The concept of an inverse problem is a familiar one to most scientists and engineers, particularly in the field of signal and image processing, imaging systems (medical, geophysical, industrial non-destructive testing, etc.), and computer vision. In imaging systems, the aim is not just to estimate unobserved images but also their geometric characteristics from observed quantities that are linked to these unobserved quantities by a known physical or mathematical relationship. In this manner techniques such as image enhancement or addition of hidden detail can be delivered. This book focuses on imaging and vision problems that can be clearly described in terms of an inverse problem where an estimate for the image and its geometrical attributes (contours and regions) is sought. The book uses a consistent methodology to examine inverse problems such as: noise removal; restoration by deconvolution; 2D or 3D reconstruction in X-ray, tomography or microwave imaging; reconstruction of the surface of a 3D object using X-ray tomography or making use of its shading; reconstruction of the surface of a 3D landscape based on several satellite photos; super-resolution; motion estimation in a sequence of images; separation of several images mixed using instruments with different sensitivities or transfer functions; and much more.

Table of Contents:
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