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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 MethodsАвторы: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2005Количество страниц: 422Добавлена в каталог: 01.03.2007Операции: Положить на полку |
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Lipschitz domain partition 136 Logical Euler — Lagrange equation 371 Logical multichannel segmentation 369 Logical truth table 370 Logical tumor detection 372 Logical union and intersection 371 Logical variables z's 370 lossless 92 Lowpass condition 66 82 Markov property 120 307 Markov random fields (MRF), cliques 120 Markov random fields (MRF), cliquish potentials 121 308 Markov random fields (MRF), Geman and Geman 338 Markov random fields (MRF), graph theory 339 Markov random fields (MRF), inpainting 307 Markov random fields (MRF), intensity regulated by edges 342 Markov random fields (MRF), neighborhood system 119 307 Markov random fields (MRF), topological domains 338 Markov transition 66 Maximal cliques 341 Maximum likelihood 62 Maxwell — Boltzmann distribution 118 Mean constraint 224 Mean curvature, global meaning 42 Mean curvature, graph surfaces 42 Mean curvature, implicit surfaces 40 Mean curvature, mean curvature motion 198 327 Mean curvature, parametric surfaces 39 Medial ultrasound 3 Median Filter 70 Medical engineering 27 Medical imaging and diagnosis 3 Medical noninvasive probing 3 Medical radiologist 27 Medical tumor detection 5 372 Methods, Fourier and spectral analysis 14 Methods, morphological transforms 12 Methods, partial differential equations 19 Methods, stochastic methods 16 Methods, variational modeling 17 Methods, wavelet analysis 15 Meyer's G-norm 186 Minimal surface problem 180 271 Minimum description length 338 Minimum surface diffusion 215 Monoids 310 Morphological 12 303 305 Mother wavelet 85 Moving Average 158 Multichannel 203 Multigrid methods 81 Multiscale characterization 108 Mumford — Shah model, 364 Mumford — Shah model, 1-D existence proof 358 Mumford — Shah model, 1-D model 345 Mumford — Shah model, admissible domain 345 Mumford — Shah model, as region-based Active Contour 332 Mumford — Shah model, asymptotic limit I 345 Mumford — Shah model, asymptotic limit II 347 Mumford — Shah model, asymptotic limit III 351 Mumford — Shah model, Bayesian rationale 140 Mumford — Shah model, boundary layer method 352 Mumford — Shah model, crack-tips 367 Mumford — Shah model, domain additivity 363 Mumford — Shah model, Euclidean invariance 362 Mumford — Shah model, exact segmentation 362 Mumford — Shah model, existence 143 355 Mumford — Shah model, flashing invariance 363 Mumford — Shah model, free boundary 132 309 Mumford — Shah model, hidden symmetries 362 Mumford — Shah model, jump set regularity 357 Mumford — Shah model, level-set approach 364 Mumford — Shah model, level-set method 366 Mumford — Shah model, nonuniqueness 355 Mumford — Shah model, Sierpinski Islands 359 Mumford — Shah model, weak formulation 143 356 Natural boundary condition 254 Neumann boundary condition 69 179 225 330 366 Newton's method 185 Noise, additive 139 147 Noise, analog model 151 Noise, application in system theory 147 Noise, Gaussian white 139 150 Noise, salt-and-pepper 8 199 noise, signal-to-noise ratio 147 Noise, white noise 150 Nonflat 203 Occlusion 309 Optical Transfer Function (OTF) 213 Ornstein — Uhlenbeck process (SDE) 154 Oscillatory behavior 289 Paley — Wiener theorem 251 Parallel implementation 205 Partition function 59 72 118 Pattern complexity 257 Pattern theory 6 Perimeter 53 Perturbation 273 Piecewise homogeneous 334 Positive distribution 95 Posterior energy 220 290 Precompact 95 Primal variable 184 Primal-dual method 185 Prime prei mages 317 PSF, Gaussian 213 PSF, motion blur 211 PSF, out-of-focus 212 PSF, point spreading function 65 211 214 Quadratic convergence 185 Quantum computers 91 quantum mechanics 294 Radon — Nikodym derivative 141 Random fields, Geman and Geman 117 Random fields, Gibbs — Markov equivalence 119 Random fields, Gibbs' ensemble 119 Random fields, homogeneous 155 Random fields, Markov random fields 119 Random fields, wide sense homogeneous (WSH) 155 Random fields, Zhu, Wu, and Mumford 117 Region competition 338 Riemannian manifolds 203 Riesz representation theorem 95 96 Scale-space theory, affine invariance 198 Scale-space theory, axiomatic approach 194 Scale-space theory, scale-space equation 