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E-grāmata: Computational Neuroanatomy: The Methods [World Scientific e-book]

(Univ Of Wisconsin-madison, Usa)
  • Formāts: 420 pages
  • Izdošanas datums: 06-Nov-2012
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789814335447
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  • World Scientific e-book
  • Cena: 156,65 €*
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Computational Neuroanatomy: The MethodsPalielināt
  • Formāts: 420 pages
  • Izdošanas datums: 06-Nov-2012
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789814335447
Citas grāmatas par šo tēmu:
World Scientific e-booksMore info about World Scientific e-books
Rokasgrāmatas mājas lapa: http://www.worldscientific.com/worldscibooks/10.1142/8036#t=toc
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 further detail.
Preface vii
1 Statistical Preliminary
1(26)
1.1 General Linear Models
1(4)
1.2 Random Fields
5(5)
1.2.1 Covariance Functions
6(1)
1.2.2 Gaussian Random Fields
7(1)
1.2.3 Differentiation and Integration of Fields
8(2)
1.2.4 Statistical Inference on Fields
10(1)
1.3 Multiple Comparisons
10(10)
1.3.1 Bonferroni Correction
12(1)
1.3.2 Random Fields Theory
13(1)
1.3.3 Poisson Clumping Heuristic
14(1)
1.3.4 Euler Characteristic Method
15(2)
1.3.5 Intrinsic Volume
17(1)
1.3.6 Euler Characteristic Density
18(2)
1.4 Statistical Power Analysis
20(7)
1.4.1 Statistical Power at a Voxel
20(2)
1.4.2 Statistical Power under Multiple Comparisons
22(5)
2 Deformation-Based Morphometry
27(22)
2.1 Image Registration
28(2)
2.2 Deformation-Based Morphometry
30(1)
2.3 Displacement Vector Fields
31(8)
2.3.1 Dynamic Model on Displacement
32(1)
2.3.2 Local Inference via Hotelling's T2-Field
33(3)
2.3.3 Detecting Local Brain Growth
36(3)
2.4 Global Inference via Integral Statistic
39(10)
2.4.1 Karhunen-Loeve Expansion
40(3)
2.4.2 Mercer's Theorem
43(2)
2.4.3 Integral Statistic on Displacement
45(4)
3 Tensor-Based Morphometry
49(20)
3.1 Jacobian Determinant
50(1)
3.2 Distributional Assumptions
51(2)
3.3 Local Volume Changes
53(3)
3.4 Longitudinal Modeling
56(6)
3.4.1 Normal Brain Development in Children
57(5)
3.5 Global Inference via Divergence Theorem
62(1)
3.6 Second Order Tensor Fields
63(6)
3.6.1 Membrane Spline Energy
63(1)
3.6.2 Vorticity Tensor Fields
64(2)
3.6.3 Generalized Variance Field
66(3)
4 Voxel-Based Morphometry
69(28)
4.1 Image Segmentation
71(8)
4.1.1 Mumford-Shah Model
71(1)
4.1.2 Level Sets
72(1)
4.1.3 Active Contours
72(3)
4.1.4 Deformable Surface Models
75(1)
4.1.5 Thin-Plate Spline Thresholding
76(3)
4.2 Mixture Models
79(8)
4.2.1 Bayesian Segmentation
79(1)
4.2.2 Mixture Models
80(2)
4.2.3 Expectation Maximization Algorithm
82(2)
4.2.4 Two Components Gaussian Mixtures
84(3)
4.3 Voxel-Based Morphometry
87(10)
4.3.1 ROI Volume Estimation in VBM
87(2)
4.3.2 Limitations of Witelson Partition
89(2)
4.3.3 General Linear Models on Tissue Densities
91(1)
4.3.4 2D VBM Applied to Corpus Callosum
92(5)
5 Geometry of Cortical Manifolds
97(30)
5.1 Surface Parameterization
98(5)
5.1.1 B-Spline Parameterization
99(1)
5.1.2 B-Spline Curves
99(1)
5.1.3 Quadratic Parameterization
