Overview

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.

Full Product Details

Author:   Ulf Grenander (Emeritus Professor, Division of Applied Mathematics, Emeritus Professor, Division of Applied Mathematics, Brown University, Rhode Island)
Publisher:   Oxford University Press
Imprint:   Clarendon Press
Dimensions:   Width: 19.60cm , Height: 5.00cm , Length: 24.90cm
Weight:   1.706kg
ISBN:  

9780198536710

ISBN 10:   0198536712
Pages:   906
Publication Date:   20 January 1994
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
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Table of Contents

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

`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

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

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 * 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 *

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