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Weickert J. — Visualization and Processing of Tensor Fields: Proceedings of the Dagstuhl Workshop
Weickert J. — Visualization and Processing of Tensor Fields: Proceedings of the Dagstuhl Workshop

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Название: Visualization and Processing of Tensor Fields: Proceedings of the Dagstuhl Workshop

Автор: Weickert J.

Аннотация:

Matrix-valued data sets — so-called second order tensor fields — have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the first edited volume that presents the state of the art in the visualization and processing of tensor fields. It contains some longer chapters dedicated to surveys and tutorials of specific topics, as well as a great deal of original work by leading experts that has not been published before. It serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as as a textbook for specialized classes and seminars for graduate and doctoral students.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 481

Добавлена в каталог: 15.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^r$-surface      7
$\alpha$-limit set      260
$\omega$-limit set      260
(r, s)-tensor, components of      10
(r, s)-tensor, definition      10
Active contour      409—411
Adaptive step-size control      261 351
ADC      see apparent diffusion coefficient
Analysis of variance test (ANOVA)      92
Anatomy of brain      see brain anatomy
Anisotropy      125 127 219 220 271
Anisotropy index      112 125 126 128 289
Anisotropy index, Euclidean      289
Anisotropy index, fractional      89 98 111 114 126—128 181 219 290 328 345
Anisotropy index, geodesic      290
Anisotropy index, Kullback — Leibler      289
Anisotropy index, lattice index      115 126 127
Anisotropy index, normalized      290
Anisotropy index, rational      126 127
Anisotropy index, relative      181 219
Anisotropy index, Riemannian      289
Anisotropy index, spherical-harmonic      90
Anisotropy index, volume ratio      126 127
Anisotropy, fractional      394
Anisotropy, linear      126 127 129 219
Anisotropy, planar      124 126 127 129 219
Anisotropy, spherical      127
Annihilation      see pairwise annihilation
Aperture problem      28 64
Apparent diffusion coefficient (ADC)      87 219 338
Apparent diffusion coefficient (ADC), profile      92 338
Apparent diffusion tensor      88
Artifact      235
Artifact, isotropy      see isotropy artifact
Artifact, topological      255
Average angular error      34
B-spline      302—312 315
B-spline, non-uniform      306
B-spline, non-uniform rational      305 315
Backward integration      261 262
Barycentric coordinates      see coordinate barycentric
Barycentric space      124 127
Basis for tensor shape change      220—223
Basis function      301
Basis function, separable      302
Basis, definition      3
Basis, dual      5
Basis, orthonormal      6
Basis, transform      4
Bayesian model      386
Beucher gradient      359
Bifurcation      231 237 238 253
Bifurcation, global      233
Bifurcation, local      232
Bifurcation, wedge      233 239
Bisection method      246
Bisector hyperplane      351
Black hole      202 211
Bloch — Torrey equation      178
Bootstrap      111
Boundary conditions, homogeneous Neumann      317 318
Boundary conditions, reflecting Neumann      353
Boundary tensor      66
Brain anatomy      127 129 219—220
Brain data      206—209
Brownian motion      123
Callosal morphology      161
Cardano circle      see eigenvalue wheel
cell      see grid cell
Cell membrane      123
Central limit theorem      110
Certainty measure      383
Change of variables      7
Characteristic greyvalue structure      50
Characteristic polynomial      see polynomial characteristic
Chart      192 193 202
Cholesky decomposition      94 168
Christoffel symbol      200 201
Closing      359
Clustering of singularities      236
Clutter      137 205 206 209—211 237 265 270 279
Co-vector      193
Coherence measure      32 42
COLOR      128
color coding      191 198 212 277
Commutator      200
Compression      269 271 276—278
Conjugate gradient method      246 248
Constraint function      242 244—248
Continuum mechanics      218
Contraction      see tensor contraction
Control point      305
Convex combination      348
Convolution      302
Convolution filter length      269 277
Coordinate chart      see chart
Coordinate function      200
Coordinate, barycentric      194 295
Coordinate, Cartesian      225
Coordinate, cylindrical      218
Coordinate, polar      228
Corner detection      39 74
Cornerness      337
Corona radiata      219
Corpus callosum      123 128 129 140 219 353 395 402
Covariant tensor      see tensor covariant
Covering space      226 229
Covering space, branch      227
creation      see pairwise creation
Critical feature      241—243
Critical point      227 242 259 260
Curvature of a fiber tract      309
Curvature, Gauss      8
Curvature, geodesic      10
Curvature, mean      8
Curvature, normal section      9
Curvature, principal      8
Curvature, radius      454
Curvature, radius of      310
Curve      192 193 199 201
Curve, closed      227
Curve, geodesic      10
Curve, normal section      9
Curve, orthogonal projection of      10
Curve, tangent      195
Data-adaptive structure tensor      see structure tensor data-adaptive
Deconvolution methods      96
Deformation      270
Deformation surface      212
Degenerate line      247 253 255
Degenerate line, double      253
Degenerate point      194 225 227—232 236—238 243—245 247 251 259 262 270
Degenerate point, double      245 255
Degenerate point, linear      245 249
Degenerate point, nonlinear      229
