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 epsilon-Neighbor Construction Node Degrees Connected Components epsilon-Filtration Numerical Implementation Discussion Mixed Effects Models Introduction Mixed Effects Models Bibliography Index