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Chan T., Shen J. — Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods
Chan T., Shen J. — Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods



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Название: Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods

Авторы: Chan T., Shen J.

Аннотация:

This book develops the mathematical foundation of modern image processing and low-level computer vision, bridging contemporary mathematics with state-of-the-art methodologies in modern image processing, whilst organizing contemporary literature into a coherent and logical structure. The authors have integrated the diversity of modern image processing approaches by revealing the few common threads that connect them to Fourier and spectral analysis, the machinery that image processing has been traditionally built on. The text is systematic and well organized: the geometric, functional, and atomic structures of images are investigated, before moving to a rigorous development and analysis of several image processors. The book is comprehensive and integrative, covering the four most powerful classes of mathematical tools in contemporary image analysis and processing while exploring their intrinsic connections and integration. The material is balanced in theory and computation, following a solid theoretical analysis of model building and performance with computational implementation and numerical examples.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 422

Добавлена в каталог: 01.03.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Gamma$-convergence      283 329 364
Aberration-free lens      211
Active contours, $\Gamma$-convergence      329
Active contours, Bayesian combination      325
Active contours, geodesic      326 352
Active contours, gradient descent      327 328
Active contours, local minima      328
Active contours, mean curvature motion      327
Active contours, piecewise homogeneous features      335
Active contours, prior and data models      325
Active contours, region- and feature-based      332
Active contours, region- and gradient-based      331
Active contours, RGB or multichannel images      337
Active contours, snakes      320
Active contours, texture images      337
Active contours, without edges      332
Aerosol scattering      208
Alternating minimization      229 243 366
Analysis and synthesis, level-set representation      129
Analysis and synthesis, lossy harmonic approximation      138
Analysis and synthesis, piecewise constant images      132
Analysis and synthesis, Poisson representation      135 138
Analysis and synthesis, wavelet representation      86
Antiharmonic component      262
Aspect ratio      258 281
Atmospheric turbulence      9 213
Bandlimited      251
Bayesian inference      62
Bayesian modeling      64
Bayesian prior model      65
Besov images, direct definition      108
Besov images, variational denoising      173
Besov images, variational inpainting      292
Besov images, wavelet characterization      110
Besov images, wavelet shrinkage      171
Blur atmospheric      208
Blur linear vs. nonlinear      214
Blur mechanical      208
Blur medium-induced      208
Blur motion      208
Blur optical      207
Blur out-of-focus      211
Blur shift-invariant      214
book organization      24
Book, how to read      26
Boundary layer solution      353
Bounded p-mean oscillations (BMO)      97
Brownian motion      67 150 153
BV, bounded variation      45
BV, Cantor singular component      141
BV, co-area formula      52
BV, deblurring      220
BV, jump set      142
BV, lower semicontinuity      49
BV, mollification      51
BV, norm definition      49
BV, Radon measure      47
BV, Rudin, Osher, and Fatemi      45
BV, special BV (SBV) images      140 356
BV, total variation      46
BV, trace along boundaries      50
BV, weak compactness      52
Canny's edge detector      276
Centrosymmetry      240
CFL condition      72
Co-area formula      54 128
Color images      203
Compact operators      216
Comparison lemma      260
Compression inpainting technique      276
Compression linear wavelet scheme      113
Compression nonlinear wavelet scheme      114
Compression, error estimation      115
Compression, thermodynamics point of view      55
Compression, wavelet representation      113
Computer graphics      4
Conditional minimizer      228
Conservation laws      286
Convex conjugates      184
Cumulative level sets      127
Curvature      284 303
Curves, curvature      32
Curves, Frenet frame      32
Curves, geodesic      33
Curves, geometry      31
Curves, tangent and normal      32
Curves, total circulation      35
Curves, total curvature      35
Curvilinear coordinates      365
DC-condition      215 221
Deblurring, double-BV blind      234
Deblurring, dual-phase uncertainty      237
Deblurring, hidden symmetries      236
Deblurring, ill-posedness      216
Deblurring, nonparametrically blind      233
Deblurring, parametric blind      226
Deblurring, parametric-field blind      230
Deblurring, regularization      217
Deblurring, Wiener filter      217
Deconvolution      220
Denoising heat diffusion      158
Denoising, inpainting approach      201
Denoising, linear diffusion      157
Denoising, median filtering      199
Denoising, nonlinear diffusion      191
Denoising, Perona — Malik model      192
Denoising, Rudin — Osher — Fatemi model      177
Denoising, scale-space theory      191
Denoising, wavelet shrinkage      160
Denoising, Wiener filter      159
Differential topology      367
Diffusion backward      216
Diffusion, curvature driven diffusion (CDD)      285
Diffusion, decaying rate      69
Diffusion, linear filtering      68
Diffusion, nonlinear filtering      70
Diffusion, optimal stopping time      69 158
Diffusion, Perona — Malik      72 301
Dilation and erosion      12
Dirac's delta function      5 94
Diskette      316
Disocclusion      310
Distance function      36
