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General Pattern Theory : A Mathematical Study of Regular Structures - Ulf Grenander

General Pattern Theory

A Mathematical Study of Regular Structures


Published: 20th January 1994
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The aim of pattern theory is to create mathematical knowledge representations of complex systems, analyze the mathematical properties of the resulting regular structures, and to apply them to practically occurring 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 behavior 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. The book is intended for statisticians and mathematicians with an interest in image analysis and pattern theory.

`this is an important book that should richly reward the persistent reader' B.D. Ripley, University of Oxford, JRSS, Sories A, Vol. 158, Part 3, 1995 `an imprssive new synthesis ... It clearly represents the bible of pattern theory, and from that perspective one cannot but recommend it.' D.J. Hand, The Open University, International Statistical Institute, Vol. 14, No. 3 - December 1994

Part I: Pattern Algebra 1: Generators and configurations 2: Images and patterns Part II: Pattern Topology 3: Some topologies on regular structures Part III: Pattern Dynamics 4: Abstract biological patterns 5: Patterns of collective behaviour 6: Patterns generated from extremum principles Part IV: Metric Pattern Theory 7: General principles of MPT 8: Pattern synthesis 9: First limit problem in MPT 10: Second limit problem in MPT 11: Mixed limit problem in MPT Part V: Pattern Deformations 12: Chapter 12: Deformation mechanisms Part VI: Pattern Inference 13: Ends and means in pattern analysis 14: Bayesian pattern inference 15: Lattice-based models 16: Continuum-based models 17: Non-Bayesian pattern inference 18: Pattern recognition Part VII: Creating Regular Structures 19: Creating generators 20: Creating acceptor functions and connectors

ISBN: 9780198536710
ISBN-10: 0198536712
Series: Oxford Mathematical Monographs
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 904
Published: 20th January 1994
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 24.9 x 19.6  x 5.0
Weight (kg): 2.14