From Representation to Inference
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Pattern Theory by Ulf Grenander
Book DescriptionPattern 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 biomedical engineering, 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 a companion 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 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, 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 at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.
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Book DetailsISBN: 9780199297061
(244mm x 188mm x 26mm)
Imprint: Oxford University Press
Publisher: Oxford University Press
Publish Date: 14-Dec-2006
Country of Publication: United Kingdom
Books By Author Ulf Grenander
Calculus of Ideas: A Mathematical Study of Human Thought, Hardback (September 2012)
A monograph that reports a thought experiment with a mathematical structure intended to illustrate the workings of a mind. It presents a mathematical theory of human thought based on pattern theory with a graph-based approach to thinking.
Probabilities on Algebraic Structures, Paperback (April 2008)
This systematic approach covers semi-groups, groups, linear vector spaces, and algebra. It states and studies fundamental probabilistic problems for these spaces, focusing on concrete results. 1963 edition.
General Pattern Theory, Hardback (January 1994)» View all books by Ulf Grenander
The aim of pattern theory is to create mathematical knowledge representations of complex systems, analyse the mathematical properties of the resulting regular structures, and to apply them to practically occuring patterns in nature and the man-made world.
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Author Biography - Ulf Grenander
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.
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