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Informationen zum Autor 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. Klappentext 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 through the forward problem. This book focuses on imagery and vision problems that can be clearly written in terms of an inverse problem where an estimate for the image and its geometrical attributes (contours and regions) is sought.The chapters of this book use 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 more. Zusammenfassung 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. Inhaltsverzeichnis 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 ...
