Image Analysis, Random Fields and Markov Chain Monte Carlo Methods

A Mathematical Introduction
2. Auflage 2003
ISBN: 978-3-540-44213-4
Verlag: Springer

Buch, Englisch, Band 27, 387 Seiten, Book w. online files / update, Format (B × H): 155 mm x 235 mm, Gewicht: 807 g

Reihe: Stochastic Modelling and Applied Probability

This second edition of G. Winkler's successful book on random field approaches to image analysis, related Markov Chain Monte Carlo methods, and statistical inference with emphasis on Bayesian image analysis concentrates more on general principles and models and less on details of concrete applications. Addressed to students and scientists from mathematics, statistics, physics, engineering, and computer science, it will serve as an introduction to the mathematical aspects rather than a survey. Basically no prior knowledge of mathematics or statistics is required.
The second edition is in many parts completely rewritten and improved, and most figures are new. The topics of exact sampling and global optimization of likelihood functions have been added.

Zielgruppe

Research

Autoren/Hrsg.

Winkler, Gerhard

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning
• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizinische Fachgebiete Bildgebende Verfahren, Nuklearmedizin, Strahlentherapie Radiologie, Bildgebende Verfahren
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Mathematik | Informatik EDV | Informatik Informatik Bildsignalverarbeitung
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Grafikprogrammierung

Inhaltsverzeichnis

I. Bayesian Image Analysis: Introduction.- 1. The Bayesian Paradigm.- 2. Cleaning Dirty Pictures.- 3. Finite Random Fields.- II. The Gibbs Sampler and Simulated Annealing.- 4. Markov Chains: Limit Theorems.- 5. Gibbsian Sampling and Annealing.- 6. Cooling Schedules.- III. Variations of the Gibbs Sampler.- 7. Gibbsian Sampling and Annealing Revisited.- 8. Partially Parallel Algorithms.- 9. Synchronous Algorithms.- IV. Metropolis Algorithms and Spectral Methods.- 10. Metropolis Algorithms.- 11. The Spectral Gap and Convergence of Markov Chains.- 12. Eigenvalues, Sampling, Variance Reduction.- 13. Continuous Time Processes.- V. Texture Analysis.- 14. Partitioning.- 15. Random Fields and Texture Models.- 16. Bayesian Texture Classification.- VI. Parameter Estimation.- 17. Maximum Likelihood Estimation.- 18. Consistency of Spatial ML Estimators.- 19. Computation of Full ML Estimators.- VII. Supplement.- 20. A Glance at Neural Networks.- 21. Three Applications.- VIII. Appendix.- A. Simulation of Random Variables.- A.1 Pseudorandom Numbers.- A.2 Discrete Random Variables.- A.3 Special Distributions.- B. Analytical Tools.- B.1 Concave Functions.- B.2 Convergence of Descent Algorithms.- B.3 A Discrete Gronwall Lemma.- B.4 A Gradient System.- C. Physical Imaging Systems.- D. The Software Package AntslnFields.- References.- Symbols.