7.2.1 Numerical implementation......Page 5
Cover......Page 1
1 INTRODUCTION......Page 10
9.1.1 Iterative resolution by the Jacobi and Gauss-Seidel iterations......Page 3
Contents......Page 6
References......Page 8
8.4.4 Recovery of regularized relative depth......Page 11
8.4.5 Algorithm......Page 12
8.5 Minimization of E3......Page 14
7.3.5 Examples......Page 17
5.2 Segmentation by maximizing the image likelihood......Page 2
9.2 The Aubert, Deriche, and Kornprobst algorithm......Page 4
8.3.3 Minimization with respect to the active curve......Page 7
8.4.1 Minimization with respect to the essential parameter vectors......Page 9
8.4.6 Example......Page 13
5.2.6 MDL interpretation of the smoothness term coefficient......Page 16
References......Page 18
References......Page 19
References......Page 20
5.3 Maximization of the mutual information between the segmentation and the image......Page 22
2.1.2 Variable domain of integration......Page 25
8.5.1 Example......Page 15
5.3.1 Curve evolution equation......Page 24
5.3.3 Algorithm summary......Page 26
5.4 Segmentation by maximizing the discrepancy between the regions image distributions......Page 27
2.2.2 Integral functionals......Page 28
5.5 Image segmentation using a region reference distribution......Page 29
5.5.1 Statistical interpretation......Page 31
5.6 Segmentation with an overlap prior......Page 32
5.6.2 Example......Page 35
References......Page 38
2.1.1 Definite integrals......Page 23
2.3 Level sets......Page 30
2.4.1 The gradient equation......Page 33
2.4.2 The Horn and Schunck formulation......Page 34
2.4.3 The Aubert, Kornprobst, and Deriche formulation......Page 36
References......Page 39
3.1 The Mumford and Shah model......Page 40
3.1.1 Bayesian interpretation......Page 41
3.1.2 Graduated non convexity implementation......Page 42
3.2.1 MDL and MAP......Page 43
3.2.2 The piecewise constant image model......Page 44
3.2.3 Numerical implementation......Page 46
3.3 The region competition algorithm......Page 47
3.3.1 Optimization......Page 48
3.4 A level set formulation of the piecewise constant Mumford-Shah model......Page 52
3.4.1 Curve evolution minimization of the Chan-Vese functional......Page 53
3.4.2 Level set representation of curve evolution......Page 55
3.4.3 Algorithm summary......Page 56
3.4.4 Numerical implementation details of the level set evolution equation......Page 57
3.5.1 The Kass-Witkin-Terzopoulos Snakes model......Page 58
3.5.2 The Geodesic active contour......Page 59
3.5.3 Examples......Page 61
References......Page 64
4.1 Introduction......Page 66
4.2 Multiregion segmentation using a partition constraint functional term......Page 68
4.3 Multiphase level set image segmentation......Page 69
4.4.1 Representation of a partition into a fixed but arbitrary number of regions......Page 73
4.4.2 Curve evolution equations......Page 74
4.4.3 Level set implementation......Page 76
4.5 Multiregion level set segmentation as regularized clustering......Page 77
4.5.1 Curve evolution equations......Page 78
4.5.2 Level set implementation......Page 80
4.6.1 Two-region segmentation: first order analysis......Page 81
4.6.2 Extension to multiregion segmentation......Page 83
4.6.3 Example......Page 85
References......Page 87
5.1 Introduction......Page 89
5.2 Segmentation by maximizing the image likelihood......Page 90
5.2.1 The Gaussian model......Page 91
5.2.2 The Gamma image model......Page 95
5.2.3 Generalization to distributions of the exponential family......Page 97
5.2.4 The Weibull image Model......Page 99
5.2.5 The Complex Wishart Model......Page 101
5.2.6 MDL interpretation of the smoothness term coefficient......Page 104
5.2.7 Generalization to multiregion segmentation......Page 105
5.2.8 Examples......Page 107
5.3 Maximization of the mutual information between the segmentation and the image......Page 110
5.3.1 Curve evolution equation......Page 112
5.3.2 Statistical interpretation......Page 114
5.4 Segmentation by maximizing the discrepancy between the regions image distributions......Page 115
5.4.2 The kernel width......Page 116
5.4.4 Example......Page 117
5.5.1 Statistical interpretation......Page 119
5.5.2 Summary of the algorithms......Page 120
5.6.1 Statistical interpretation......Page 123
References......Page 126
6.1 Introduction......Page 129
6.2 Definition of a region merging prior......Page 131
6.4 An entropic region merging prior......Page 132
6.4.2 Segmentation functional......Page 133
6.4.3 Minimization equations......Page 134
6.4.4 A region merging interpretation of the level set evolution equations......Page 136
6.5.1 Segmentation with the entropic region merging prior......Page 138
6.5.3 Computation time......Page 139
References......Page 143
7.1 Introduction......Page 144
7.2 Piecewise constant MDL estimation and segmentation of optical flow......Page 146
7.2.1 Numerical implementation......Page 148
7.2.2 Example......Page 150
7.3.1 Formulation......Page 152
7.3.2 Functional minimization......Page 156
7.3.3 Level set implementation......Page 160
References......Page 163
8.1 Introduction......Page 166
8.2 The functionals......Page 169
8.3.1 Minimization with respect to the screws of motion......Page 171
8.3.3 Minimization with respect to the active curve......Page 172
8.3.4 Algorithm......Page 173
8.3.7 Example......Page 174
8.4.3 Minimization with respect to......Page 176
8.4.5 Algorithm......Page 177
8.4.6 Example......Page 178
8.5 Minimization of E3......Page 179
8.5.1 Example......Page 180
References......Page 183
9.1 The Horn and Schunck optical flow estimation algorithm......Page 186
9.1.1 Iterative resolution by the Jacobi and Gauss-Seidel iterations......Page 188
9.1.2 Evaluation of derivatives......Page 189
9.3 Construction of stereoscopic images of a computed 3D interpretation......Page 191
References......Page 193
Index......Page 194