Statistical and Computational Methods in Brain Image Analysis

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
Discussion

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
Introduction
Modeling Surface Deformation
Surface Parameterization
Surface-Based Morphological Measures
Surface-Based Diffusion Smoothing
Statistical Inference on the Cortical Surface
Results
Discussion

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

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

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

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

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

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

Sparse Networks
Introduction
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
Summary

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

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

Mixed Effects Models
Introduction
Mixed Effects Models

Bibliography

Index