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