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

General Pattern Theory: A Mathematical Study of Regular Structures

byUlf Grenander

Hardcover | May 1, 1979

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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 therepresentations (regular structures) algorithms are derived for the understanding, recognition, and restoration of observed patterns. The algorithms are investigated through computer experiments.

About The Author

Ulf Grenander, Emeritus Professor, Division of Applied Mathematics, Brown University, Rhode Island.
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Details & Specs

Title:General Pattern Theory: A Mathematical Study of Regular StructuresFormat:HardcoverDimensions:904 pages, 9.65 × 9.65 × 0.03 inPublished:May 1, 1979Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198536712

ISBN - 13:9780198536710

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Table of Contents

Part I: Pattern Algebra1. Generators and configurations2. Images and patternsPart II: Pattern Topology3. Some topologies on regular structuresPart III: Pattern Dynamics4. Abstract biological patterns5. Patterns of collective behaviour6. Patterns generated from extremum principlesPart IV: Metric Pattern Theory7. General principles of MPT8. Pattern synthesis9. First limit problem in MPT10. Second limit problem in MPT11. Mixed limit problem in MPTPart V: Pattern Deformations12. Chapter 12: Deformation mechanismsPart VI: Pattern Inference13. Ends and means in pattern analysis14. Bayesian pattern inference15. Lattice-based models16. Continuum-based models17. Non-Bayesian pattern inference18. Pattern recognitionPart VII: Creating Regular Structures19. Creating generators20. Creating acceptor functions and connectors

Editorial Reviews

`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