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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:

Partial differential equations and variational methods were introduced into image processing about 15 years ago, and intensive research has been carried out since then. The main goal of this work is to present the variety of image analysis applications and the precise mathematics involved. It is intended for two audiences. The first is the mathematical community, to show the contribution of mathematics to this domain and to highlight some unresolved theoretical questions. The second is the computer vision community, to present a clear, self-contained, and global overview of the mathematics involved in image processing problems. This book will be useful to researchers and graduate students in mathematics and computer vision.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 286

Добавлена в каталог: 01.03.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Active contours      152
Approximate limit      42 201
Approximate, derivative      42 70
Axiom, locality      98
Axiom, recursivity      97
Axiom, Regularity      97
Bernstein method      170
Bhattacharyya distance      218
Camera model      185
Characteristics, curve      120
Characteristics, equations      121
Characteristics, lines      242
Characteristics, method of      120 245
Classification      210
Classification, regular      212
Classification, supervised      210
Coarea formula      56 214 227
Coercive      26 150 192
Compactness, weak sequential      26
Condition, CFL      244
Condition, entropy      249 251
Condition, Rankine — Hugoniot      248
Conjecture, Mumford — Shah      133 137 145
Conjecture, Osher — Rudin      125
Convergence, BV-w*      41 44
Convergence, gamma convergence      34 70 146 219 226
Convergence, strong      24
Convergence, weak      24
Convergence, weak*      25
Crack tip      133 141
Curvature, mean curvature motion      159 261
Curvature, radius      52
Curvature, tensor      52
Cut-off* function      200
Derivative length      139 158
Derivative of domain integral      139
Derivative, approximate      42 70
Derivative, Gateaux      30 176 213
Derivative, Radon — Nikodym derivative      38
Diffusion, nonlinear      88
Diffusion, operator      65
Diffusion, tensor      105
Direct method of the calculus of variations      26 134 192 199
Discrete image      3 118 147 252
Domain of dependence      244
Dual variable      70 72 192 202 222 255
EDGE      111 160
Elliptic equation      65
Elliptic, approximation by elliptic functionals      146
Elliptic, degenerate      47
Equation, backward heat      113
Equation, Burgers      245
Equation, eikonal      44
Equation, Euler — Lagrange      31 63 64 70 72 78 108 154
Equation, Hamilton — Jacobi equations      46 163
Equation, heat      85 252
Equation, mean curvature motion      159 261
Equation, transport      242
Equicontinuous, uniformly      57
Eulerian formulation      161 163
Fast marching algorithm      263
Filter, Gaussian      85
Filter, high-pass      111
Filter, low-pass      86 111
Filter, Osher and Rudin shock filters      118 124
Finite differences      230
Finite differences, backward      243
Finite differences, centered      243 259
Finite differences, derivatives      232 253
Finite differences, forward      243
Finite elements      230
Fixed-point, Schauder’s fixed-point theorem      117
Formula, chain rule      201
Formula, coarea      56 214 227
Formula, integration by part      55
Functional, coercive      26 150 192
Functional, convex      27
Functional, equicoercive      34
Functional, lower semicontinuous      26 44 67 198
Functional, Mumford — Shah      133
Functional, nonconvex      80 199
Functional, relaxed      31 67 92 193
Gamma convergence      34 70 146 219 226
Gaussian kernel      85
Generalized solution      118
Half-quadratic minimization      70 72 192 202 222 255
Hamiltonian      47
Hamiltonian, degenerate elliptic      47
Ill-posed      58 62 80 113 125
Inequality, Cauchy      54
Inequality, Cauchy — Schwarz      54 158 170
Inequality, Gronwall      54 115 173
Inequality, Jensen      54
Inequality, Minkowski      55
Inequality, Poincare      55
Inequality, Poincare — Wirtinger      55 68 80
Inequality, Young      55
Invariance      77
Invariance, gray-level      78 87 98
Invariance, gray-scale      102
Invariance, isometry      78 87 102
Invariance, projection      102
