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Author: Ulf Grenander
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 936
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Book Description
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. Starting from an algebraic formulation of such representations they are studied in terms of their topological, dynamical and probabilistic aspects. Patterns are expressed through their typical behaviour as well as through their variability around their typical form. Employing the representations (regular structures) algorithms are derived for the understanding, recognition, and restoration of observed patterns. The algorithms are investigated through computer experiments.
Author: Ulf Grenander
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 936
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Book Description
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. Starting from an algebraic formulation of such representations they are studied in terms of their topological, dynamical and probabilistic aspects. Patterns are expressed through their typical behaviour as well as through their variability around their typical form. Employing the representations (regular structures) algorithms are derived for the understanding, recognition, and restoration of observed patterns. The algorithms are investigated through computer experiments.
Author: The Council for Museums, Archives & Libraries
Publisher:
ISBN: 9780412388101
Category :
Languages : en
Pages :
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Book Description
Author: Ulf Grenander
Publisher: Oxford University Press
ISBN: 0198505701
Category : Computers
Languages : en
Pages : 633
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Book Description
Pattern Theory 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 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.
Author: Ulf Grenander
Publisher: World Scientific
ISBN: 9814383198
Category : Computers
Languages : en
Pages : 236
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Book Description
This monograph 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. The method illustrated and produced by extensive computer simulations is related to neural networks. Based mainly on introspection, it is speculative rather than empirical such that it differs radically in attitude from the conventional wisdom of current cognitive science.
Author: Ulf Grenander
Publisher:
ISBN: 9783540901747
Category : Pattern perception
Languages : en
Pages : 509
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Book Description
Author: Ulf Grenander
Publisher: JHU Press
ISBN: 9780801851889
Category : Mathematics
Languages : en
Pages : 258
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Book Description
"A dazzling tour de force on patterns. It is a substantial, original contribution by a leader-indeed, originator-in the field, and has the potential for significant impact on the direction of future research." -- Alan F. Karr, National Institute of Statistical Sciences
Author: Ulf Grenander
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 256
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Book Description
"A dazzling tour de force on patterns. It is a substantial, original contribution by a leader-indeed, originator-in the field, and has the potential for significant impact on the direction of future research." -- Alan F. Karr, National Institute of Statistical Sciences
Author: U. Grenander
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 530
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Book Description
This book consists of updated and considerably expanded lecture notes. I am grateful to F. John, J. P. LaSalle, L. Sirovich and G. Whitham for accepting this preliminary manu script for the series Applied Mathematical Sciences published by Springer-Verlag. Many colleagues and students have helped with their comments and suggestions. Among them are D. E. McClure, I. Frolow, J. Silverstein, R. A. Vitale, and I would like to thank especially W. Freiberger for all his encouragement and help in many different ways. The work has been supported by the Division of Mathematica and Computer Sciences of the National Science Foundation, and I appreciate the positive interest shown by John Pasta, Kent curtis, Bruce Barnes and other program directors, over the years. I am indebted to E. Fonseca for her untiring and careful preparation of the manuscript, to E. Addison for her skillful help with the many diagrams, and to K. H. Avery, D. P. Libutti, K. MacDougall and S. V. Spinacci for the final typing. I gratefully acknowledge permission to reproduce figures, as mentioned in the text, to: American Elsevier Publishing Company, Inc., A. J. Larkin, and M. Gardner. I dedicate this work to my wife, Emma-Stina. June, 1975 Ulf Grenander, Providence TABLE OF CONTENTS INTRODUCTION 1 CHAPTER 1. THE GENERATORS 6 l. Generators and Their Properties 6 2. Abstract Generators 10 3. Concrete Generators 13 4.
Author: Ulf Grenander
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 552
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Book Description
Some probability theory on abstract spaces; Inference in abstract sample space; Inference in abstract parameter space.
Author: Ulf Grenander
Publisher:
ISBN:
Category : Pattern perception
Languages : en
Pages : 222
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Book Description
