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A Generative Theory of Shape

  • Book
  • © 2001

Overview

Authors:
  1. Michael Leyton

    1. Center for Cognitive Science, Rutgers University Psychology Department, New Brunswick, USA

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

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Table of contents (22 chapters)

  1. Front Matter

    Pages I-XVI
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  2. Transfer

    Pages 1-34

  3. Recoverability

    Pages 35-76

  4. Mathematical Theory of Transfer, I

    Pages 77-114

  5. Mathematical Theory of Transfer, II

    Pages 115-134

  6. Theory of Grouping

    Pages 135-159

  7. Robot Manipulators

    Pages 161-173

  8. Algebraic Theory of Inheritance

    Pages 175-183

  9. Reference Frames

    Pages 185-212

  10. Relative Motion

    Pages 213-227

  11. Surface Primitives

    Pages 229-238

  12. Unfolding Groups, I

    Pages 239-255

  13. Unfolding Groups, II

    Pages 257-270

  14. Unfolding Groups, III

    Pages 271-298

  15. Mechanical Design and Manufacturing

    Pages 299-363

  16. A Mathematical Theory of Architecture

    Pages 365-395

  17. Solid Structure

    Pages 397-422

  18. Wreath Formulation of Splines

    Pages 423-441

  19. Wreath Formulation of Sweep Representations

    Pages 443-454

  20. Process Grammar

    Pages 455-466
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Keywords

About this book

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.

Authors and Affiliations

  • Center for Cognitive Science, Rutgers University Psychology Department, New Brunswick, USA

    Michael Leyton

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