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AuthorWinkler, Gerhard. author
TitleImage Analysis, Random Fields and Dynamic Monte Carlo Methods [electronic resource] : A Mathematical Introduction / by Gerhard Winkler
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1995
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Descript XIV, 324 p. online resource


The book is mainly concerned with the mathematical foundations of Bayesian image analysis and its algorithms. This amounts to the study of Markov random fields and dynamic Monte Carlo algorithms like sampling, simulated annealing and stochastic gradient algorithms. The approach is introductory and elemenatry: given basic concepts from linear algebra and real analysis it is self-contained. No previous knowledge from image analysis is required. Knowledge of elementary probability theory and statistics is certainly beneficial but not absolutely necessary. The necessary background from imaging is sketched and illustrated by a number of concrete applications like restoration, texture segmentation and motion analysis


I. Bayesian Image Analysis: Introduction -- 1. The Bayesian Paradigm -- 2. Cleaning Dirty Pictures -- 3. Random Fields -- II. The Gibbs Sampler and Simulated Annealing -- 4. Markov Chains: Limit Theorems -- 5. Sampling and Annealing -- 6. Cooling Schedules -- 7. Sampling and Annealing Revisited -- III. More on Sampling and Annealing -- 8. Metropolis Algorithms -- 9. Alternative Approaches -- 10. Parallel Algorithms -- IV. Texture Analysis -- 11. Partitioning -- 12. Texture Models and Classification -- V. Parameter Estimation -- 13. Maximum Likelihood Estimators -- 14. Spacial ML Estimation -- VI. Supplement -- 15. A Glance at Neural Networks -- 16. Mixed Applications -- VII. Appendix -- A. Simulation of Random Variables -- B. The Perron-Frobenius Theorem -- C. Concave Functions -- D. A Global Convergence Theorem for Descent Algorithms -- References

Mathematics Radiology Software engineering Computer simulation Pattern recognition Probabilities Statistics Mathematics Probability Theory and Stochastic Processes Pattern Recognition Simulation and Modeling Imaging / Radiology Software Engineering/Programming and Operating Systems Statistics for Engineering Physics Computer Science Chemistry and Earth Sciences


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