图像分析、随机场和动态蒙特卡罗方法PDF电子书下载

Introduction 1

Part Ⅰ．Bayesian Image Analysis:Introduction 13

1．The Bayesian Paradigm 13

1.1 The Space of Images 13

1.2 The Space of Observations 15

1.3 Prior and Posterior Distribution 16

1.4 Bayesian Decision Rules 19

2．Cleaning Dirty Pictures 23

2.1 Distortion of Images 23

2.1.1 Physical Digital Imaging Systems 23

2.1.2 Posterior Distributions 26

2.2 Smoothing 29

2.3 Piecewise Smoothing 35

2.4 Boundary Extraction 43

3．Random Fields 47

3.1 Markov Random Fields 47

3 2 Gibbs Fields and Potentials 51

3.3 More on Potentials 57

Part Ⅱ．The Gibbs Sampler and Simulated Annealing 65

4．Markov Chains:Limit Theorems 65

4.1 Preliminaries 65

4.2 The Contraction Coefficient 69

4.3 Homogeneous Markov Chains 73

4.4 Inhomogeneous Markov Chains 76

5．Sampling and Annealing 81

5.1 Sampling 81

5.2 Simulated Annealing 88

5.3 Discussion 94

6．Cooling Schedules 99

6.1 The ICM Algorithm 99

6.2 Exact MAPE Versus Fast Cooling 102

6.3 Finite Time Annealing 111

7．Sampling and Annealing Revisited 113

7.1 A Law of Large Numbers for Inhomogeneous Markov Chains 113

7.1.1 The Law of Large Numbers 113

7.1.2 A Counterexample 118

7.2 A General Theorem 121

7.3 Sampling and Annealing under Constraints 125

7.3.1 Simulated Annealing 126

7.3.2 Simulated Annealing under Constraints 127

7.3.3 Sampling with and without Constraints 129

Part Ⅲ．More on Sampling and Annealing 133

8．Metropolis Algorithms 133

8.1 The Metropolis Sampler 133

8.2 Convergence Theorems 134

8.3 Best Constants 139

8.4 About Visiting Schemes 141

8.4.1 Systematic Sweep Strategies 141

8.4.2 The Influence of Proposal Matrices 143

8.5 The Metropolis Algorithm in Combinatorial Optimization 148

8.6 Generalizations and Modifications 151

8.6.1 Metropolis-Hastings Algorithms 151

8.6.2 Threshold Random Search 153

9．Alternative Approaches 155

9.1 Second Largest Eigenvalues 155

9.1.1 Convergence Reproved 155

9.1.2 Sampling and Second Largest Eigenvalues 159

9.1.3 Continuous Time and Space 163

10．Parallel Algorithms 167

10.1 Partially Parallel Algorithms 168

10.1.1 Synchroneous Updating on Independent Sets 168

10.1.2 The Swendson-Wang Algorithm 171

10.2 Synchroneous Algorithms 173

10.2.1 Introduction 173

10.2.2 Invariant Distributions and Convergence 174

10.2.3 Support of the Limit Distribution 178

10.3 Synchroneous Algorithms and Reversibility 182

10.3.1 Preliminaries 183

10.3.2 Invariance and Reversibility 185

10.3.3 Final Remarks 189

Part Ⅳ．Texture Analysis 195

11．Partitioning 195

11.1 Introduction 195

11.2 How to Tell Textures Apart 195

11.3 Features 196

11.4 Bayesian Texture Segmentation 198

11.4.1 The Features 198

11.4.2 The Kolmogorov-Smirnov Distance 199

11.4.3 A Partition Model 199

11.4.4 Optimization 201

11.4.5 A Boundary Model 203

11.5 Julesz's Conjecture 205

11.5.1 Introduction 205

11.5.2 Point Processes 205

12．Texture Models and Classification 209

12.1 Introduction 209

12.2 Texture Models 210

12.2.1 The φ-Model 210

12.2.2 The Autobinomial Model 211

12.2.3 Automodels 213

12.3 Texture Synthesis 214

12.4 Texture Classification 216

12.4.1 General Remarks 216

12.4.2 Contextual Classification 218

12.4.3 MPM Methods 219

Part Ⅴ．Parameter Estimation 225

13．Maximum Likelihood Estimators 225

13.1 Introduction 225

13.2 The Likelihood Function 225

13.3 Objective Functions 230

13.4 Asymptotic Consistency 233

14．Spacial ML Estimation 237

14.1 Introduction 237

14.2 Increasing Observation Windows 237

14.3 The Pseudolikelihood Method 239

14.4 The Maximum Likelihood Method 246

14.5 Computation of ML Estimators 247

14.6 Partially Observed Data 253

Part Ⅵ．Supplement 257

15．A Glance at Neural Networks 257

15.1 Introduction 257

15.2 Boltzmann Machines 257

15.3 A Learning Rule 262

16．Mixed Applications 269

16.1 Motion 269

16.2 Tomographic Image Reconstruction 274

16.3 Biological Shape 276

Part Ⅶ．Appendix 283

A．Simulation of Random Variables 283

A.1 Pseudo-random Numbers 283

A.2 Discrete Random Variables 286

A.3 Local Gibbs Samplers 289

A.4 Further Distributions 290

A.4.1 Binomial Variables 290

A.4.2 Poisson Variables 292

A.4.3 Gaussian Variables 293

A.4.4 The Rejection Method 296

A.4.5 The Polar Method 297

B．The Perron-Frobenius Theorem 299

C．Concave Functions 301

D．A Global Convergence Theorem for Descent Algorithms 305

References 307

Index 321