100(3)
5.1.4 Fourier Descriptors
103(1)
5.2 Surface Normals and Curvatures
103(6)
5.2.1 Surface Normals
104(2)
5.2.2 Gaussian and Mean Curvatures
106(1)
5.2.3 Curvatures of Polynomial Surfaces
107(2)
5.3 Laplace-Beltrami Operator
109(13)
5.3.1 Eigenfunctions of Laplace-Beltrami Operator
110(2)
5.3.2 Multiplicity of Eigenfunctions
112(1)
5.3.3 Laplace-Beltrami Shape Descriptors
113(1)
5.3.4 Second Eigenfunctions
114(1)
5.3.5 Dirichlet Energy
115(4)
5.3.6 Fiedler's Vector
119(3)
5.4 Finite Element Methods
122(5)
5.4.1 Pieacewise Linear Functions
122(1)
5.4.2 Mass and Stiffness Matrices
123(4)
6 Smoothing on Cortical Manifolds
127(34)
6.1 Gaussian Kernel Smoothing
129(4)
6.1.1 Isotropic Gaussian Kernel
130(1)
6.1.2 Anisotropic Gaussian Kernel
131(2)
6.2 Diffusion Smoothing
133(8)
6.2.1 Diffusion in Euclidean Space
133(1)
6.2.2 Diffusion in ID
134(2)
6.2.3 Diffusion on Triangular Mesh
136(2)
6.2.4 Finite Difference Scheme
138(3)
6.3 Heat Kernel Smoothing
141(11)
6.3.1 Heat Kernel
143(2)
6.3.2 Heat Kernel Smoothing
145(3)
6.3.3 Iterated Kernel Smoothing
148(2)
6.3.4 Smoothing via Laplace-Beltrami Eigenfunctions
150(2)
6.4 Smoothness of Random Fields
152(4)
6.4.1 Resels of Field
154(1)
6.4.2 Effective Bandwidth
155(1)
6.4.3 Unbiased Estimator of eFWHM
155(1)
6.5 Gaussianness of Random Fields
156(5)
6.5.1 Quantiles
156(1)
6.5.2 Empirical Distribution
157(1)
6.5.3 Quantile Quantile Plots
157(2)
6.5.4 Checking Gaussianness in Cortical Thickness
159(2)
7 Surface-Based Morphometry
161(56)
7.1 Surface Flattening
163(4)
7.2 Cortical Thickness
167(8)
7.2.1 Cortical Thickness via Laplace Equation
167(3)
7.2.2 Cortical Thickness vs. Gray Matter Density
170(1)
7.2.3 Distance Map
171(4)
7.3 Partial Correlation Mapping
175(8)
7.3.1 Partial Correlations
176(1)
7.3.2 Statistical Inference on Correlations
177(4)
7.3.3 Brain-Behavior Correlations
181(1)
7.3.4 Facial Emotion Discrimination Tasks
182(1)
7.4 Tensor-Based Surface Morphometry
183(13)
7.4.1 Surface Deformation
184(2)
7.4.2 Metric Tensor Computation on Surfaces
186(3)
7.4.3 Statistical Inference on Surfaces
189(1)
7.4.4 Quantifying Brain Growth
190(1)
7.4.5 Tensor Computation via SPHARM
191(5)
7.5 Multivariate General Linear Models
196(5)
7.5.1 Roy's Maximum Root
198(1)
7.5.2 SurfStat
199(2)
7.6 Mixed Effect Models on Surface Shape Change
201(7)
7.6.1 Longitudinal Imaging Data
202(2)
7.6.2 Mixed Effect Models
204(1)
7.6.3 Restricted Maximum Likelihood Estimation
205(1)
7.6.4 Longitudinal Hippocampus Shape Model
206(1)
7.6.5 Functional Mixed Effect Models
207(1)
7.7 Sparse Surface Shape Recovery
208(9)
7.7.1 Sparse Regression on Surface Data
210(3)
7.7.2 Effect of Aging on Hippocampus Shape
213(4)
8 Weighted Fourier Representation
217(60)
8.1 Fourier Series in Hilbert Space
219(2)
8.2 Weighted Fourier Representation
221(7)
8.2.1 Cauchy Problem
222(1)
8.2.2 Heat Kernel Smoothing
223(1)
8.2.3 Kernel Regression
224(1)
8.2.4 Iterative Residual Fitting Algorithm
225(1)
8.2.5 Best Model Selection
226(2)
8.3 Weighted Spherical Harmonic Representation
228(8)
8.3.1 Spherical Harmonics
228(1)
8.3.2 Spherical Harmonic Representation
229(3)
