Inverse Problems in Vision and 3D Tomography

Preface 13

Chapter 1. Introduction to Inverse Problems in Imaging and Vision 15
Ali MOHAMMAD-DJAFARI

1.1. Inverse problems 16

1.2. Specific vision problems 21

1.3. Models for time-dependent quantities 26

1.4. Inverse problems with multiple inputs and multiple outputs (MIMO) 27

1.5. Non-linear inverse problems 30

1.6. 3D reconstructions 33

1.7. Inverse problems with multimodal observations 33

1.8. Classification of inversion methods: analytical or algebraic 34

1.9. Standard deterministic methods 40

1.10. Probabilistic methods 44

1.11. Problems specific to vision 50

1.12. Introduction to the various chapters of the book 52

1.13. Bibliography 55

Chapter 2. Noise Removal and Contour Detection 59
Pierre CHARBONNIER and Christophe COLLET

2.1. Introduction 61

2.2. Statistical segmentation of noisy images 72

2.3. Multi-band multi-scale Markovian regularization 79

2.4. Bibliography 88

Chapter 3. Blind Image Deconvolution 97
Laure BLANC-FÉRAUD, Laurent MUGNIER and André JALOBEANU

3.1. Introduction 97

3.2. The blind deconvolution problem 98

3.3. Joint estimation of the PSF and the object 103

3.4. Marginalized estimation of the impulse response 107

3.5. Various other approaches 112

3.6. Multi-image methods and phase diversity 114

3.7. Conclusion 115

3.8. Bibliography 116

Chapter 4. Triplet Markov Chains and Image Segmentation 123
Wojciech PIECZYNSKI

4.1. Introduction 124

4.2. Pairwise Markov chains (PMCs) 127

4.3. Copulas in PMCs 130

4.4. Parameter estimation 132

4.5. Triplet Markov chains (TMCs) 136

4.6. TMCs and non-stationarity 139

4.7. Hidden Semi-Markov chains (HSMCs) and TMCs 140

4.8. Auxiliary multivariate chains 144

4.9. Conclusions and outlook 148

4.10. Bibliography 149

Chapter 5. Detection and Recognition of a Collection of Objects in a Scene 155
Xavier DESCOMBES, Ian JERMYN and Josiane ZERUBIA

5.1. Introduction 155

5.2. Stochastic approaches 156

5.3. Variational approaches 167

5.4. Bibliography 184

Chapter 6. Apparent Motion Estimation and Visual Tracking 191
Etienne MÉMIN and Patrick PÉREZ

6.1. Introduction: from motion estimation to visual tracking 191

6.2. Instantaneous estimation of apparent motion 193

6.3. Visual tracking 219

6.4. Conclusions 240

6.5. Bibliography 241

Chapter 7. Super-resolution 251
Ali MOHAMMAD-DJAFARI and Fabrice HUMBLOT

7.1. Introduction 251

7.2. Modeling the direct problem 252

7.3. Classical SR methods 257

7.4. SR inversion methods 261

7.5. Methods based on a Bayesian approach 265

7.6. Simulation results 271

7.7. Conclusion 272

7.8. Bibliography 274

Chapter 8. Surface Reconstruction from Tomography Data 277
Charles SOUSSEN and Ali MOHAMMAD-DJAFARI

8.1. Introduction 277

8.2. Reconstruction of localized objects 280

8.3. Use of deformable contours for 3D reconstruction 284

8.4. Appropriate surface models and algorithmic considerations 293

8.5. Reconstruction of a polyhedric active contour 298

8.6. Conclusion 303

8.7. Bibliography 305

Chapter 9. Gauss-Markov-Potts Prior for Bayesian Inversion in Microwave Imaging 309
Olivier FÉRON, Bernard DUCHÊNE and Ali MOHAMMAD-DJAFARI

9.1. Introduction 310

9.2. Experimental configuration and modeling of the direct problem 311

9.3. Inversion in the linear case 315

9.4. Inversion in the non-linear case 325

9.5. Conclusion 335

9.6. Bibliography 336

Chapter 10. Shape from Shading 339
Jean-Denis DUROU

10.1. Introduction 339

10.2. Modeling of shape from shading 340

10.3. Resolution of shape from shading 353

10.4. Conclusion 371

10.5. Bibliography 372

Chapter 11. Image Separation 377
Hichem SNOUSSI and Ali MOHAMMAD-DJAFARI

11.1. General introduction 377

11.2. Blind image separation 378

11.3. Bayesian formulation 384

11.4. Stochastic algorithms 390

11.5. Simulation results 398

11.6. Conclusion 401

11.7. Appendix 1: a posteriori distributions 407

11.8. Bibliography 409

Chapter 12. Stereo Reconstruction in Satellite and Aerial Imaging 411
Julie DELON and Andrés ALMANSA

12.1. Introduction 411

12.2. Principles of satellite stereovision 412

12.3. Matching 415

12.4. Regularization 421

12.5. Numerical considerations 425

12.6. Conclusion 432

12.7. Bibliography 434

Chapter 13. Fusion and Multi-modality 437
Christophe COLLET, Farid FLITTI, Stéphanie BRICQ and André JALOBEANU

13.1. Fusion of optical multi-detector images without loss of information 437

13.2. Fusion of multi-spectral images using hidden Markov trees 438

13.3. Segmentation of multimodal cerebral MRI using an a priori probabilistic map 448

13.4. Bibliography 458

List of Authors 461

Index 463