Inverse Problems in Vision and 3D Tomography

Ali Mohammad-Djafari, BSc, MSc, PhD, works at the Centre National de la Recherche Scientifique (CNRS) and Laboratoire des Signaux et Systèmes (L2S). He is currently director of research and his main scientific interests are in developing new probabilistic methods based on Bayesian inference, information theory and maximum entropy approaches for inverse problems in general, and more specifically in imaging and vision.

"Apart from the high price I can recommend this book if you are interested in imaging or artificial vision." (I Programmer, 3 February 2011)

• Preface 13Chapter 1. Introduction to Inverse Problems in Imaging and Vision 15Ali MOHAMMAD-DJAFARI1.1. Inverse problems 161.2. Specific vision problems 211.3. Models for time-dependent quantities 261.4. Inverse problems with multiple inputs and multiple outputs (MIMO) 271.5. Non-linear inverse problems 301.6. 3D reconstructions 331.7. Inverse problems with multimodal observations 331.8. Classification of inversion methods: analytical or algebraic 341.9. Standard deterministic methods 401.10. Probabilistic methods 441.11. Problems specific to vision 501.12. Introduction to the various chapters of the book 521.13. Bibliography 55Chapter 2. Noise Removal and Contour Detection 59Pierre CHARBONNIER and Christophe COLLET2.1. Introduction 612.2. Statistical segmentation of noisy images 722.3. Multi-band multi-scale Markovian regularization 792.4. Bibliography 88Chapter 3. Blind Image Deconvolution 97Laure BLANC-FÉRAUD, Laurent MUGNIER and André JALOBEANU3.1. Introduction 973.2. The blind deconvolution problem 983.3. Joint estimation of the PSF and the object 1033.4. Marginalized estimation of the impulse response 1073.5. Various other approaches 1123.6. Multi-image methods and phase diversity 1143.7. Conclusion 1153.8. Bibliography 116Chapter 4. Triplet Markov Chains and Image Segmentation 123Wojciech PIECZYNSKI4.1. Introduction 1244.2. Pairwise Markov chains (PMCs) 1274.3. Copulas in PMCs 1304.4. Parameter estimation 1324.5. Triplet Markov chains (TMCs) 1364.6. TMCs and non-stationarity 1394.7. Hidden Semi-Markov chains (HSMCs) and TMCs 1404.8. Auxiliary multivariate chains 1444.9. Conclusions and outlook 1484.10. Bibliography 149Chapter 5. Detection and Recognition of a Collection of Objects in a Scene 155Xavier DESCOMBES, Ian JERMYN and Josiane ZERUBIA5.1. Introduction 1555.2. Stochastic approaches 1565.3. Variational approaches 1675.4. Bibliography 184Chapter 6. Apparent Motion Estimation and Visual Tracking 191Etienne MÉMIN and Patrick PÉREZ6.1. Introduction: from motion estimation to visual tracking 1916.2. Instantaneous estimation of apparent motion 1936.3. Visual tracking 2196.4. Conclusions 2406.5. Bibliography 241Chapter 7. Super-resolution 251Ali MOHAMMAD-DJAFARI and Fabrice HUMBLOT7.1. Introduction 2517.2. Modeling the direct problem 2527.3. Classical SR methods 2577.4. SR inversion methods 2617.5. Methods based on a Bayesian approach 2657.6. Simulation results 2717.7. Conclusion 2727.8. Bibliography 274Chapter 8. Surface Reconstruction from Tomography Data 277Charles SOUSSEN and Ali MOHAMMAD-DJAFARI8.1. Introduction 2778.2. Reconstruction of localized objects 2808.3. Use of deformable contours for 3D reconstruction 2848.4. Appropriate surface models and algorithmic considerations 2938.5. Reconstruction of a polyhedric active contour 2988.6. Conclusion 3038.7. Bibliography 305Chapter 9. Gauss-Markov-Potts Prior for Bayesian Inversion in Microwave Imaging 309Olivier FÉRON, Bernard DUCHÊNE and Ali MOHAMMAD-DJAFARI9.1. Introduction 3109.2. Experimental configuration and modeling of the direct problem 3119.3. Inversion in the linear case 3159.4. Inversion in the non-linear case 3259.5. Conclusion 3359.6. Bibliography 336Chapter 10. Shape from Shading 339Jean-Denis DUROU10.1. Introduction 33910.2. Modeling of shape from shading 34010.3. Resolution of shape from shading 35310.4. Conclusion 37110.5. Bibliography 372Chapter 11. Image Separation 377Hichem SNOUSSI and Ali MOHAMMAD-DJAFARI11.1. General introduction 37711.2. Blind image separation 37811.3. Bayesian formulation 38411.4. Stochastic algorithms 39011.5. Simulation results 39811.6. Conclusion 40111.7. Appendix 1: a posteriori distributions 40711.8. Bibliography 409Chapter 12. Stereo Reconstruction in Satellite and Aerial Imaging 411Julie DELON and Andrés ALMANSA12.1. Introduction 41112.2. Principles of satellite stereovision 41212.3. Matching 41512.4. Regularization 42112.5. Numerical considerations 42512.6. Conclusion 43212.7. Bibliography 434Chapter 13. Fusion and Multi-modality 437Christophe COLLET, Farid FLITTI, Stéphanie BRICQ and André JALOBEANU13.1. Fusion of optical multi-detector images without loss of information 43713.2. Fusion of multi-spectral images using hidden Markov trees 43813.3. Segmentation of multimodal cerebral MRI using an a priori probabilistic map 44813.4. Bibliography 458List of Authors 461Index 463