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Aubert G., Kornprobst P. — Mathematical Problems in Image Processing: Partial Differential Equations And the Calculus of Variations
Aubert G., Kornprobst P. — Mathematical Problems in Image Processing: Partial Differential Equations And the Calculus of Variations



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Название: Mathematical Problems in Image Processing: Partial Differential Equations And the Calculus of Variations

Авторы: Aubert G., Kornprobst P.

Аннотация:

Mathematical Problems in Image Processing is a major, elegant, and unique contribution to the applied mathematics literature, oriented toward applications in image processing and computer vision.... Researchers and practitioners working in the field will benefit by adding this book to their personal collection. Students and instructors will benefit by using this book as a graduate course textbook.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd

Год издания: 2006

Количество страниц: 377

Добавлена в каталог: 01.03.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Active contours      173
Approximate, derivative      48 76
Approximate, limit      48 268
Axiom, locality      108
Axiom, recursivity      107
Axiom, Regularity      108
Bernstein method      190
Bhattacharyya distance      287
C++ source codes      343
Camera model      251
Characteristics, curve      130
Characteristics, equations      131
Characteristics, lines      320
Characteristics, method of      130 323
Classification      281
Classification, regular      283
Classification, supervised      282
Coarea formula      62 285 299
Coercive      32 171 258
Compactness, weak sequential      32
Condition, CFL      322
Condition, entropy      327 329
Condition, Rankine — Hugoniot      326
Conjecture, Mumford — Shah      153 157 165
Conjecture, Osher — Rudin      135
Convergence, BV-w*      47 50
Convergence, gamma convergence      40 80 166 291 297
Convergence, strong      31
Convergence, weak      31
Convergence, weak*      31
Crack tip      153 162
Curvature, mean curvature motion      179 339
Curvature, radius      58
Curvature, tensor      58
Cut-off function      222 267
Derivative, approximate      48 76
Derivative, Gateaux      36 210 285
Derivative, length      159 178
Derivative, of domain integral      159
Derivative, Radon — Nikodym derivative      44
Diffusion, nonlinear      98
Diffusion, operator      71
Diffusion, tensor      115 302
Digital image      3 307
Direct method of the calculus of variations      32 154 258 266
Discrete differential operators      76 235 308
Discrete image      128 168 330
Distance function      183 195 339
Domain of dependence      322
Dual variable      80 258 270 294 333
EDGE      121 180
Elastica model      217
Elliptic, approximation by elliptic functionals      166
Elliptic, degenerate      52
Elliptic, equation      71
Envelope, lower semicontinuous      198
Envelope, upper semicontinuous      198
Equation, backward heat      123
Equation, Burgers      323
Equation, eikonal      50
Equation, Euler — Lagrange      37 69 70 76 82 87 118 174
Equation, Hamilton — Jacobi equations      52 184
Equation, heat      95 140 330
Equation, mean curvature motion      179 339
Equation, transport      320
Equicontinuous, uniformly      64
Eulerian formulation      182 184
Fast marching algorithm      341
filling in      215 225 304
Filter, bilateral      138
Filter, Gaussian      95 138
Filter, high-pass      121
Filter, low-pass      96 121
Filter, neighborhood      138
Filter, nonlocal means      146
Filter, Osher and Rudin shock filters      128 134
Filter, Susan      141
Filter, Yaroslavsky      141
Finite, differences      308
Finite, differences, backward      321
Finite, differences, centered      321 337
Finite, differences, derivatives      310 331
Finite, differences, forward      321
Finite, elements      308
Fixed-point Schauder's fixed-point theorem      127
Formula, chain rule      267 268
Formula, coarea      62 285 299
Formula, integration by part      62
Functional coercive      32 171 258
Functional convex      33
Functional equicoercive      40
Functional lower semicontinuous      33 50 73 265 302
Functional Mumford — Shah      153
Functional nonconvex      90 266
Functional relaxed      38 73 102 260
Gamma convergence      40 80 166 291 297
Gaussian kernel      95
Generalized solution      128
Half-quadratic minimization      80 258 270 294 333
Hamiltonian      52
Hamiltonian, degenerate elliptic      52
Hamiltonian, discontinuous      198
Ill-posed      64 68 90 123 135
Image, characteristics      4
Image, color      3 299
Image, digital      3 307
Image, gray-scale      3
Image, natural      75
Image, vector-valued      299
Inequality, Cauchy      60
Inequality, Cauchy — Schwarz      60 178 190
Inequality, Gronwall      60 125 193
Inequality, Jensen      61
Inequality, Minkowski      61
Inequality, Poincare      61 236
Inequality, Poincare — Wirtinger      61 74 89
Inequality, Young      61
Inpainting      215 248 304
Invariance      87
Invariance, gray-level      87 97 108
