图像分析中的模型和逆问题PDF|Epub|txt|kindle电子书版本网盘下载

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1 Introduction1

1.1 About Modeling3

1.1.1 Bayesian Approach3

1.1.2 Inverse Problem8

1.1.3 Energy-Based Formulation10

1.1.4 Models11

1.2 Structure of the Book14

Ⅰ Spline Models21

2 Nonparametric Spline Models23

2.1 Definition23

2.2 Optimization26

2.2.1 Bending Spline26

2.2.2 Spline Under Tension28

2.2.3 Robustness31

2.3 Bayesian Interpretation34

2.4 Choice of Regularization Parameter36

2.5 Approximation Using a Surface39

2.5.1 L-Spline Surface40

2.5.2 Quadratic Energy43

2.5.3 Finite Element Optimization46

3 Parametric Spline Models51

3.1 Representation on a Basis of B-Splines51

3.1.1 Approximation Spline53

3.1.2 Construction of B-Splines54

3.2 Extensions57

3.2.1 Multidimensional Case57

3.2.2 Heteroscedasticity62

3.3 High-Dimensional Splines67

3.3.1 Revealing Directions68

3.3.2 Projection Pursuit Regression70

4 Auto-Associative Models75

4.1 Analysis of Multidimensional Data75

4.1.1 A Classical Approach76

4.1.2 Toward an Alternative Approach80

4.2 Auto-Associative Composite Models82

4.2.1 Model and Algorithm82

4.2.2 Properties84

4.3 Projection Pursuit and Spline Smoothing86

4.3.1 Proiection Index87

4.3.2 Spline Smoothing90

4.4 Illustration93

Ⅱ Markov Models97

5 Fundamental Aspects99

5.1 Definitions99

5.1.1 Finite Markov Fields100

5.1.2 Gibbs Fields101

5.2 Markov-Gibbs Equivalence103

5.3 Examples106

5.3.1 Bending Energy106

5.3.2 Bernoulli Energy107

5.3.3 Gaussian Energy108

5.4 Consistency Problem109

6 Bayesian Estimation113

6.1 Principle113

6.2 Cost Functions118

6.2.1 Cost Function Examples119

6.2.2 Calculation Problems121

7 Simulation and Optimization123

7.1 Simulation124

7.1.1 Homogeneous Markov Chain124

7.1.2 Metropolis Dynamic125

7.1.3 Simulated Gibbs Distribution127

7.2 Stochastic Optimization130

7.3 Probabilistic Aspects134

7.4 Deterministic Optimization138

7.4.1 ICM Algorithm138

7.4.2 Relaxation Algorithms141

8 Parameter Estimation147

8.1 Complete Data148

8.1.1 Maximum Likelihood149

8.1.2 Maximum Pseudolikelihood150

8.1.3 Logistic Estimation153

8.2 Incomplete Data156

8.2.1 Maximum Likelihood157

8.2.2 Gibbsian EM Algorithm161

8.2.3 Bayesian Calibration170

Ⅲ Modeling in Action175

9 Model-Building177

9.1 Multiple Spline Approximation177

9.1.1 Choice of Data and Image Characteristics179

9.1.2 Definition of the Hidden Field181

9.1.3 Building an Energy183

9.2 Markov Modeling Methodology185

9.2.1 Details for Implementation185

10 Degradation in Imaging189

10.1 Denoising190

10.1.1 Models with Explicit Discontinuities190

10.1.2 Models with Implicit Discontinuities198

10.2 Deblurring201

10.2.1 A Particularly Ill-Posed Problem202

10.2.2 Model with Implicit Discontinuities204

10.3 Scatter205

10.3.1 Direct Problem206

10.3.2 Inverse Problem211

10.4 Sensitivity Functions and Image Fusion216

10.4.1 A Restoration Problem217

10.4.2 Transfer Function Estimation221

10.4.3 Estimation of Stained Transfer Function224

11 Detection of Filamentary Entities227

11.1 Valley Detection Principle228

11.1.1 Definitions228

11.1.2 Bayes-Markov Formulation230

11.2 Building the Prior Energy231

11.2.1 Detection Term231

11.2.2 Regularization Term234

11.3 Optimization236

11.4 Extension to the Case of an Image Pair239

12 Reconstruction and Projections243

12.1 Projection Model243

12.1.1 Transmission Tomography243

12.1.2 Emission Tomography246

12.2 Regularized Reconstruction247

12.2.1 Regularization with Explicit Discontinuities248

12.2.2 Three-Dimensional Reconstruction252

12.3 Reconstruction with a Single View256

12.3.1 Generalized Cylinder256

12.3.2 Training the Deformations259

12.3.3 Reconstruction in the Presence of Occlusion261

13 Matching269

13.1 Template and Hidden Outline270

13.1.1 Rigid Transformations270

13.1.2 Spline Model of a Template272

13.2 Elastic Deformations276

13.2.1 Continuous Random Fields276

13.2.2 Probabilistic Aspects282

References289

Author Index301

Subject Index305