 155, 156, 159, 160, 273–276, 279, 289, 295 sphalerite 98 sphericity 74 spring 111, 122, 159, 188, 189, 193, 197 spot size 37, 119, 120, 189, 190, 208, 222, 223, 232 stage 17, 21, 22, 27, 31, 34, 210, 222, 232, 239, 240 automated stage 238, 254 motorized stage 230–232, 236, 244, 246, 247– 249 standard 5, 18, 21, 26, 32, 36–40, 108, 128, 132, 134, 135, 139, 140, 169, 171, 176, 183, 222 standard deviation 39, 93, 110–112, 116, 119, 136, 137, 178, 197, 259 stannite 98 statistics 59–62, 65–67, 81, 82, 84, 85, 93, 119, 136– 137, 152, 177–181, 183, 197, 198, 229, 240, 244, 249 multivariate statistics 64, 98 spatial statistics 59, 60, 82, 85, 93 stereology 59, 67, 68, 70, 73, 78–80, 82, 85, 222, 223 STFT see short time Fourier transform stochastic Geometry 85 storage capacity or space 11, 14, 27, 107, 125, 129 stray marks 170, 172, 173, 183 subtraction 41, 52, 111, 113, 131, 134

329 Sudbury 91 sulﬁdes 89, 91, 93, 204 sulfur 93 summer 111, 122, 144, 151, 152, 159, 188, 189, 286 sun spot 274 surface area 54, 89, 94, 101, 206–208 support 4, 60, 61, 66, 70, 93 SYRACO 241 target 13, 21, 27, 38, 39, 205 taxa 240, 242–245, 266, 268 taxonomy 230 test (testing) 3, 6, 13, 31, 40, 65, 85, 87–101, 107, 110, 116, 117, 126, 131, 133, 134, 139, 152, 178, 189, 206, 210, 220, 223, 241, 243, 244, 247, 249, 266–271 texton 62 texture 21, 54, 62, 73, 84, 187, 204, 212–214, 262– 263 Thiessen polygon 85 thin section 5, 7, 15, 16, 17, 20–22, 27, 55, 61, 67, 79, 93, 98, 149, 150, 190, 203–223 threshold 90, 94, 98, 99, 100, 129–131, 144, 176, 217, 235, 246–248 automated thresholding technique 92, 93, 98, 234 threshold response 130 thresholding 6, 52, 53, 54, 102, 144, 209, 211– 213, 217, 219, 223, 234 tides 185, 274, 290 TIFF 6, 28, 130, 139, 149, 171 till 176–178, 180, 181 sub-glacial till 165, 176 time scale 2, 143–163 time series 105, 106, 108, 116, 122, 124, 126, 143– 163 tint 43 tomography 39, 176 tones (mid-tones) 132, 134, 135, 138 training 241–245, 249, 263–268 training (data) Set 243, 264, 266 translation 44–46, 48–50, 70, 83, 115–116, 119, 121, 241, 275, 278, 291 translation parameter 277, 278 transparency 17, 20, 70, 169, 170, 191, 205 tree rings 143, 144, 161 trigonometry 274 tristimulus values 44–47, 108, 116, 117 TV 30, 31, 37–39, 57, 209, 236, 240 ultimate eroded set 74 umbo 288 universe 60, 61

upwelling 122 UV see ultraviolet light validation 87–88, 195 variance 62–66, 88, 131, 136–138, 151, 154–156, 158, 161, 177, 199, 255–257, 274 variability 24, 89, 90, 93, 115, 123, 126, 133, 134, 144, 145, 151, 155, 157, 159, 161, 163, 188, 193, 214, 244, 246, 253, 258 varves 60, 98, 111, 122–124, 143–146, 149, 150, 152, 187–200 clastic varves 193, 194 organic varves 193, 194 varve chronology 188, 195 varve thickness 144, 145, 148, 151, 152, 154– 156, 159, 161–163, 191, 193, 197 see also varved sediments video 15, 25, 31, 60, 64, 69, 117, 128, 231, 236, 246–248 voids 109, 111 volt or voltage 25, 168, 189, 205, 248 Voronoï polygon 85 Wadell 77, 78 wallpaper 62 warm ﬁeld emission gun 31, 236 water content 21, 106, 107, 123, 177 watershed segmentation 54–56, 172, 286 wavelength 16, 18, 19, 21, 64, 105, 107, 116, 145, 148, 149, 151, 154, 155, 159–161, 163 wavelength dispersive spectroscopy (WDS) 213 wavelet 4, 147–149, 151, 154–157, 159–163, 273, 278, 280, 283–285, 287, 290, 291 discrete wavelet transform 273, 279, 280, 281, 290, 291 Haar wavelet 279, 282 Morlet wavelet 147, 148, 149, 155, 163 mother wavelet 147, 148, 278, 279, 282, 291 wavelet coefﬁcient 147, 148, 149, 151, 154, 160, 161, 281, 282 wavelet transform 143, 145, 147, 276–280 WDS see wavelength dispersive spectroscopy weight 45, 53, 67, 78–81, 89, 136, 241, 249, 263– 265 WFT see windowed Fourier transform white 19, 21, 28, 42–46, 50, 52, 54–57, 61, 69, 76, 99, 109, 111, 113, 121, 128, 130, 131, 133– 140, 149, 155, 160, 172, 196, 213, 217, 234, 236, 238, 246, 258, 259 white point calibration 44 width 37–39, 42, 62, 96, 108, 109, 147, 148, 150, 170, 257 winter 111, 122, 144, 151, 152, 159, 188, 189, 193, 285, 286, 288 working Distance 12, 37, 208, 209, 222, 223, 239, 240 wüstite 89

330 X-ray or X-radiograph 2–5, 11, 13–16, 21, 22, 24– 27, 33, 39, 57, 102, 121, 122, 149, 150, 159–161, 165–183, 187–200, 208 X-ray attenuation or absorption 15, 25, 168 X-ray densitometry 187, 188, 190, 192, 195, 197, 199, 200 X-ray scattering 169

X-ray source 25, 177, 188, 190, 200 X-ray tube 25 X-Y center 174, 179, 183, 217 XPL see crossed polarized light XYZ 44, 45, 46, 116, 117 yellow 19, 43, 50