rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    non sort: A
    title: Generative Theory of Shape
  name:
    name part: Leyton, Michael.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2001
    edition: 1st ed. 2001.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XV, 549 p. online resource.
  abstract: 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.
  table of contents: Transfer -- Recoverability -- Mathematical Theory of Transfer, I -- Mathematical Theory of Transfer, II -- Theory of Grouping -- Robot Manipulators -- Algebraic Theory of Inheritance -- Reference Frames -- Relative Motion -- Surface Primitives -- Unfolding Groups, I -- Unfolding Groups, II -- Unfolding Groups, III -- Mechanical Design and Manufacturing -- A Mathematical Theory of Architecture -- Solid Structure -- Wreath Formulation of Splines -- Wreath Formulation of Sweep Representations -- Process Grammar -- Conservation Laws of Physics -- Music -- Against the Erlanger Program.
  note: by Michael Leyton.
  subject:
    topic: Optical data processing
  subject:
    topic: Geometry
  subject:
    topic: Application software
  subject:
    topic: Computer graphics
  subject:
    topic: Group theory
  subject:
    topic: Computer-aided engineering
  subject:
    topic: Image Processing and Computer Vision
  subject:
    topic: Geometry
  subject:
    topic: Computer Applications
  subject:
    topic: Computer Graphics
  subject:
    topic: Group Theory and Generalizations
  subject:
    topic: Computer-Aided Engineering (CAD, CAE) and Design
  classification: TA1630-1650
  classification: 006.6
  classification: 006.37
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Computer Science, 2145
  identifier: 9783540454885
  identifier: https://doi.org/10.1007/3-540-45488-8
  record info:
    record creation date: 121227
    record change date: 20191026022214.0
    record identifier: 978-3-540-45488-5