Invariance, scale      87 102
Invariance, translation      78 87 98
Isophotes      64
Lebesgue decomposition theorem      38
Lebesgue, points      42
Level-set method      162 212 260
Limit, approximate lower/upper limit      42
Lower semicontinuous, functional      26 44 67 198
Measure, absolutely continuous      38 193
Measure, bounded      37
Measure, convex function of      44 198
Measure, Hausdorff      41
Measure, mutually singular      38
Measure, positive      37
Measure, Radon      37
Measure, signed      37
Measure, vector-valued      37
Minimizing sequence      26
Minmod function      259
Model, Alvarez — Guichard — Lions — Morel scale space theory      97
Model, Caselles — Kimmel — Sapiro      155
Model, Catte et al.      113
Model, degradation      60
Model, Horn and Schunck      187
Model, Kass — Witkin — Terzopoulos      153
Model, Nitzberg — Shiota      118
Model, Osher — Rudin      118
Model, Perona — Malik      88 111 112 256
Model, smoothing-enhancing      90
Model, variational model for restoration      64 255
Model, Weickert      103
Mollifier      56
Motion, 2-D motion field      184
Motion, apparent      184
movies      103
Narrow band      215 264
Negligible set      37
Operator, divergence      256
Operator, domain      91
Operator, maximal monotone      91-93
Operator, minmod      259
Operator, monotone      91
Operator, morphological      103
Operator, multivalued      91
Operator, range      91
Operator, surjective      91
Optical flow      184 195 256
Optical flow constraint (OFC)      186 193
Partition condition      212
Partitioning process      211
PDEs, backward parabolic      84 90
PDEs, enhancing PDEs      118
PDEs, forward parabolic      84 90
PDEs, hyperbolic      84 242
PDEs, smoothing      85 86
PDEs, smoothing-enhancing      90 111
PDEs, system of coupled      215
Perimeter      40 220
Perimeter, minimal      211
Phase transitions      219
Polar function      32 147
Precise representation      43 193
Principle, comparison      98
Principle, extremum      105
Principle, maximum      50 87 172
Process, dynamical      215
Process, restoration      218
Regularity of the edge set      141
Regularity, Bonnet results      145
Regularity, heat equation      88
Regularization of the Perona and Malik model      113
Regularization, edge-preserving      65 80
Regularization, Tikhonov — Arsenin regularization      63
Relaxed functional      31 67 92 193
Scale, Alvarez — Guichard — Lions — Morel scale space theory      97
Scale, parameter      86
Scale, space      80
Scale, variable      84
Scheme, conservative      250 251
Scheme, consistent      236 251
Scheme, convergent      234
Scheme, Crank — Nicholson      241
Scheme, explicit      232
Scheme, implicit      241
Scheme, monotone      251
Scheme, order of accuracy      236
Scheme, order of convergence      234
Scheme, pointwise consistent      235
Scheme, pointwise convergent      233
Scheme, stable      237 243
Scheme, stable, (un)conditionally      238
Scheme, symbol      240
Scheme, truncature error      236
Scheme, upwind      244
Seed initialization      218
Semigroup      88 91
SEQUENCE      182
Sequence, restoration      204
Sequence, sampling      182
Sequence, segmentation      195 256
Snakes      153
Space of bounded variation      39 67 135 190 199
Space of special functions of bounded variation      136
Space, Banach      24
Space, reflexive      25 67
Space, separable      25
Subdifferential      91
Subdifferential of a convex function      91
Subjet      49
Superjet      49
Theorem, Arzela — Ascoli      57 171
Theorem, dominated convergence      57
Theorem, Fubini      87
Theorem, Gauss — Green      55
Theorem, Green      56 79 93 139
Theorem, Lax — Wendroff      251
Theorem, Lebesgue decomposition theorem      38
Theorem, Schauder      117
Topology, BV-w*      41 44
Topology, strong      24
Topology, weak      24
Topology, weak*      25
Total variation      xxiii 37 43 63 70 110 125 188
Triple junction      133 141
Vector distance function      178
Viscosity, Crandall — Ishii lemma      49 167
Viscosity, duplication of variables      51 167
Viscosity, solution      48 98 166 167 174
Viscosity, subsolution      48 166
Viscosity, supersolution      48 166
Viscosity, vanishing viscosity method      48
Von Neumann criterion      241 243
Weak solution      247
Well-posed      58 89 113 114 190 198 230 235
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