Computational neuroanatomy: the methods
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, NJ [u.a.]
World Scientific
2013
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 403 S. Ill., graph. Darst. |
| ISBN: | 9789814335430 9814335436 |
Internformat
MARC
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| 007 | t | ||
| 008 | 121116s2013 ad|| |||| 00||| eng d | ||
| 020 | |a 9789814335430 |9 978-981-4335-43-0 | ||
| 020 | |a 9814335436 |9 981-4335-43-6 | ||
| 035 | |a (OCoLC)820399367 | ||
| 035 | |a (DE-599)BSZ348759223 | ||
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| 100 | 1 | |a Chung, Moo K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Computational neuroanatomy |b the methods |c Moo K. Chung |
| 264 | 1 | |a Hackensack, NJ [u.a.] |b World Scientific |c 2013 | |
| 300 | |a XV, 403 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Bioinformatik |0 (DE-588)4611085-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Neuroanatomie |0 (DE-588)4171577-9 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Bioinformatik |0 (DE-588)4611085-9 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-025391780 | ||
Datensatz im Suchindex
| _version_ | 1804149637604442113 |
|---|---|
| adam_text | Contents
Preface vii
1.
Statistical Preliminary
1
1.1
General Linear Models
.................... 1
1.2
Random Fields
........................ 5
1.2.1
Covariance Functions
................ 6
1.2.2
Gaussian Random Fields
.............. 7
1.2.3
Differentiation and Integration of Fields
...... 8
1.2.4
Statistical Inference on Fields
........... 10
1.3
Multiple Comparisons
.................... 10
1.3.1
Bonferroni Correction
................ 12
1.3.2
Random Fields Theory
............... 13
1.3.3
Poisson
Clumping Heuristic
............ 14
1.3.4
Euler
Characteristic Method
............ 15
1.3.5
Intrinsic Volume
................... 17
1.3.6
Euler
Characteristic Density
............ 18
1.4
Statistical Power Analysis
.................. 20
1.4.1
Statistical Power at a Voxel
............ 20
1.4.2
Statistical Power under Multiple Comparisons
. . 22
2.
Deformation-Based Morphometry
27
2.1
Image Registration
...................... 28
2.2
Deformation-Based Morphometry
.............. 30
2.3
Displacement Vector Fields
................. 31
2.3.1
Dynamic Model on Displacement
......... 32
2.3.2
Local Inference via Hotelling s T2-Field
...... 33
2.3.3
Detecting Local Brain Growth
........... 36
χ
Computational Neuroanatomy: The Methods
2.4
Global Inference via Integral Statistic
........... 39
2.4.1
Karhunen-Loève
Expansion
............. 40
2.4.2
Mercer s Theorem
.................. 43
2.4.3
Integral Statistic on Displacement
......... 45
3.
Tensor-Based Morphometry
49
3.1
Jacobian Determinant
.................... 50
3.2
Distributional Assumptions
................. 51
3.3
Local Volume Changes
.................... 53
3.4
Longitudinal Modeling
.................... 56
3.4.1
Normal Brain Development in Children
...... 57
3.5
Global Inference via Divergence Theorem
......... 62
3.6
Second Order Tensor Fields
................. 63
3.6.1
Membrane Spline Energy
.............. 63
3.6.2
Vorticity Tensor Fields
............... 64
3.6.3
Generalized Variance Field
............. 66
4.
Voxel-Based Morphometry
69
4.1
Image Segmentation
..................... 71
4.1.1
Mumford-Shah Model
................ 71
4.1.2
Level Sets
...................... 72
4.1.3
Active Contours
................... 72
4.1.4
Deformable Surface Models
............. 75
4.1.5
Thin-Plate Spline Thresholding
.......... 76
4.2
Mixture Models
........................ 79
4.2.1
Bayesian Segmentation
............... 79
4.2.2
Mixture Models
................... 80
4.2.3
Expectation Maximization Algorithm
....... 82
4.2.4
Two Components Gaussian Mixtures
....... 84
4.3
Voxel-Based Morphometry
.................. 87
4.3.1
ROI
Volume Estimation in VBM
......... 87
4.3.2
Limitations of Witelson Partition
......... 89
4.3.3
General Linear Models on Tissue Densities
.... 91
4.3.4
2D VBM Applied to Corpus Callosum
...... 92
5.
