Markov Random Field Modeling in Image Analysis (eBook)

Foreword by Anil K. Jain 7
Foreword by Rama Chellappa 9
Preface to the Third Edition 11
Preface to the Second Edition 12
Preface to the First Edition 13
Contents 15
Introduction 20
1.1 Labeling for Image Analysis 22
1.2 Optimization-Based Approach 27
1.3 The MAP-MRF Framework 32
1.4 Validation of Modeling 37
Mathematical MRF Models 40
2.1 Markov Random Fields and Gibbs Distributions 40
2.2 Auto-models 49
2.3 Multi-level Logistic Model 51
2.4 The Smoothness Prior 53
2.5 Hierarchical GRF Model 56
2.6 The FRAME Model 56
2.7 Multiresolution MRF Modeling 59
2.8 Conditional Random Fields 62
2.9 Discriminative Random Fields 63
2.10 Strong MRF Model 64
2.11 K-MRF and Nakagami-MRF Models 65
2.12 Graphical Models: MRF’s versus Bayesian Networks 66
Low-Level MRF Models 68
3.1 Observation Models 69
3.2 Image Restoration and Reconstruction 70
3.3 Edge Detection 79
3.4 Texture Synthesis and Analysis 84
3.5 Optical Flow 90
3.6 Stereo Vision 93
3.7 Spatio-temporal Models 95
3.8 Bayesian Deformable Models 97
High-Level MRF Models 110
4.1 Matching under Relational Constraints 110
4.2 Feature-Based Matching 117
4.3 Optimal Matching to Multiple Overlapping Objects 132
4.4 Pose Computation 140
4.5 Face Detection and Recognition 146
Discontinuities in MRF’s 148
5.1 Smoothness, Regularization, and Discontinuities 149
5.2 The Discontinuity Adaptive MRF Model 155
5.3 Total Variation Models 165
5.4 Modeling Roof Discontinuities 170
5.5 Experimental Results 175
MRF Model with Robust Statistics 179
6.1 The DA Prior and Robust Statistics 180
6.2 Experimental Comparison 191
MRF Parameter Estimation 200
7.1 Supervised Estimation with Labeled Data 201
7.2 Unsupervised Estimation with Unlabeled Data 216
7.3 Estimating the Number of MRF’s 227
7.4 Reduction of Nonzero Parameters 230
Parameter Estimation in Optimal Object Recognition 232
8.1 Motivation 232
8.2 Theory of Parameter Estimation for Recognition 234
8.3 Application in MRF Object Recognition 245
8.4 Experiments 251
8.5 Conclusion 258
Minimization – Local Methods 259
9.1 Problem Categorization 259
9.2 Classical Minimization with Continuous Labels 262
9.3 Minimization with Discrete Labels 263
9.4 Constrained Minimization 278
9.5 Augmented Lagrange-Hopfield Method 283
Minimization – Global Methods 288
10.1 Simulated Annealing 289
10.2 Mean Field Annealing 291
10.3 Graduated Nonconvexity 294
10.4 Graph Cuts 300
10.5 Genetic Algorithms 304
10.6 Experimental Comparisons 312
10.7 Accelerating Computation 325
References 330
List of Notation 366
Index 368