Invariance, gray-scale      112
Invariance, isometry      87 97 112
Invariance, projection      112
Invariance, scale      97 112
Invariance, translation      87 97 108
Isophotes      70
Lagrange multipliers      79
Lebesgue, Lebesgue decomposition theorem      44
Lebesgue, points      48
Level set method      182 284 338
Limit, approximate lower/upper limit      48
Lower semicontinuous envelope      198
Lower semicontinuous functional      33 50 73 265 302
Measure, absolutely continuous      44 259
Measure, bounded      43
Measure, convex function of      49 265
Measure, Hausdorff      47
Measure, mutually singular      44
Measure, positive      43
Measure, Radon      43
Measure, signed      43
Measure, vector-valued      43
Minimizing sequence      32
Minmod function      337
Model, Alvarez — Guichard — Lions — Morel scale space theory      107
Model, Caselles — Kimmel — Sapiro      175
Model, Catte et al.      123
Model, degradation      66
Model, Horn and Schunck      254
Model, Kass — Witkin — Terzopoulos      173
Model, Meyer      233
Model, Nitzberg — Shiota      128
Model, Osher — Rudin      128
Model, Perona — Malik      98 121 122 334
Model, Rudin — Osher — Fatemi      69 228
Model, smoothing-enhancing      100
Model, variational model for restoration      70 333
Model, Weickert      113
Modulus of continuity      200
Mollifier      62
Motion, 2-D motion field      250
Motion, apparent      250
movies      113
Narrow band      287 342
Negligible set      44
Neighborhood filters      137
Operator, divergence      334
Operator, domain      101
Operator, maximal monotone      101-103
Operator, minmod      337
Operator, monotone      101
Operator, morphological      113
Operator, multivalued      101
Operator, range      101
Operator, surjective      101
Optical flow      250 262 280 334
Optical flow, constraint (OFC)      252 260
Oscillating patterns      229
Partition condition      284
Partitioning process      282
PDEs, backward parabolic      94 100
PDEs, enhancing PDEs      128
PDEs, forward parabolic      94 100
PDEs, hyperbolic      94 320
PDEs, smoothing      95 96
PDEs, smoothing-enhancing      100 121
PDEs, system of coupled      287
Perimeter      46 292
Perimeter, minimal      282
Phase transitions      290
Polar function      38 168
Polar transform      78
Precise representation      49 259
Principle, comparison      108
Principle, extremum      115
Principle, maximum      56 97 192
Process, dynamical      287
Process, restoration      290
Projection algorithm      79 237
Quasiconvexity      34 301
Regularity of the edge set      162
Regularity, Bonnet results      165
Regularity, heat equation      98
Regularization of the Perona and Malik model      123
Regularization, edge-preserving      71 90
Regularization, Tikhonov — Arsenin regularization      69 301
Relaxed functional      38 73 102 260
Scale, Alvarez — Guichard — Lions — Morel scale space theory      107
Scale, parameter      96
Scale, space      89
Scale, variable      94
Scheme, conservative      328 329
Scheme, consistent      314 329
Scheme, convergent      312
Scheme, Crank — Nicholson      319
Scheme, explicit      310
Scheme, implicit      319
Scheme, monotone      329
Scheme, order of accuracy      314
Scheme, order of convergence      312
Scheme, pointwise consistent      313
Scheme, pointwise convergent      311
Scheme, stable      315 321
Scheme, stable, (un)conditionally      316
Scheme, symbol      318
Scheme, truncature error      314
Scheme, upwind      322
Seed initialization      287
Semigroup      98 101
SEQUENCE      249
Sequence, restoration      271
Sequence, sampling      250
Sequence, segmentation      261 334
Skeleton      195
Snakes      174
Space of bounded variation      45 73 75 155 257 265
Space of special functions of bounded variation      156
Space, Banach      30
Space, Besov      248
Space, reflexive      31 73
Space, separable      31
Staircase effect      75 143
Structure tensor      24 300
Subdifferential      78 101
Subjet      55
Superjet      55
Texture      225 229
Theorem, Arzela — Ascoli      63 192
Theorem, dominated convergence      64
Theorem, Fubini      97
Theorem, Gauss — Green      62
Theorem, Green      62 89 103 160
Theorem, Lax — Wendroff      329
Theorem, Lebesgue decomposition theorem      44
Theorem, Schauder      127
Topology, BV—w*      47 50
Topology, strong      31
Topology, weak      31
Topology, weak*      31
Total variation      xxix 43 49 70 80 107 120 135 220 254 277 301
Triple junction      153 162
Upper level sets      216
Upper semicontinuous envelope      198
Vector distance function      211
Viscosity, Crandall — Ishii lemma      55 187
Viscosity, discontinuous solution      199
Viscosity, duplication of variables      57 187
Viscosity, solution      54 108 186 187 194
Viscosity, subsolution      54 186 198
Viscosity, supersolution      54 186 199
Viscosity, vanishing viscosity method      54
Von Neumann criterion      319 321
Weak solution      325
Well-posed      64 99 123 124 257 265 308 313
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