Downsampling      79 87
Dual method      178 183
Edge tube      276
Edgel      339
Edges      175
Edges, active contours      318
Edges, as Markov random fields      340
Edges, as on-off binary patterns      340
Edges, Brownian paths      323
Edges, Canny's detector      319
Edges, canyon function      329 364
Edges, Cauchy decay      321
Edges, data models      320
Edges, David Marr      318
Edges, embedded      269
Edges, Euler's elastica      325
Edges, Gaussian decay      322
Edges, Geman and Geman      341
Edges, homogeneous constraints      318
Edges, length      324
Edges, Mumford — Shah      344
Edges, nonedge pixels      320
Edges, pixelwise characterization      318
Edges, preservation      191
Edges, prior models      322
Edges, Sobolev regularity      323
Edges, zero crossing      319
Einstein's summation rule      254
Elliptic operator      288
Ensembles canonical (CE)      58
Ensembles microcanonical (MCE)      58
Entropy deblurring      216
Entropy, maximum entropy learning      124
Entropy, Second Law      56
Entropy, variational meaning      56
Equations dilation      81
Equations refinement      81
Equations wavelet      86
Euler — Lagrange equation      178 224 284 293
Euler's elastica      35 131 270 307
Existence, deblurring BV images      222
Existence, double-BV deblurring      238
Existence, field blind deblurring      231
Existence, minimal surface      202
Existence, Mumford — Shah segmentation      355
Existence, regularized Perona — Malik      194
Existence, TV denoising      178
Existence, TV inpainting      271
Existence, variational shrinkage      164
Eyes, cortices      2
Eyes, Huble and Wiesel      95
Eyes, photoreceptors      2
Eyes, visual neurons      5
Filtering, filter bank      123
Filtering, finite impulse response (FIR)      249
Filtering, Gabor filters      124
Filtering, Laplacian filter      123
Filtering, linear      67
Filtering, linear highpass filter      122
Filtering, visual filters      122 333
Fitting, overfitting      189
Fitting, underfitting      188
Fourier domain      218
Frobenius norm      206
Frobenius' Theorem      266
Geman and Geman      61
Generators      315
Geodesic      326
Geometric curve models      264
Geometric optics      212
Gestalt vision      309
Gibbs' sampler      343
Ginsburg — Landau      330
Gradient descent      327
Hausdorff dimension      44
Hausdorff measure      44 311
Heaviside function      48
Heisenberg's uncertainty principle      104
Hessian operator      34 195 297
Highpass condition      86
Histograms      125
Holder spaces      109
Hubble telescope      9
Ill-posedness      216
Image processing, contrast enhancement      6
Image processing, deblurring      9
Image processing, denoising      8
Image processing, inpainting and interpolation      9
Image processing, segmentation      11
Images as $L^p$ functions      96
Images as Besov functions      107
Images as BV functions      98
Images as distributions      93
Images as ensembles      116
Images as generalized functions      93
Images as Sobolev functions      98
Images, acquisition      1
Images, information content      95 97
Images, modeling      91
Images, models via curve models      268
Images, representation      91
Images, textures      115
Imaging a multilayer model      139
Imaging, aperture imaging      211
Imaging, CAT, CT      3
Imaging, MRI      4
Imaging, radio frequency      4
Imaging, SAR      2
Imaging, thermal      2
Imaging, ultrasound      3
Implicit scheme      288
Incompressible fluids      300
Inequality Poincare's      223 235
Inequality Sobolev's      232
Inequality Young's      230
Inpainting, anisotropic diffusion      301
Inpainting, axiomatic      245 295 303
Inpainting, Besov image model      293
Inpainting, biharmonic      263
Inpainting, BV images      270
Inpainting, curvature driven diffusion (CDD)      302
Inpainting, digital zooming      274
Inpainting, disocclusion      277
Inpainting, edge decoding      278
Inpainting, error analysis      279
Inpainting, Euler's elastica      284
Inpainting, gradient-equalizer      297
Inpainting, Green's second formula      259
Inpainting, main challenges      256
Inpainting, Markov random fields      307
Inpainting, mean interpolant      295
Inpainting, median interpolant      296
Inpainting, missing wavelet coefficients      291
Inpainting, Mumford — Shah      282
Inpainting, Mumford — Shah — Euler      287
Inpainting, Navier — Stokes      245 286 300
Inpainting, scratch removal      278
Inpainting, Sobolev images      258
Inpainting, text removal      278
Inpainting, texture      289
Inpainting, transport mechanism      286 299
Interior solution      353
Interpolation, cubic spline      250
Interpolation, Lagrange function      247
Interpolation, maximum principle      247
Interpolation, polynomial      246
Interpolation, radial basis functions      253
Interpolation, spline      249
Interpolation, thin-plate splines      254
Interpolation, trigonometric      248
Inverse filtering      218
Inverse problems      5
Ito's formula      154
JPEG2000      291
Kalman filter      160
Kanizsa's Entangled Man      272
Knot theory      309
Kolmogrov turbulence      214
Lagged fixed-point iteration      181 225
Lagrange multipliers      126 277
Laurent polynomials      248
Layer-cake representation      97
Learning theory      6
Least square      204
Lens law      212
Level-set method, Dirac's delta measure      367
Level-set method, interface motions      367
Level-set method, length representation      367
Level-set method, level-set function      367
Level-set method, Lipschitz continuous      367
Level-set method, mollified Dirac's delta      368
Level-set method, multiphase formulations      367
Level-set method, Mumford — Shah segmentation      366
Level-set method, Osherand Sethian      126 366
Level-set method, topological changes      367
Level-set synthesis      129
Linear sensor      93
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