Pattern Theory
Oxford University Press (Verlag)
978-0-19-850570-9 (ISBN)
The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via condition structure. Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn. Chapters 10 and 11 continue with transformations and patterns indexed over the continuum. Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy. Finally, Chapters 17 and 18 look at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.
Ulf Grenander is the L. Herbert Ballou University Professor at Brown University. He is a member of the Royal Swedish Academy of Science and an honorary fellow of the Royal Statistical Society in London Michael Miller is the Professor of Electrical and Computer Engineering, Director of the Center for Imaging Science, and Professor of Biomedical Engineering at Johns Hopkins University, Baltimore. He completed his Ph.D. in Biomedical Engineering at The Johns Hopkins University in 1983.
1. Introduction ; 2. The Bayes paradigm, estimation and information measures ; 3. Probabilistic directed acyclic graphs and their entropies ; 4. Markov random fields on undirected graphs ; 5. Gaussian random fields on undirected graphs ; 6. The canonical representations of general pattern theory ; 7. Matrix group actions transforming patterns ; 8. Manifolds, active modes, and deformable templates ; 9. Second order and Gaussian fields ; 10. Metrics spaces for the matrix groups ; 11. Metrics spaces for the infinite dimensional diffeomorphisms ; 12. Metrics on photometric and geometric deformable templates ; 13. Estimation bounds for automated object recognition ; 14. Estimation on metric spaces with photometric variation ; 15. Information bounds for automated object recognition ; 16. Computational anatomy: shape, growth and atrophy comparison via diffeomorphisms ; 17. Computational anatomy: hypothesis testing on disease ; 18. Markov processes and random sampling ; 19. Jump diffusion inference in complex scenes
| Erscheint lt. Verlag | 14.12.2006 |
|---|---|
| Zusatzinfo | numerous halftones, colour plates, line drawings and mathematical examples |
| Verlagsort | Oxford |
| Sprache | englisch |
| Maße | 195 x 251 mm |
| Gewicht | 1518 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Medizin / Pharmazie ► Physiotherapie / Ergotherapie ► Orthopädie | |
| Technik ► Medizintechnik | |
| ISBN-10 | 0-19-850570-1 / 0198505701 |
| ISBN-13 | 978-0-19-850570-9 / 9780198505709 |
| Zustand | Neuware |
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