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A Generative Theory of Shape

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2145)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Pages 1-34
  3. Pages 35-76
  4. Pages 135-159
  5. Pages 161-173
  6. Pages 185-212
  7. Pages 213-227
  8. Pages 229-238
  9. Pages 239-255
  10. Pages 257-270
  11. Pages 271-298
  12. Pages 397-422
  13. Pages 455-466
  14. Pages 477-493
  15. Back Matter
    Pages 531-554

About this book

Introduction

The purpose of this book is to develop a generative theory of shape that has two properties we regard as fundamental to intelligence –(1) maximization of transfer: whenever possible, new structure should be described as the transfer of existing structure; and (2) maximization of recoverability: the generative operations in the theory must allow maximal inferentiability from data sets. We shall show that, if generativity satis?es these two basic criteria of - telligence, then it has a powerful mathematical structure and considerable applicability to the computational disciplines. The requirement of intelligence is particularly important in the gene- tion of complex shape. There are plenty of theories of shape that make the generation of complex shape unintelligible. However, our theory takes the opposite direction: we are concerned with the conversion of complexity into understandability. In this, we will develop a mathematical theory of und- standability. The issue of understandability comes down to the two basic principles of intelligence - maximization of transfer and maximization of recoverability. We shall show how to formulate these conditions group-theoretically. (1) Ma- mization of transfer will be formulated in terms of wreath products. Wreath products are groups in which there is an upper subgroup (which we will call a control group) that transfers a lower subgroup (which we will call a ?ber group) onto copies of itself. (2) maximization of recoverability is insured when the control group is symmetry-breaking with respect to the ?ber group.

Keywords

Complex Shape Computer Vision Editing Erlanger Program Geometric Invariants Geometric Objects Geometric Shape Geometric Structure Group Theory Robot Navigation complexity kinematics machine vision robot robotics

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-45488-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2001
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-42717-9
  • Online ISBN 978-3-540-45488-5
  • Series Print ISSN 0302-9743
  • Buy this book on publisher's site