| Foreword by Anil K. Jain | 7 |
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| Foreword by Rama Chellappa | 9 |
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| Preface to the Third Edition | 11 |
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| Preface to the Second Edition | 12 |
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| Preface to the First Edition | 13 |
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| Contents | 15 |
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| Introduction | 20 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 6.1 The DA Prior and Robust Statistics | 180 |
| 6.2 Experimental Comparison | 191 |
| MRF Parameter Estimation | 200 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| List of Notation | 366 |
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| Index | 368 |