Neuroscience Chapman & Hall/CRC i S n Mathematical and Computational Imaging Sciences t Statistical and Computational Methods a B t Brain Image Analysis in i r s a t i i c n a l I a m The massive amount of nonstandard high-dimensional brain imaging n Statistical and data being generated is often difficult to analyze using current a d techniques. This challenge in brain image analysis requires new g C Computational Methods computational approaches and solutions. But none of the research e o papers or books in the field describe the quantitative techniques m A with detailed illustrations of actual imaging data and computer Brain in p codes. Using MATLAB® and case study data sets, Statistical and n u Computational Methods in Brain Image Analysis is the first book a t to explicitly explain how to perform statistical analysis on brain l a Image y t imaging data. i s o n The book focuses on methodological issues in analyzing structural i Analysis s a brain imaging modalities such as MRI and DTI. Real imaging l applications and examples elucidate the concepts and methods. In M addition, most of the brain imaging data sets and MATLAB codes e are available on the author’s website. t h By supplying the data and codes, this book enables researchers to o start their statistical analyses immediately. Also suitable for graduate d s students, it provides an understanding of the various statistical and Moo K. Chung computational methodologies used in the field as well as important and technically challenging topics. C h u n g K11644 K11644_Cover.indd 1 5/28/13 12:50 PM Statistical and Computational Methods Brain Image in Analysis K11644_Printer_PDF.indd 1 5/27/13 1:46 AM Chapman & Hall/CRC Mathematical and Computational Imaging Sciences Series Editors Chandrajit Bajaj Guillermo Sapiro Center for Computational Visualization Department of Electrical The University of Texas at Austin and Computer Engineering University of Minnesota Aims and Scope This series aims to capture new developments and summarize what is known over the whole spectrum of mathematical and computational imaging sciences. It seeks to encourage the integration of mathematical, statistical and computational methods in image acquisition and processing by publishing a broad range of textbooks, reference works and handbooks. The titles included in the series are meant to appeal to students, researchers and professionals in the mathematical, statistical and computational sciences, application areas, as well as interdisciplinary researchers involved in the field. The inclusion of concrete examples and applications, and programming code and examples, is highly encouraged. Published Titles Statistical and Computational Methods in Brain Image Analysis by Moo K. Chung Theoretical Foundations of Digital Imaging Using MATLAB® by Leonid P. Yaroslavsky Rough Fuzzy Image Analysis: Foundations and Methodologies by Sankar K. Pal and James F. Peters Proposals for the series should be submitted to the series editors above or directly to: CRC Press, Taylor & Francis Group 3 Park Square, Milton Park, Abingdon, OX14 4RN, UK K11644_Printer_PDF.indd 2 5/27/13 1:46 AM Chapman & Hall/CRC Mathematical and Computational Imaging Sciences Statistical and Computational Methods Brain Image in Analysis Moo K. Chung Waisman Laboratory for Brain Imaging and Behavior University of Wisconsin-Madison, USA K11644_Printer_PDF.indd 3 5/27/13 1:46 AM CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2014 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20130524 International Standard Book Number-13: 978-1-4398-3636-1 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. 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Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2014 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper Version Date: 20130524 International Standard Book Number-13: 978-1-4398-3635-4 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. 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Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com K11644_Printer_PDF.indd 4 5/27/13 1:46 AM To my beautiful wife Hyun Mi Park Contents Preface xv 1 Introduction to Brain and Medical Images 1 1.1 Image Volume Data . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Amygdala Volume Data . . . . . . . . . . . . . . . . . 4 1.2 Surface Mesh Data . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Topology of Surface Data . . . . . . . . . . . . . . . . 6 1.2.2 Amygdala Surface Data . . . . . . . . . . . . . . . . . 9 1.3 Landmark Data . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.1 Affine Transforms . . . . . . . . . . . . . . . . . . . . 11 1.3.2 Least Squares Estimation . . . . . . . . . . . . . . . . 13 1.4 Vector Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Tensor and Curve Data . . . . . . . . . . . . . . . . . . . . . 17 1.6 Brain Image Analysis Tools . . . . . . . . . . . . . . . . . . . 19 1.6.1 SurfStat . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.6.2 Public Image Database . . . . . . . . . . . . . . . . . 20 2 Bernoulli Models for Binary Images 21 2.1 Sum of Bernoulli Distributions . . . . . . . . . . . . . . . . . 21 2.2 Inference on Proportion of Activation . . . . . . . . . . . . . 23 2.2.1 One Sample Test . . . . . . . . . . . . . . . . . . . . . 23 2.2.2 Two Sample Test . . . . . . . . . . . . . . . . . . . . . 26 2.3 MATLAB Implementation . . . . . . . . . . . . . . . . . . . . . 27 3 General Linear Models 29 3.1 General Linear Models . . . . . . . . . . . . . . . . . . . . . 29 3.1.1 R-square. . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1.2 GLM for Whole Brain Images . . . . . . . . . . . . . . 32 3.2 Voxel-Based Morphometry . . . . . . . . . . . . . . . . . . . 32 3.2.1 Mixture Models. . . . . . . . . . . . . . . . . . . . . . 34 3.2.2 EM-Algorithm . . . . . . . . . . . . . . . . . . . . . . 36 3.2.3 Two-Components Gaussian Mixture . . . . . . . . . . 37 3.3 Case Study: VBM in Corpus Callosum . . . . . . . . . . . . 40 3.3.1 White Matter Density Maps. . . . . . . . . . . . . . . 42 3.3.2 Manipulating Density Maps . . . . . . . . . . . . . . . 42 3.3.3 Numerical Implementation . . . . . . . . . . . . . . . 45 vii