Geometry of Cortical Manifolds
97
5.1
Surface Parameterization
.................. 98
5.1.1
B-Spline Parameterization
............. 99
Contents xi
5.1.2 B-Spline
Curves...................
99
5.1.3
Quadratic Parameterization
............ 100
5.1.4
Fourier Descriptors
................. 103
5.2
Surface Normals and Curvatures
.............. 103
5.2.1
Surface Normals
................... 104
5.2.2
Gaussian and Mean Curvatures
.......... 106
5.2.3
Curvatures of Polynomial Surfaces
......... 107
5.3
Laplace-Beltrami Operator
................. 109
5.3.1
Eigenfunctions of Laplace-Beltrami Operator
. . . 110
5.3.2
Multiplicity of Eigenfunctions
........... 112
5.3.3
Laplace-Beltrami Shape Descriptors
........ 113
5.3.4
Second Eigenfunctions
............... 114
5.3.5
Dirichlet Energy
................... 115
5.3.6
Fiedler s Vector
................... 119
5.4
Finite Element Methods
................... 122
5.4.1
Pieacewise Linear Functions
............ 122
5.4.2
Mass and Stiffness Matrices
............ 123
6.
Smoothing on Cortical Manifolds
127
6.1
Gaussian Kernel Smoothing
................. 129
6.1.1 Isotropie
Gaussian Kernel
.............. 130
6.1.2 Anisotropie
Gaussian Kernel
............ 131
6.2
Diffusion Smoothing
..................... 133
6.2.1
Diffusion in Euclidean Space
............ 133
6.2.2
Diffusion in ID
.................... 134
6.2.3
Diffusion on Triangular Mesh
............ 136
6.2.4
Finite Difference Scheme
.............. 138
6.3
Heat Kernel Smoothing
................... 141
6.3.1
Heat Kernel
..................... 143
6.3.2
Heat Kernel Smoothing
............... 145
6.3.3
Iterated Kernel Smoothing
............. 148
6.3.4
Smoothing via Laplace-Beltrami Eigenfunctions
. 150
6.4
Smoothness of Random Fields
................ 152
6.4.1
Resels of Field
.................... 154
6.4.2
Effective Bandwidth
................. 155
6.4.3
Unbiased Estimator of eFWHM
.......... 155
6.5
Gaussianness of Random Fields
............... 156
6.5.1
Quantiles
....................... 156
6.5.2
Empirical Distribution
............... 157
xii
Computational Neuroanatomy: The Methods
6.5.3
Quantile Quantile Plots
............... 157
6.5.4
Checking Gaussianness in Cortical Thickness
. . . 159
7.
