Synopses & Reviews
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.
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