Pattern Theory: From representation to inference

Paperback | December 14, 2006

byUlf Grenander, Michael I. Miller

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Pattern Theory: From Representation to Inference provides a comprehensive and accessible overview of the modern challenges in signal, data and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedicalengineering, mathematics, computer science and electrical engineering with a good background in mathematics and probability, the text includes numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on acompanion website. 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 conditioning structure and Chapters 7 and 8 examine the second central component of pattern theory: groups of geometrictransformation 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, and Chapters 10, 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, and finally Chapters 17 and 18 look atinference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.

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Pattern Theory: From Representation to Inference provides a comprehensive and accessible overview of the modern challenges in signal, data and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedicalengineering, mathematics, computer science and elec...

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...

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Format:PaperbackDimensions:608 pages, 9.69 × 7.44 × 1.02 inPublished:December 14, 2006Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199297061

ISBN - 13:9780199297061

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Table of Contents

1. Introduction2. The Bayes paradigm, estimation and information measures3. Probabilistic directed acyclic graphs and their entropies4. Markov random fields on undirected graphs5. Gaussian random fields on undirected graphs6. The canonical representations of general pattern theory7. Matrix group actions transforming patterns8. Manifolds, active modes, and deformable templates9. Second order and Gaussian fields10. Metrics spaces for the matrix groups11. Metrics spaces for the infinite dimensional diffeomorphisms12. Metrics on photometric and geometric deformable templates13. Estimation bounds for automated object recognition14. Estimation on metric spaces with photometric variation15. Information bounds for automated object recognition16. Computational anatomy: shape, growth and atrophy comparison via diffeomorphisms17. Computational anatomy: hypothesis testing on disease18. Markov processes and random sampling19. Jump diffusion inference in complex scenes