Surface-Based Morphometry
161
7.1
Surface Flattening
...................... 163
7.2
Cortical Thickness
...................... 167
7.2.1
Cortical Thickness via Laplace Equation
..... 167
7.2.2
Cortical Thickness vs. Gray Matter Density
... 170
7.2.3
Distance Map
.................... 171
7.3
Partial Correlation Mapping
................. 175
7.3.1
Partial Correlations
................. 176
7.3.2
Statistical Inference on Correlations
........ 177
7.3.3
Brain-Behavior Correlations
............ 181
7.3.4
Facial Emotion Discrimination Tasks
....... 182
7.4
Tensor-Based Surface Morphometry
............ 183
7.4.1
Surface Deformation
................. 184
7.4.2
Metric Tensor Computation on Surfaces
...... 186
7.4.3
Statistical Inference on Surfaces
.......... 189
7.4.4
Quantifying Brain Growth
............. 190
7.4.5
Tensor Computation via SPHARM
........ 191
7.5
Multivariate General Linear Models
............ 196
7.5.1
Roy s Maximum Root
................ 198
7.5.2
SurfStat
....................... 199
7.6
Mixed Effect Models on Surface Shape Change
...... 201
7.6.1
Longitudinal Imaging Data
............. 202
7.6.2
Mixed Effect Models
................ 204
7.6.3
Restricted Maximum Likelihood Estimation
... 205
7.6.4
Longitudinal Hippocampus Shape Model
..... 206
7.6.5
Functional Mixed Effect Models
.......... 207
7.7
Sparse Surface Shape Recovery
............... 208
7.7.1
Sparse Regression on Surface Data
......... 210
7.7.2
Effect of Aging on Hippocampus Shape
...... 213
8.
Weighted Fourier Representation
217
8.1
Fourier Series in Hubert Space
............... 219
8.2
Weighted Fourier Representation
.............. 221
8.2.1
Cauchy Problem
................... 222
8.2.2
Heat Kernel Smoothing
............... 223
Contents xiii
8.2.3 Kernel Regression.................. 224
8.2.4 Iterative Residual
Fitting Algorithm........
225
8.2.5 Best Model
Selection
................ 226
8.3
Weighted Spherical
Harmonie
Representation
....... 228
8.3.1
Spherical Harmonics
................. 228
8.3.2
Spherical Harmonic Representation
........ 229
8.3.3
Iterative Residual Fitting on Spherical Harmonics
232
8.4
Gibbs Phenomenon
...................... 236
8.4.1
Reduction of Gibbs Phenomenon
......... 238
8.4.2
The Overshoot of Gibbs Phenomenon
....... 240
8.5
SPHARM
Correspondance
.................. 241
8.6
Cortical Asymmetry
..................... 245
8.6.1
Hemisphere Correspondence
............ 245
8.6.2
Abnormal Cortical Asymmetry in Autism
..... 248
8.6.3
FWHM of Heat Kernel
............... 250
8.7
Logistic Discriminant Analysis on Cortical Surface
.... 252
8.7.1
Logistic Model
.................... 252
8.7.2
Maximum Likelihood Estimation
.......... 253
8.7.3
Best Model Selection
................ 254
8.7.4
Classification Accuracy
............... 255
8.8
Tiling Surfaces with
Orthonormal
Basis
.......... 257
8.8.1
Orhonormal Basis on a Sphere
........... 258
8.8.2
Orthonormal
Basis on Manifolds
.......... 260
8.8.3
Numerical Implementation
............. 263
8.8.4
Pullback Representation
.............. 265
8.9
Basis Function Expansion on Multiple Shells
....... 267
8.9.1
Eigenfunction Expansion in a Solid Ball
...... 269
8.9.2
Iterative Residual Fitting
.............. 272
8.9.3 3D
Resampling of 2D Surface Data
........ 273
9.
Structural Brain Connectivity
277
9.1
White Matter Fiber Tractography
............. 278
9.1.1
Diffusion Tensors
.................. 278
9.1.2
Streamlines
...................... 279
9.1.3
Probabilistic Methods
................ 279
9.2
Probabilistic Connectivity
.................. 281
9.3
Cosine Series Representation of Fiber Tracts
....... 284
9.3.1
Cosine Basis in a Unit Interval
........... 285
9.3.2
Cosine Series Representation of
3D
Curves
.... 286
xiv
Computational Neuroanatomy: The Methods
9.3.3
Optimal Degree Selection
.............. 288
9.3.4
Distance Between Tracts
.............. 291
9.3.5
Tract Registration
.................. 293
9.3.6
Limitation of Cosine Series Representation
.... 294
9.4
Parcellation-Free Brain Networks
.............. 296
9.4.1
Why Parcellation Free?
