Markov Random Field Modeling in Image Analysis

By: Stan Z. Li

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Hardcover | 2 April 2009 | Edition Number 3

At a Glance

Hardcover
384 Pages

Edition Type
Revised

Dimensions(cm)
23.5 x 15.88 x 2.54

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Markov random field (MRF) theory provides a basis for modeling contextual constraints in visual processing and interpretation. It enables us to develop optimal vision algorithms systematically when used with optimization principles. This book presents a comprehensive study on the use of MRFs for solving computer vision problems. Various vision models are presented in a unified framework, including image restoration and reconstruction, edge and region segmentation, texture, stereo and motion, object matching and recognition, and pose estimation. This third edition includes the most recent advances and has new and expanded sections on topics such as: Bayesian Network; Discriminative Random Fields; Strong Random Fields; Spatial-Temporal Models; Learning MRF for Classification. This book is an excellent reference for researchers working in computer vision, image processing, statistical pattern recognition and applications of MRFs. It is also suitable as a text for advanced courses in these areas.

Industry Reviews

From the reviews of the third edition:

"Prof. Li's book ... provides a comprehensive introduction to the area of MRF in general and to its applications in image processing in specific. ... is very well written with a plethora of references for the reader that wants to delve further into specific areas. ... In conclusion, this book is very thorough, both in a mathematic and a descriptive manner. Anyone interested in image processing and its applications ... can benefit from the variety of provided examples and its wide range of references." (Apostolos Georgakis, IAPR Newsletter, Vol. 31 (4), October, 2009)

"This book elegantly and effectively elaborates on MRF theory and related topics. Each chapter includes the problem definition, related mathematical formulation and method explanations, and very useful examples. ... This is an excellent book on MRF theory for image analysis. Researchers and graduate students will find this book very useful for understanding the theory clearly." (Fatih Kurugollu, ACM Computing Reviews, November, 2009)

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You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Stochastics Computing & I.T.Computer Science Image Processing Artificial Intelligence Computer Vision Probability & Statistics Databases Data Capture & Analysis

