Statistical and Computational Methods in Brain Image Analysis  book cover
1st Edition

Statistical and Computational Methods in Brain Image Analysis

ISBN 9781439836354
Published July 23, 2013 by CRC Press
416 Pages 167 B/W Illustrations

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Book Description

The massive amount of nonstandard high-dimensional brain imaging data being generated is often difficult to analyze using current techniques. This challenge in brain image analysis requires new computational approaches and solutions. But none of the research papers or books in the field describe the quantitative techniques with detailed illustrations of actual imaging data and computer codes. Using MATLAB® and case study data sets, Statistical and Computational Methods in Brain Image Analysis is the first book to explicitly explain how to perform statistical analysis on brain imaging data.

The book focuses on methodological issues in analyzing structural brain imaging modalities such as MRI and DTI. Real imaging applications and examples elucidate the concepts and methods. In addition, most of the brain imaging data sets and MATLAB codes are available on the author’s website.

By supplying the data and codes, this book enables researchers to start their statistical analyses immediately. Also suitable for graduate students, it provides an understanding of the various statistical and computational methodologies used in the field as well as important and technically challenging topics.

Table of Contents

Introduction to Brain and Medical Images
Image Volume Data
Surface Mesh Data
Landmark Data
Vector Data
Tensor and Curve Data
Brain Image Analysis Tools

Bernoulli Models for Binary Images
Sum of Bernoulli Distributions
Inference on Proportion of Activation
MATLAB Implementation

General Linear Models
General Linear Models
Voxel-Based Morphometry
Case Study: VBM in Corpus Callosum
Testing Interactions

Gaussian Kernel Smoothing
Kernel Smoothing
Gaussian Kernel Smoothing
Numerical Implementation
Case Study: Smoothing of DWI Stroke Lesions
Effective FWHM
Checking Gaussianness
Effect of Gaussianness on Kernel Smoothing

Random Fields Theory
Random Fields
Simulating Gaussian Fields
Statistical Inference on Fields
Expected Euler Characteristics

Anisotropic Kernel Smoothing
Anisotropic Gaussian Kernel Smoothing
Probabilistic Connectivity in DTI
Riemannian Metric Tensors
Chapman-Kolmogorov Equation
Cholesky Factorization of DTI
Experimental Results

Multivariate General Linear Models
Multivariate Normal Distributions
Deformation-Based Morphometry (DBM)
Hotelling’s T2 Statistic
Multivariate General Linear Models
Case Study: Surface Deformation Analysis

Cortical Surface Analysis
Modeling Surface Deformation
Surface Parameterization
Surface-Based Morphological Measures
Surface-Based Diffusion Smoothing
Statistical Inference on the Cortical Surface

Heat Kernel Smoothing on Surfaces
Heat Kernel Smoothing
Numerical Implementation
Random Field Theory on Cortical Manifold
Case Study: Cortical Thickness Analysis

Cosine Series Representation of 3D Curves
Parameterization of 3D Curves
Numerical Implementation
Modeling a Family of Curves
Case Study: White Matter Fiber Tracts

Weighted Spherical Harmonic Representation
Spherical Coordinates
Spherical Harmonics
Weighted-SPHARM Package
Surface Registration
Encoding Surface Asymmetry
Case Study: Cortical Asymmetry Analysis

Multivariate Surface Shape Analysis
Surface Parameterization
Weighted Spherical Harmonic Representation
Gibbs Phenomenon in SPHARM 
Surface Normalization
Image and Data Acquisition
Numerical Implementation

Laplace-Beltrami Eigenfunctions for Surface Data
Heat Kernel Smoothing
Generalized Eigenvalue Problem
Numerical Implementation
Experimental Results
Case Study: Mandible Growth Modeling

Persistent Homology
Rips Filtration
Heat Kernel Smoothing of Functional Signal
Min-max Diagram
Case Study: Cortical Thickness Analysis

Sparse Networks
Massive Univariate Methods
Why Are Sparse Models Needed?
Persistent Structures for Sparse Correlations
Persistent Structures for Sparse Likelihood
Case Study: Application to Persistent Homology
Sparse Partial Correlations

Sparse Shape Models
Amygdala and Hippocampus Shape Models
Data Set
Sparse Shape Representation
Case Study: Subcortical Structure Modeling
Statistical Power
Power under Multiple Comparisons

Modeling Structural Brain Networks
DTI Acquisition and Preprocessing
ε-Neighbor Construction
Node Degrees
Connected Components
Numerical Implementation

Mixed Effects Models
Mixed Effects Models



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Moo K. Chung, Ph.D. is an associate professor in the Department of Biostatistics and Medical Informatics at the University of Wisconsin-Madison. He is also affiliated with the Waisman Laboratory for Brain Imaging and Behavior. He has won the Vilas Associate Award for his applied topological research (persistent homology) to medical imaging and the Editor’s Award for best paper published in Journal of Speech, Language, and Hearing Research. Dr. Chung received a Ph.D. in statistics from McGill University. His main research area is computational neuroanatomy, concentrating on the methodological development required for quantifying and contrasting anatomical shape variations in both normal and clinical populations at the macroscopic level using various mathematical, statistical, and computational techniques.


"The writing style is pleasing and the book has the important virtue of using a consistent mathematical notation and terminology throughout the book, unlike collections of chapters from various authors that are usually published on this kind of topic. One important and interesting aspect of this book is the use of MATLAB code to illustrate the theory that the author is developing. In addition, the data mentioned in the text are provided so that the reader can experiment and learn using the same examples as the ones described in the book. This provides an excellent supplement and will appeal to students starting in the field as well as researchers wanting to refresh their knowledge or learn more about some aspects of brain analysis. … a very good book to have in a lab, and it is a pleasure to recommend it."
Australian & New Zealand Journal of Statistics, 56(4), 2014

"… a great new reference text to the field of structural brain imaging. The presence of MATLAB code will make it easy for people to play around with the various data formats and more easily get involved in this exciting field. As a researcher already involved in neuroimaging data analysis, I have a feeling that this is a book I will return to often as a reference source, and I am happy to have it as part of my library."
—Martin A. Lindquist, Journal of the American Statistical Association, September 2014, Vol. 109

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