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Image processing and analysis. Variational, PDE, wavelet, and stochastic methods. (English) Zbl 1095.68127
Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 0-89871-589-X/pbk; 978-0-89871-787-7/ebook). xxi, 400 p. (2005).
This book presents a large survey of recent mathematical approaches to image analysis: variational, pde, wavelet, and stochastic methods. It is written for graduate students and researchers in domains using image processing and computer vision. The presentation is clear and reachable with some mathematical background on functional analysis. The book is divided into seven chapters: An introduction presents basic problems using examples, and gives an overview of methodologies. The second chapter describes the fundamentals of the mathematical tools to be used in the followings chapters: differential geometry, bounded variation functions, Bayesian inference, filtering and wavelets, reconstruction, the prototype being the Radon transform. Chapter 3 treats image modeling. Chapter 4 treats image denoising. Chapter 5 treats image deblurring. Chapter 6 treats image inpainting. The last chapter treats image segmentation.

MSC:
68U10 Computing methodologies for image processing
68-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science
68-02 Research exposition (monographs, survey articles) pertaining to computer science
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