General Pattern Theory: A Mathematical Study of Regular Structures

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Ulf Grenander (Emeritus Professor, Division of Applied Mathematics, Emeritus Professor, Division of Applied Mathematics, Brown University, Rhode Island)

General Pattern Theory

A Mathematical Study of Regular Structures

Ulf Grenander (Emeritus Professor, Division of Applied Mathematics, Emeritus Professor, Division of Applied Mathematics, Brown University, Rhode Island)

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English

Clarendon Press
20 January 1994

Probability & statistics; Applied mathematics; Neural networks & fuzzy systems; Computer vision

Series: Oxford Mathematical Monographs

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.

By: Ulf Grenander (Emeritus Professor Division of Applied Mathematics Emeritus Professor Division of Applied Mathematics Brown University Rhode Island)
Imprint: Clarendon Press
Country of Publication: United Kingdom
Dimensions: Height: 249mm, Width: 196mm, Spine: 50mm
Weight: 2g
ISBN: 9780198536710
ISBN 10: 0198536712
Series: Oxford Mathematical Monographs
Pages: 906
Publication Date: 20 January 1994
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
Publisher's Status: Active

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

Reviews for General Pattern Theory: A Mathematical Study of Regular Structures

`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