Degenerate point, planar      245 249
Degenerate point, triple      245 253
Delta method      110 113
Denoising      345
Denoising, discontinuity-preserving      346 353
Denoising, spatial      115
Denoising, variational      116 166
Denoising, voxelwise      113
Density of lines      198
Density of spots      276
Derivative, covariant      200
Derivative, directional      200 201
Derivative, Lie      see Lie derivative
Derivative, partial      200
Determinant      11
Deviation vector      197 198 201 202
Deviator      220 228 234 250 336
Diagonalizable      6
Diffeomorphism      7
Differential      7
Differential equation      200
Differential equation, partial      315—324 399—412
Diffusion ellipsoid      see ellipsoid
Diffusion spectrum imaging (DSI)      95
Diffusion tensor      12 88 123 215 220 404
Diffusion tensor imaging      88 121 122 165 194 206—209 211 215 219 221 255 299 320 345 354 374 401
Diffusion tensor imaging, biomedical      83
Diffusion tensor imaging, reconstruction      88
Diffusion tensor imaging, visualization      125—139
Diffusion tensor magnetic resonance, imaging      see diffusion tensor imaging
Diffusion tensor, 3D      123
Diffusion weighted imaging      85 109 206
Diffusion weighted magnetic resonance, imaging      see diffusion weighted imaging
Diffusion weighting factor      87
Diffusion, anisotropic      26 322 403 407
Diffusion, directional      12
Diffusion, linear      320 322 402
Diffusion, matrix-valued      26 402—406
Diffusion, nonlinear      24 322 402 406
Diffusivity function      25 32 318 402
Dijkstra's algorithm      199
Dilation      359
DIMENSION      3
Discriminant      242 244—248 252
Distribution, Gaussian      108 287
Distribution, probability      287
Divergence, Kullback — Leibler      287
Divergence, Kullback — Leibler, symmetrized      288
DT-MRI      see diffusion tensor imaging
DTI      see diffusion tensor imaging
DW-MRI      see diffusion weighted imaging
DWI      see diffusion weighted imaging
Dynamical system      229 258
Edge detection      220
Edge detector      74
Eigendecomposition      203 215 220 244 247 291 345
Eigenspace      6
Eigenvalue      6 124 194 204 215—220 230 242 243 259 261 271 348
Eigenvalue statistics      126 217 219—220 223
Eigenvalue, degenerated      194
Eigenvalue, gradient      220—222
Eigenvalue, sign      271
Eigenvalue, wheel      217 245
Eigenvector      6 124 193—198 203 204 225 243 261 271
Eigenvector, field      225—228 257—259 262 269 277
Eigenvector, flow      237
Eigenvector, principal      128 194 196—198 209
Eigenvector, radial      228
Einstein field equations      200 202
Einstein's convention      10
Elastic matching      330
Ellipsoid      124 128 202 203
Ellipsoid, metric      203—206 210 212
Ellipsoid, projection      203
Ellipsoid, rendering      203
Ellipsoid, shadow      204
Energy functional      see variational energy
Equation, differential      see differential equation
Erosion      359
Euclidean space      192 193
Euler method      134 259
Euler-Lagrange equation      171 200 317 330 406 407
expansion      269 271 276—278
Extremal line      199
Fast-LIC      275
Feature analysis      74
Feature line      251—253
Feature, critical      see critical feature
Feature, unstable      243
Fiber orientation      128 172 219
Fiber orientation distribution (FOD)      97
Fiber tracking      156 168
Fiber tract      130 309
Fiber-tracking      98
Field line      195
Finite difference      330
Finite element method      330
Fixed Point Iteration      24
Flow      226
Flow field      242
Fluid dynamics, computational      208 211 258 354
Focal point      259
Focusing strategy      350 351
Force field      270
Form, bilinear      7
Form, first fundamental      7
Form, linear      5
Form, second fundamental      8
Fractional anisotropy      see anisotropy index fractional
Frobenius inner product      286
Functional iteration      see fixed point iteration
Gauss, curvature      8
Gauss, frame      7
Gauss, map      7
Gaussian bell      50
Gaussian noise      88
Gaussian smoothing      18
General relativity      see relativity
Generalized anisotropy      183
Generator of a tensor field      301
Generator of B-splines      303
Geodesic      10 195 199—202 211 212
Geodesic bundle      201 202 212
Geodesic deviation      201
Geodesic, distance      137 286
Geodesic, interpolation      296
Geomechanics      270
Gibbs random field      116
Gibbs sampler      389
Global structure      207 208
Glyph      125 130 191 192 204—209 249
Glyph, Haber      see Haber glyph
Glyph, Reynold      see Reynold glyph
Glyph, shape icon      205
Glyph, superquadric      132 204 218 222
Glyph, van Gogh keystroke      205 212
Gradient descent      350 351
Graph, topological      233 234 237
Graphical primitive      125 203 205
Gravitational lens      202
Gray matter      219 220
Grid of wavenumbers      95 96
Grid, cell      234 247 248 255 258 261 278
Grid, curvilinear      253
Grid, cycle      258 261 262
Grid, face      248 251 261 262
Grid, hexahedral      247 255 278
Grid, regular      315
Grid, tetrahedral      259 262
Haber glyph      205 208 212
HARDI      see high angular resolution diffusion imaging
Hedgehog      203
High angular resolution diffusion imaging (HARDI)      122 125 219
Higher order tensor model      92 179
Human-computer interaction      138
Hyper-LIC      198
Hyperboloid      202
Hyperstreamline      134 198 212 242 249 252 254 257—265 270
Hyperstreamline, closed      257—265
Hyperstreamsurface      261 262 264
Icon      see glyph
Ill-posed      169
Image registration      327
Image restoration      315—324 406
Implicit function      244
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