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Image analysis, random fields and dynamic Monte Carlo methods: a mathematical introduction. (English) Zbl 0821.68125
Applications of Mathematics. 27. Berlin: Springer-Verlag. xiv, 324 p. (1995).
This book is devoted to the study of the Bayesian paradigm approach to image analysis. The book is divided in five main Parts followed by a supplement and some appendices: I- The Bayesian Paradigm, II- The Gibbs Sampler and simulated Annealing, III- More on sampling and Annealing, IV- Texture Analysis, V- Parameter Estimation, VI- Supplement, VII- Appendix.
Part I provides an introduction on Bayesian methods based on image cleaning examples. Part II shows how the necessary optimization procedures can be written using simulated annealing. The popular Metropolis algorithm and some alternative approaches are postponed to part III and it is the Gibbs sampler description (clear and simple) that is used as first entry point to annealing methods. Parts IV present one of the main application which is texture segmentation and classification. Part V treats of the difficult problem of determining the models to be used and peculiarly the choice of the energy functions, focusing on methods related to maximum likelihood estimations. The supplement part presents mixed applications including neural networks. Finally the appendix proposes mathematical proofs of some used theorems and insights to the way of generating random variables. In summary this book is rigorous and pleasant introduction to statistical methods in imaging.

68U10 Computing methodologies for image processing
68U20 Simulation (MSC2010)
65C05 Monte Carlo methods
93Exx Stochastic systems and control
65K10 Numerical optimization and variational techniques
65Y05 Parallel numerical computation
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
62M40 Random fields; image analysis