8.3.3 Iterative Residual Fitting on Spherical Harmonics
232(4)
8.4 Gibbs Phenomenon
236(5)
8.4.1 Reduction of Gibbs Phenomenon
238(2)
8.4.2 The Overshoot of Gibbs Phenomenon
240(1)
8.5 SPHARM Correspondance
241(4)
8.6 Cortical Asymmetry
245(7)
8.6.1 Hemisphere Correspondence
245(3)
8.6.2 Abnormal Cortical Asymmetry in Autism
248(2)
8.6.3 FWHM of Heat Kernel
250(2)
8.7 Logistic Discriminant Analysis on Cortical Surface
252(5)
8.7.1 Logistic Model
252(1)
8.7.2 Maximum Likelihood Estimation
253(1)
8.7.3 Best Model Selection
254(1)
8.7.4 Classification Accuracy
255(2)
8.8 Tiling Surfaces with Orthonormal Basis
257(10)
8.8.1 Orhonormal Basis on a Sphere
258(2)
8.8.2 Orthonormal Basis on Manifolds
260(3)
8.8.3 Numerical Implementation
263(2)
8.8.4 Pullback Representation
265(2)
8.9 Basis Function Expansion on Multiple Shells
267(10)
8.9.1 Eigenfunction Expansion in a Solid Ball
269(3)
8.9.2 Iterative Residual Fitting
272(1)
8.9.3 3D Resampling of 2D Surface Data
273(4)
9 Structural Brain Connectivity
277(58)
9.1 White Matter Fiber Tractography
278(3)
9.1.1 Diffusion Tensors
278(1)
9.1.2 Streamlines
279(1)
9.1.3 Probabilistic Methods
279(2)
9.2 Probabilistic Connectivity
281(3)
9.3 Cosine Series Representation of Fiber Tracts
284(12)
9.3.1 Cosine Basis in a Unit Interval
285(1)
9.3.2 Cosine Series Representation of 3D Curves
286(2)
9.3.3 Optimal Degree Selection
288(3)
9.3.4 Distance Between Tracts
291(2)
9.3.5 Tract Registration
293(1)
9.3.6 Limitation of Cosine Series Representation
294(2)
9.4 Parcellation-Free Brain Networks
296(12)
9.4.1 Why Parcellation Free?
297(2)
9.4.2 Epsilon Neighbor Networks
299(3)
9.4.3 Connected Components
302(1)
9.4.4 Epsilon Filtration
303(2)
9.4.5 Electrical Circuit Model for Fiber Tracts
305(3)
9.5 Structural Brain Connectivity without DTI
308(10)
9.5.1 Correlating Jacobiau Determinants
309(1)
9.5.2 Seed-Based Connectivity
310(2)
9.5.3 Parcellation-Based Connectivity
312(1)
9.5.4 Validation
313(3)
9.5.5 RV-Coefficient
316(2)
9.6 Network Complexity Measures
318(7)
9.6.1 Degree Distribution
318(2)
9.6.2 Small-Worldness
320(1)
9.6.3 Fractal Dimension
321(2)
9.6.4 Clustering Coefficient
323(2)
9.7 Sparse Brain Network Models
325(7)
9.7.1 Correlation Thresholding
325(2)
9.7.2 Sparse Partial Correlation
327(2)
9.7.3 Sparse Network Recovery
329(3)
9.8 Dynamic Network Modeling
332(3)
10 Topological Data Analysis
335(32)
10.1 Detecting Topological Defect in Images
336(2)
10.2 Expected Euler Characteristic
338(2)
10.3 Rips Complex
340(3)
10.3.1 Topology
341(1)
10.3.2 Simplex
342(1)
10.3.3 Rips complex
342(1)
10.4 Persistence Diagrams
343(9)
10.4.1 Morse Functions
343(2)
10.4.2 Persistence Diagrams
345(2)
10.4.3 Persistence Diagram for Cortical Thickness
347(4)
10.4.4 Inference on Persistent Diagrams
351(1)
10.5 Min-Max Diagrams
352(5)
10.5.1 Why Critical Values?
352(1)
10.5.2 Iterative Pairing and Deletion Algorithm
353(2)
10.5.3 Statistical Inference on Mix-Max Diagrams
355(2)
10.6 Graph Filtrations
357(10)
10.6.1 Weighted Graphs
358(3)
10.6.2 Single Linkage Matrix
361(2)
10.6.3 Persistent Brain Networks
363(4)
Bibliography 367(32)
Index 399
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