Welcome to this MRF book. If the download is slow, you may be interested in getting Chapter 1 of this document in one file (371K). If you are interested in buying a copy but have difficulty finding it in your local bookstores, you may contact Springer-Verlag or order through Amazon.com Bookstore. Happy reading!

The 2nd edition, entitled Markov Random Field Modeling in Image Analysis is published in 2001.

Markov Random Field
Modeling in Computer Vision

Stan Z. Li

© Springer-Verlag 1995

ISBN 0-387-70145-1 Spinger-Verlag New York Berlin Heidelberg Tokyo
ISBN 3-540-70145-1 Spinger-Verlag Berlin Heidelberg New York Tokyo
ISBN 4-431-70145-1 Spinger-Verlag Tokyo Berlin Heidelberg New York

``An excellent book --- very thorough and very clearly written.''

--- Stuart Geman

--- Charles A. Bouman

Summary

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. The book covers the following parts essential to the subject: introduction to fundamental theories, formulations of MRF vision models, MRF parameter estimation, and optimization algorithms. 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 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.

• 1.1 Visual Labeling
  • 1.1.1 Sites and Labels
  • 1.1.2 The Labeling Problem
  • 1.1.3 Labeling Problems in Vision
  • 1.1.4 Labeling with Contextual Constraints
• 1.2 Markov Random Fields and Gibbs Distributions
  • 1.2.1 Neighborhood System and Cliques
  • 1.2.2 Markov Random Fields
  • 1.2.3 Gibbs Random Fields
  • 1.2.4 Markov-Gibbs Equivalence
  • 1.2.5 Normalized and Canonical Forms
• 1.3 Useful MRF Models
  • 1.3.1 Auto-Models
  • 1.3.2 Multi-Level Logistic Model
  • 1.3.3 The Smoothness Prior
  • 1.3.4 Hierarchical GRF Model
• 1.4 Optimization-Based Vision
  • 1.4.1 Research Issues
  • 1.4.2 Role of Energy Functions
  • 1.4.3 Formulation of Objective Functions
  • 1.4.4 Optimality Criteria
• 1.5 Bayes Labeling of MRFs
  • 1.5.1 Bayes Estimation
  • 1.5.2 MAP-MRF Labeling
  • 1.5.3 Regularization
  • 1.5.4 Summary of MAP-MRF Approach

• 2.1 Observation Models
• 2.2 Image Restoration and Reconstruction
  • 2.2.1 MRF Priors for Image Surfaces
    • MRF Prior for Piecewise Constant Surfaces
    • MRF Prior for Piecewise Continuous Surfaces
  • 2.2.2 Piecewise Constant Restoration
    • Deriving Posterior Energy
    • Energy Minimization
  • 2.2.3 Piecewise Continuous Restoration
    • Deriving Posterior Energy
    • Energy Minimization
  • 2.2.4 Surface Reconstruction
    • Regularization Solution
• 2.2 Edge Detection
  • 2.2.1 Edge Labeling using Line Process
  • 2.2.2 Forbidden Edge Patterns
• 2.3 Texture Synthesis and Analysis
  • 2.3.1 MRF Texture Modeling
  • 2.3.2 Texture Segmentation
• 2.4 Optical Flow
  • 2.4.1 Variational Approach
  • 2.4.2 Flow Discontinuities

• 3.1 Smoothness, Regularization and Discontinuities
  • 3.1.1 Regularization and Discontinuities
    • Standard Regularization
    • Line Process Model and Its Approximations
  • 3.1.2 Other Regularization Models
• 3.2 The Discontinuity Adaptive MRF Model
  • 3.2.1 Defining the DA Model
  • 3.2.2 Relations with Previous Models
  • 3.2.3 Discrete Data and 2D Cases
  • 3.2.4 Solution Stability
• 3.3 Computation of DA Solutions
  • 3.3.1 Solving the Euler Equation
  • 3.3.2 Experimental Results
• 3.4 Conclusion

