Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
A complete and very informative review of mathematical advances in image analysis in the past twenty years. Covers a wide range of techniques in a very affordable style. --Jean Michel Morel, CMLA ENS Cachan, France...This book fills a niche that is quite blank at the present time: a fairly comprehensive overview of the entire area of mathematically-oriented image analysis... --Kevin R. Vixie, Los Alamos National LaboratoryImaging knows many different approaches, often leading to different heuristics when solving processing problems. The strong point of this book is that it integrates the different aspects and solution methods in a modern mathematical framework. After a broad introduction sketching the imaging problems and giving guidelines for potential readers (students, mathematicians, image processing researchers, generally interested readers), the necessary mathematical tools are introduced. The latter is a crisp and insightful survey of geometry, function spaces, thermodynamics, Bayesian statistics, differential equations, wavelets, etc. Then one chapter is devoted to image modeling and representation and the remaining four chapters treat applications: denoising, deblurring, inpainting, and segmentation. Each time the different origins and models for noise, blur, etc., are discussed and solution methods are proposed based on techniques such as those mentioned in the book s subtitle. The book makes an excellent read to get acquainted with modern mathematical methods to solve these low-level vision problems. Reviewed by A. Bultheel Copyright American Mathematical Society 2007 --American Mathematical Society MathSciNet