............... 297
9.4.2 Epsilon
Neighbor Networks
............. 299
9.4.3
Connected Components
............... 302
9.4.4 Epsilon
Filtration
.................. 303
9.4.5
Electrical Circuit Model for Fiber Tracts
..... 305
9.5
Structural Brain Connectivity without DTI
........ 308
9.5.1
Correlating Jacobian Determinants
........ 309
9.5.2
Seed-Based Connectivity
.............. 310
9.5.3
Parcellation-Based Connectivity
.......... 312
9.5.4
Validation
...................... 313
9.5.5
RV-Coefficient
.................... 316
9.6
Network Complexity Measures
............... 318
9.6.1
Degree Distribution
................. 318
9.6.2
Small-Worldness
................... 320
9.6.3
Fractal Dimension
.................. 321
9.6.4
Clustering Coefficient
................ 323
9.7
Sparse Brain Network Models
................ 325
9.7.1
Correlation Thresholding
.............. 325
9.7.2
Sparse Partial Correlation
............. 327
9.7.3
Sparse Network Recovery
.............. 329
9.8
Dynamic Network Modeling
................. 332
10.
Topological Data Analysis
335
10.1
Detecting Topological Defect in Images
.......... 336
10.2
Expected
Euler
Characteristic
................ 338
10.3
Rips Complex
......................... 340
10.3.1
Topology
....................... 341
10.3.2
Simplex
........................ 342
10.3.3
Rips complex
..................... 342
10.4
Persistence Diagrams
..................... 343
10.4.1
Morse Functions
................... 343
10.4.2
Persistence Diagrams
................ 345
10.4.3
Persistence Diagram for Cortical Thickness
.... 347
10.4.4
Inference on Persistent Diagrams
......... 351
Contents xv
10.5
Min-Max
Diagrams
...................... 352
10.5.1
Why Critical Values?
................ 352
10.5.2
Iterative Pairing and Deletion Algorithm
..... 353
10.5.3
Statistical Inference on Mix-Max Diagrams
.... 355
10.6
Graph Piltrations
....................... 357
10.6.1
Weighted Graphs
.................. 358
10.6.2
Single Linkage Matrix
................ 361
10.6.3
Persistent Brain Networks
............. 363
Bibliography
367
Index
399
|
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| id | DE-604.BV040545963 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:26:12Z |
| institution | BVB |
| isbn | 9789814335430 9814335436 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025391780 |
| oclc_num | 820399367 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XV, 403 S. Ill., graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Chung, Moo K. Verfasser aut Computational neuroanatomy the methods Moo K. Chung Hackensack, NJ [u.a.] World Scientific 2013 XV, 403 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bioinformatik (DE-588)4611085-9 gnd rswk-swf Neuroanatomie (DE-588)4171577-9 gnd rswk-swf Neuroanatomie (DE-588)4171577-9 s Bioinformatik (DE-588)4611085-9 s b DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025391780&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chung, Moo K. Computational neuroanatomy the methods Bioinformatik (DE-588)4611085-9 gnd Neuroanatomie (DE-588)4171577-9 gnd |
| subject_GND | (DE-588)4611085-9 (DE-588)4171577-9 |
| title | Computational neuroanatomy the methods |
| title_auth | Computational neuroanatomy the methods |
| title_exact_search | Computational neuroanatomy the methods |
| title_full | Computational neuroanatomy the methods Moo K. Chung |
| title_fullStr | Computational neuroanatomy the methods Moo K. Chung |
| title_full_unstemmed | Computational neuroanatomy the methods Moo K. Chung |
| title_short | Computational neuroanatomy |
| title_sort | computational neuroanatomy the methods |
| title_sub | the methods |
| topic | Bioinformatik (DE-588)4611085-9 gnd Neuroanatomie (DE-588)4171577-9 gnd |
| topic_facet | Bioinformatik Neuroanatomie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025391780&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT chungmook computationalneuroanatomythemethods |