198 Scale-space theory, Witkin's linear theory 194 Scaling function 81 Segmentation as an inverse problem 317 Segmentation, active contour for textures 338 Segmentation, bar code scanning 345 Segmentation, multichannel logical 369 Segmentation, Mumford and Shah 18 Segmentation, partition 11 Segmentation, piecewise smooth 140 Segmentation, statistical estimation 138 Segmentation, variational optimization 138 Semigroup 310 Shannon 54 Shannon's sampling theorem 251 Sierpinski gasket 359 Signal detection theory 117 Simulated annealing 343 Singular perturbations 352 Singular values 206 Sobolev blind deblurring 237 Sobolev inequality 232 Sobolev regularity 234 Sobolev space 48 Spectral graph theory 342 Stability 146 158 197 198 207 240 305 Statistical inference, significance test 62 Statistical mechanics, ensembles 58 Statistical mechanics, Gibbs' distribution 59 Statistical mechanics, heat capacity 60 Statistical mechanics, Helmholtz energy 59 Statistical mechanics, variational derivation 61 Statistics of level sets 131 Steepest descent 286 Stirling's asymptotic formula 200 Stochastic differential equations 153 Stochastic signals, 1-D signals 147 Stochastic signals, autocorrelation 148 Stochastic signals, cross-correlation 149 Stochastic signals, ergodicity 151 Stochastic signals, joint distribution function 147 Stochastic signals, power spectral density 148 Stochastic signals, stationary 148 Stochastic signals, wide sense stationary (WSS) 148 Stream function 300 Subgradients 184 Surfaces, first fundamental form 37 Surfaces, Guassian curvature K 38 Surfaces, implicit 36 Surfaces, mean curvature 38 Surfaces, normal map 43 Surfaces, parametric 36 Surfaces, principal curvatures 38 Surfaces, second fundamental form 37 Telescoping formula 345 Texture Meyer's class 289 Thermodynamics, extensive variables 56 Thermodynamics, first law 55 Thermodynamics, intensive variables 56 Thermodynamics, second law 55 Thin-plate splines 246 Threshold 218 Total variation (TV), as a Radon measure 46 Total variation (TV), curve length 34 Total variation (TV), denoising model 177 Total variation (TV), digital TV 275 Total variation (TV), for signed measures 47 Total variation (TV), geometric meaning 54 Total variation (TV), inpainting model 270 Total variation (TV), median filtering 176 Total variation (TV), piecewise constant 99 Total variation (TV), Rudin, Osher, and Fatemi 175 Total variation (TV), self-contained digital theory 275 Total variation (TV), total absolute curvature 35 Total variation (TV), vrobust statistics 174 Transform, analysis and synthesis 92 Transform, biological 92 Transform, fast wavelets 88 Transform, Fourier 66 Transform, Haar's 92 Transform, Legendre 59 Transform, morphological 196 Transform, wavelets 165 Transform, windowed Fourier 76 Transform, x-transform 249 Transform, z-transform 248 Tunable parameter 336 Upsampling 88 Vanishing moments, radial basis functions 254 Vanishing moments, wavelets 105 Vision, depth perception 6 Vision, motion estimation 6 Visual potentials 126 Vorticity equation 300 wavelet equation 86 Wavelet shrinkage, Besov images 171 Wavelet shrinkage, denoising 160 Wavelet shrinkage, Donoho and Johnstone 160 Wavelet shrinkage, hard truncation 164 Wavelet shrinkage, minimum shrinkage 162 Wavelet shrinkage, near optimality 170 Wavelet shrinkage, solid and orthosymmetric 167 Wavelet shrinkage, statistical theory of singletons 160 Wavelet shrinkage, uniform shrinkage 173 Wavelet shrinkage, uniform shrinkage condition 162 Wavelet shrinkage, variational formulation 163 Wavelets, 2-D Haar wavelets 102 Wavelets, 2-D tensor products 99 Wavelets, analysis filter bank 88 Wavelets, biorthogonal 88 Wavelets, Coifman — Meyer 80 Wavelets, detail space 83 Wavelets, dilation equation 81 Wavelets, dyadic similarity 81 Wavelets, fast algorithm 86 Wavelets, filter banks 86 Wavelets, Gabor wavelets 76 Wavelets, localized small wave 73 Wavelets, Maivar — Wilson 77 Wavelets, Marr's wavelets 75 Wavelets, multiresolution analysis 73 Wavelets, orthonormal condition 83 Wavelets, redundancy 77 Wavelets, response to edges 107 Wavelets, synthesis filter bank 88 Wavelets, vanishing moments 105 Wiener filter, deblurring 217 219 Wiener filter, denoising 159 Wiener filter, explicit formula 160 219 Wiener filter, orthogonal condition 159 Wiener process 152 Windowed Fourier transform 76 Zero-crossing 75
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