Computational neuroanatomy : the methods / Moo K. Chung.

Format:

Book

Author/Creator:

Chung, Moo K.

Language:

English

Subjects (All):

Neuroanatomy--Mathematics.

Neuroanatomy.

Neuroanatomy--Statistical methods.

Physical Description:

1 online resource (xv, 403 pages) : illustrations (some color)

Edition:

1st ed.

Place of Publication:

Teaneck, NJ : World Scientific, c2013.

Language Note:

English

Summary:

Computational neuroanatomy is an emerging field that utilizes various non-invasive brain imaging modalities, such as MRI and DTI, in quantifying the spatiotemporal dynamics of the human brain structures in both normal and clinical populations. This discipline emerged about twenty years ago and has made substantial progress in the past decade. The main goals of this book are to provide an overview of various mathematical, statistical and computational methodologies used in the field to a wide range of researchers and students, and to address important yet technically challenging topics in furth

Contents:

Preface; Contents; 1. Statistical Preliminary; 1.1 General Linear Models; 1.2 Random Fields; 1.2.1 Covariance Functions; 1.2.2 Gaussian Random Fields; 1.2.3 Differentiation and Integration of Fields; 1.2.4 Statistical Inference on Fields; 1.3 Multiple Comparisons; 1.3.1 Bonferroni Correction; 1.3.2 Random Fields Theory; 1.3.3 Poisson Clumping Heuristic; 1.3.4 Euler Characteristic Method; 1.3.5 Intrinsic Volume; 1.3.6 Euler Characteristic Density; 1.4 Statistical Power Analysis; 1.4.1 Statistical Power at a Voxel; 1.4.2 Statistical Power under Multiple Comparisons

2. Deformation-Based Morphometry; 2.1 Image Registration; 2.2 Deformation-Based Morphometry; 2.3 Displacement Vector Fields; 2.3.1 Dynamic Model on Displacement; 2.3.2 Local Inference via Hotelling's T2-Field; 2.3.3 Detecting Local Brain Growth; 2.4 Global Inference via Integral Statistic; 2.4.1 Karhunen-Lo eve Expansion; 2.4.2 Mercer's Theorem; 2.4.3 Integral Statistic on Displacement; 3. Tensor-Based Morphometry; 3.1 Jacobian Determinant; 3.2 Distributional Assumptions; 3.3 Local Volume Changes; 3.4 Longitudinal Modeling; 3.4.1 Normal Brain Development in Children

3.5 Global Inference via Divergence Theorem; 3.6 Second Order Tensor Fields; 3.6.1 Membrane Spline Energy; 3.6.2 Vorticity Tensor Fields; 3.6.3 Generalized Variance Field; 4. Voxel-Based Morphometry; 4.1 Image Segmentation; 4.1.1 Mumford-Shah Model; 4.1.2 Level Sets; 4.1.3 Active Contours; 4.1.4 Deformable Surface Models; 4.1.5 Thin-Plate Spline Thresholding; 4.2 Mixture Models; 4.2.1 Bayesian Segmentation; 4.2.2 Mixture Models; 4.2.3 Expectation Maximization Algorithm; 4.2.4 Two Components Gaussian Mixtures; 4.3 Voxel-Based Morphometry; 4.3.1 ROI Volume Estimation in VBM

4.3.2 Limitations of Witelson Partition; 4.3.3 General Linear Models on Tissue Densities; 4.3.4 2D VBM Applied to Corpus Callosum; 5. Geometry of Cortical Manifolds; 5.1 Surface Parameterization; 5.1.1 B-Spline Parameterization; 5.1.2 B-Spline Curves; 5.1.3 Quadratic Parameterization; 5.1.4 Fourier Descriptors; 5.2 Surface Normals and Curvatures; 5.2.1 Surface Normals; 5.2.2 Gaussian and Mean Curvatures; 5.2.3 Curvatures of Polynomial Surfaces; 5.3 Laplace-Beltrami Operator; 5.3.1 Eigenfunctions of Laplace-Beltrami Operator; 5.3.2 Multiplicity of Eigenfunctions

5.3.3 Laplace-Beltrami Shape Descriptors; 5.3.4 Second Eigenfunctions; 5.3.5 Dirichlet Energy; 5.3.6 Fiedler's Vector; 5.4 Finite Element Methods; 5.4.1 Pieacewise Linear Functions; 5.4.2 Mass and Stiffness Matrices; 6. Smoothing on Cortical Manifolds; 6.1 Gaussian Kernel Smoothing; 6.1.1 Isotropic Gaussian Kernel; 6.1.2 Anisotropic Gaussian Kernel; 6.2 Diffusion Smoothing; 6.2.1 Diffusion in Euclidean Space; 6.2.2 Diffusion in 1D; 6.2.3 Diffusion on Triangular Mesh; 6.2.4 Finite Difference Scheme; 6.3 Heat Kernel Smoothing; 6.3.1 Heat Kernel; 6.3.2 Heat Kernel Smoothing; 6.3.3 Iterated Kernel Smoothing

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

981-4335-44-4

1-299-13306-1

OCLC:

828792986