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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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Предметный указатель
283 329 364 Aberration-free lens 211 Active contours, 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 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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