• 4.1 The DA Prior and Robust Statistics
  • 4.1.1 Robust M Estimator
  • 4.1.2 Problems with M Estimator
  • 4.1.3 Redefinition of M Estimator
  • 4.1.4 AM Estimator
  • 4.1.5 Convex DA and M-Estimation Models
• 4.2 Experimental Comparison
  • 4.2.1 Location Estimation
  • 4.2.2 Rotation Angle Estimation

• 5.1 Matching under Relational Constraints
  • 5.1.1 Relational Structure Representation
  • 5.1.2 Work in Relational Matching
• 5.2 MRF-Based Matching
  • 5.2.1 Posterior Probability and Energy
  • 5.2.2 Matching to Multiple Objects
  • 5.2.3 Experiments
    • Matching Objects of Point Patterns
    • Matching Objects of Line Patterns
    • Matching Curved Objects under Similarity Transformations
  • 5.2.4 Extensions
    • Incorporating Higher Constraints
    • Coupled MRFs for Matching of Different Features
    • Relationships with Low Level MRF Models
• 5.3 Pose Computation
  • 5.3.1 Pose Clustering and Estimation
  • 5.3.2 Simultaneous Matching and Pose
  • 5.3.3 Discussion

• 6.1 Supervised Estimation with Labeled Data
  • 6.1.1 Maximum Likelihood
  • 6.1.2 Pseudo-Likelihood
  • 6.1.3 Coding Method
  • 6.1.4 Mean Field Approximations
  • 6.1.5 Least Squares Fit
• 6.2 Unsupervised Estimation with Unlabeled Data
  • 6.2.1 Simultaneous Restoration and Estimation
  • 6.2.2 Simultaneous Segmentation and Estimation
  • 6.2.3 Expectation-Maximization
  • 6.2.4 Cross Validation
• 6.3 Further Issues
  • 6.3.1 Estimating the Number of MRFs
  • 6.3.2 Reduction of Nonzero Parameters

• 7.1 Motivation
• 7.2 Theory of Parameter Estimation for Recognition
  • 7.2.1 Optimization-Based Object Recognition
  • 7.2.2 Criteria for Parameter Estimation
    • Correctness
    • Instability
    • Optimality
  • 7.2.3 Linear Classification Function
  • 7.2.4 A Non-parametric Learning Algorithm
  • 7.2.5 Reducing Search Space
• 7.3 Application in MRF Object Recognition
  • 7.3.1 Posterior Energy
  • 7.3.2 Energy in Linear Form
  • 7.3.3 How Minimal Configuration Changes
  • 7.3.4 Parametric Estimation under Gaussian Noise
• 7.4 Experiments
  • 7.4.1 Recognition of Line Patterns
  • 7.4.2 Recognition of Curved Objects
• 7.5 Conclusion

• 8.1 Classical Minimization with Continuous Labels
• 8.2 Minimization with Discrete Labels
  • 8.2.1 Iterated Conditional Modes
  • 8.2.2 Relaxation Labeling
    • Representation of Continuous RL
    • Maximization Formulation
    • Iterative Updating Equations
    • Local vs. Global Solutions
  • 8.2.3 Highest Confidence First
  • 8.2.4 Dynamic Programming
• 8.3 Constrained Minimization
  • 8.3.1 Penalty Method
  • 8.3.2 Lagrange Method
  • 8.3.3 Hopfield Method
  • 8.3.4 RL using Lagrange-Hopfield Method

• 9.1 Simulated Annealing
  • 9.1.1 Random Sampling Algorithms
  • 9.1.2 Annealing
• 9.2 Mean Field Annealing
• 9.3 Graduated Non-Convexity
  • 9.3.1 Annealing Labeling for MAP-MRF Matching
• 9.4 Genetic Algorithms
• 9.5 Experimental Comparison
• 9.6 Accelerating Computation
  • 9.6.1 Multi-resolution Methods
  • 9.6.2 Use of Heuristics
• 9.7 Model Debugging

If the download is slow, you may be interested in getting Chapter 1 of this document in one file (371K). If you are interested in buying a copy but have difficulty finding it in your local bookstores, you may contact Springer-Verlag or order through Amazon.com Bookstore. Happy reading! ... PS: The 2nd edition is to be published in 2001.

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