《图像分析、随机场和动态蒙特卡罗方法》

Introduction1

Part Ⅰ．Bayesian Image Analysis:Introduction13

1．The Bayesian Paradigm13

1.1 The Space of Images13

1.2 The Space of Observations15

1.3 Prior and Posterior Distribution16

1.4 Bayesian Decision Rules19

2．Cleaning Dirty Pictures23

2.1 Distortion of Images23

2.1.1 Physical Digital Imaging Systems23

2.1.2 Posterior Distributions26

2.2Smoothing29

2.3 Piecewise Smoothing35

2.4 Boundary Extraction43

3．Random Fields47

3.1 Markov Random Fields47

3 2 Gibbs Fields and Potentials51

3.3 More on Potentials57

Part Ⅱ．The Gibbs Sampler and Simulated Annealing65

4．Markov Chains:Limit Theorems65

4.1 Preliminaries65

4.2 The Contraction Coefficient69

4.3 Homogeneous Markov Chains73

4.4 Inhomogeneous Markov Chains76

5．Sampling and Annealing81

5.1Sampling81

5.2 Simulated Annealing88

5.3 Discussion94

6．Cooling Schedules99

6.1 The ICM Algorithm99

6.2 Exact MAPE Versus Fast Cooling102

6.3 Finite Time Annealing111

7．Sampling and Annealing Revisited113

7.1 A Law of Large Numbers for Inhomogeneous Markov Chains113

7.1.1 The Law of Large Numbers113

7.1.2 A Counterexample118

7.2 A General Theorem121

7.3 Sampling and Annealing under Constraints125

7.3.1Simulated Annealing126

7.3.2 Simulated Annealing under Constraints127

7.3.3 Sampling with and without Constraints129

Part Ⅲ．More on Sampling and Annealing133

8．Metropolis Algorithms133

8.1 The Metropolis Sampler133

8.2 Convergence Theorems134

8.3 Best Constants139

8.4 About Visiting Schemes141

8.4.1Systematic Sweep Strategies141

8.4.2 The Influence of Proposal Matrices143

8.5 The Metropolis Algorithm in Combinatorial Optimization148

8.6Generalizations and Modifications151

8.6.1 Metropolis-Hastings Algorithms151

8.6.2 Threshold Random Search153

9．Alternative Approaches155

9.1 Second Largest Eigenvalues155

9.1.1 Convergence Reproved155

9.1.2 Sampling and Second Largest Eigenvalues159

9.1.3 Continuous Time and Space163

10．Parallel Algorithms167

10.1 Partially Parallel Algorithms168

10.1.1 Synchroneous Updating on Independent Sets168

10.1.2 The Swendson-Wang Algorithm171

10.2 Synchroneous Algorithms173

10.2.1 Introduction173

10.2.2 Invariant Distributions and Convergence174

10.2.3 Support of the Limit Distribution178

10.3 Synchroneous Algorithms and Reversibility182

10.3.1 Preliminaries183

10.3.2 Invariance and Reversibility185

10.3.3 Final Remarks189

Part Ⅳ．Texture Analysis195

11．Partitioning195

11.1 Introduction195

11.2 How to Tell Textures Apart195

11.3 Features196

11.4 Bayesian Texture Segmentation198

11.4.1 The Features198

11.4.2 The Kolmogorov-Smirnov Distance199

11.4.3 A Partition Model199

11.4.4 Optimization201

11.4.5 A Boundary Model203

11.5 Julesz's Conjecture205

11.5.1 Introduction205

11.5.2 Point Processes205

12．Texture Models and Classification209

12.1 Introduction209

12.2 Texture Models210

12.2.1 The φ-Model210

12.2.2 The Autobinomial Model211

12.2.3 Automodels213

12.3 Texture Synthesis214

12.4 Texture Classification216

12.4.1 General Remarks216

12.4.2 Contextual Classification218

12.4.3 MPM Methods219

Part Ⅴ．Parameter Estimation225

13．Maximum Likelihood Estimators225

13.1 Introduction225

13.2 The Likelihood Function225

13.3 Objective Functions230

13.4 Asymptotic Consistency233

14．Spacial ML Estimation237

14.1 Introduction237

14.2 Increasing Observation Windows237

14.3 The Pseudolikelihood Method239

14.4 The Maximum Likelihood Method246

14.5 Computation of ML Estimators247

14.6 Partially Observed Data253

Part Ⅵ．Supplement257

15．A Glance at Neural Networks257

15.1 Introduction257

15.2 Boltzmann Machines257

15.3 A Learning Rule262

16．Mixed Applications269

16.1 Motion269

16.2 Tomographic Image Reconstruction274

16.3 Biological Shape276

Part Ⅶ．Appendix283

A．Simulation of Random Variables283

A.1 Pseudo-random Numbers283

A.2 Discrete Random Variables286

A.3 Local Gibbs Samplers289

A.4 Further Distributions290

A.4.1 Binomial Variables290

A.4.2 Poisson Variables292

A.4.3 Gaussian Variables293

A.4.4 The Rejection Method296

A.4.5 The Polar Method297

B．The Perron-Frobenius Theorem299

C．Concave Functions301

D．A Global Convergence Theorem for Descent Algorithms305

References307

Index321