Graphical & Digital Media Applications

Foreword	p. ix
Foreword	p. xi
Preface to the Third Edition	p. xiii
Preface to the Second Edition	p. xv
Preface to the First Edition	p. xvii
Introduction	p. 1
Labeling for Image Analysis	p. 3
Sites and Labels	p. 3
The Labeling Problem	p. 4
Labeling Problems in Image Analysis	p. 5
Labeling with Contextual Constraints	p. 7
Optimization-Based Approach	p. 8
Research Issues	p. 9
Role of Energy Functions	p. 10
Formulation of Objective Functions	p. 11
Optimality Criteria	p. 12
The MAP-MRF Framework	p. 13
Bayes Estimation	p. 13
MAP-MRF Labeling	p. 15
Regularization	p. 16
Summary of the MAP-MRF Approach	p. 17
Validation of Modeling	p. 18
Mathematical MRF Models	p. 21
Markov Random Fields and Gibbs Distributions	p. 21
Neighborhood System and Cliques	p. 21
Markov Random Fields	p. 24
Gibbs Random Fields	p. 26
Markov-Gibbs Equivalence	p. 28
Normalized and Canonical Forms	p. 29
Auto-models	p. 30
Multi-level Logistic Model	p. 32
The Smoothness Prior	p. 34
Hierarchical GRF Model	p. 37
The FRAME Model	p. 37
Multiresolution MRF Modeling	p. 40
Conditional Random Fields	p. 43
Discriminative Random Fields	p. 44
Strong MRF Model	p. 45
<$>{\cal K}<$>-MRF and Nakagami-MRF Models	p. 46
Graphical Models: MRF's versus Bayesian Networks	p. 47
Low-Level MRF Models	p. 49
Observation Models	p. 50
Image Restoration and Reconstruction	p. 51
MRF Priors for Image Surfaces	p. 51
Piecewise Constant Restoration	p. 54
Piecewise Continuous Restoration	p. 56
Surface Reconstruction	p. 58
Edge Detection	p. 60
Edge Labeling Using Line Process	p. 61
Forbidden Edge Patterns	p. 63
Texture Synthesis and Analysis	p. 65
MRF Texture Modeling	p. 65
Texture Segmentation	p. 69
Optical Flow	p. 71
Variational Approach	p. 71
Flow Discontinuities	p. 73
Stereo Vision	p. 74
Spatio-temporal Models	p. 76
Bayesian Deformable Models	p. 78
Formulation of EigenSnake	p. 80
Experiments	p. 86
High-Level MRF Models	p. 91
Matching under Relational Constraints	p. 91
Relational Structure Representation	p. 92
Work in Relational Matching	p. 96
Feature-Based Matching	p. 98
Posterior Probability and Energy	p. 99
Matching to Multiple Objects	p. 101
Extensions	p. 103
Experiments	p. 105
Optimal Matching to Multiple Overlapping Objects	p. 113
Formulation of MAP-MRF Estimation	p. 113
Computational Issues	p. 117
Pose Computation	p. 121
Pose Clustering and Estimation	p. 121
Simultaneous Matching and Pose Estimation	p. 124
Discussion	p. 127
Face Detection and Recognition	p. 127
Discontinuities in MRF's	p. 129
Smoothness, Regularization, and Discontinuities	p. 130
Regularization and Discontinuities	p. 131
Other Regularization Models	p. 135
The Discontinuity Adaptive MRF Model	p. 136
Defining the DA Model	p. 136
Relations with Previous Models	p. 141
Discrete Data and 2D Cases	p. 142
Solution Stability	p. 143
Computational Issues	p. 144
Total Variation Models	p. 146
Total Variation Norm	p. 147
TV Models	p. 147
Multichannel TV	p. 150
Modeling Roof Discontinuities	p. 151
Roof-Edge Model	p. 152
MAP-MRF Solution	p. 154
Computational Issues	p. 155
Experimental Results	p. 156
Step-Edge-Preserving Smoothing	p. 156
Roof-Edge-Preserving Smoothing	p. 157
MRF Model with Robust Statistics	p. 161
The DA Prior and Robust Statistics	p. 162
Robust M-Estimator	p. 163
Problems with M-Estimator	p. 165
Redefinition of M-Estimator	p. 166
AM-Estimator	p. 167
Convex Priors for DA and M-Estimation	p. 168
Half-Quadratic Minimization	p. 170
Experimental Comparison	p. 173
Location Estimation	p. 173
Rotation Angle Estimation	p. 177
MRF Parameter Estimation	p. 183
Supervised Estimation with Labeled Data	p. 184
Maximum Likelihood	p. 184
Pseudo-likelihood	p. 188
Coding Method	p. 188
Mean Field Approximations	p. 190
Least Squares Fit	p. 191
Markov Chain Monte Carlo Methods	p. 194
Learning in the FRAME Model	p. 198
Unsupervised Estimation with Unlabeled Data	p. 199
Simultaneous Restoration and Estimation	p. 200
Simultaneous Segmentation and Estimation	p. 202
Expectation-Maximization	p. 206
Cross Validation	p. 208
Estimating the Number of MRF's	p. 210
Akaike Information Criterion (AIC)	p. 211
Reversible Jump MCMC	p. 211
Reduction of Nonzero Parameters	p. 213
Parameter Estimation in Optimal Object Recognition	p. 215
Motivation	p. 215
Theory of Parameter Estimation for Recognition	p. 217
Optimization-Based Object Recognition	p. 218
Criteria for Parameter Estimation	p. 219
Linear Classification Function	p. 222
A Nonparametric Learning Algorithm	p. 225
Reducing Search Space	p. 227
Application in MRF Object Recognition	p. 228
Posterior Energy	p. 228
Energy in Linear Form	p. 229
How the Minimal Configuration Changes	p. 230
Parametric Estimation under Gaussian Noise	p. 232
Experiments	p. 234
Recognition of Line Patterns	p. 234
Recognition of Curved Objects	p. 238
Convergence	p. 240
Conclusion	p. 241
Minimization - Local Methods	p. 243
Problem Categorization	p. 243
Classical Minimization with Continuous Labels	p. 246
Minimization with Discrete Labels	p. 247
Interated Conditional Modes	p. 247
Relaxation Labeling	p. 248
Belief Propagation	p. 253
Convex Relaxation	p. 255
Highest Confidence First	p. 258
Dynamic Programming	p. 260
Constrained Minimization	p. 262
Penalty Functions	p. 263
Lagrange Multipliers	p. 264
Hopfield Method	p. 265
Augmented Lagrange-Hopfield Method	p. 267
MAP-MRF Estimation as Constrained Optimization	p. 268
The ALH Method	p. 269
Minimization - Global Methods	p. 273
Simulated Annealing	p. 274
Mean Field Annealing	p. 276
Graduated Nonconvexity	p. 279
GNC Algorithm	p. 279
Annealing Labeling for MAP-MRF Matching	p. 284
Graph Cuts	p. 285
Max-Flow	p. 285
Two-Label Graph Cuts	p. 286
Multilabel Graph Cuts	p. 287
Genetic Algorithms	p. 289
Standard GA	p. 290
Hybrid GA: Comb Algorithm	p. 291
Experimental Comparisons	p. 297
Comparing Various Relaxation Labeling Algorithms	p. 297
Comparing the ALH Algorithm with Others	p. 304
Comparing the Comb Algorithm with Others	p. 306
Accelerating Computation	p. 310
Multiresolution Methods	p. 311
Use of Heuristics	p. 313
References	p. 315
List of Notation	p. 351
Index	p. 353
Table of Contents provided by Ingram. All Rights Reserved.

Markov Random Field Modeling in Image Analysis

At a Glance

Hardcover

Industry Reviews

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Defective items

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