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|a 9783540454885
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|a 10.1007/3-540-45488-8
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|a Leyton, Michael.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a A Generative Theory of Shape
|h [electronic resource] /
|c by Michael Leyton.
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|a 1st ed. 2001.
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg :
|b Imprint: Springer,
|c 2001.
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|a XV, 549 p.
|b online resource.
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|a text
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|a Lecture Notes in Computer Science,
|x 0302-9743 ;
|v 2145
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|a 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.
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|a 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.
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|a Geometry.
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|a Computer graphics.
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|a Group theory.
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|a Computer-aided engineering.
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|a Image Processing and Computer Vision.
|0 http://scigraph.springernature.com/things/product-market-codes/I22021
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|a Geometry.
|0 http://scigraph.springernature.com/things/product-market-codes/M21006
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|a Computer Applications.
|0 http://scigraph.springernature.com/things/product-market-codes/I23001
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|a Computer Graphics.
|0 http://scigraph.springernature.com/things/product-market-codes/I22013
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|a Group Theory and Generalizations.
|0 http://scigraph.springernature.com/things/product-market-codes/M11078
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|a Computer-Aided Engineering (CAD, CAE) and Design.
|0 http://scigraph.springernature.com/things/product-market-codes/I23044
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783662207628
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|i Printed edition:
|z 9783540427179
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|a Lecture Notes in Computer Science,
|x 0302-9743 ;
|v 2145
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|u https://doi.org/10.1007/3-540-45488-8
|z Full Text via HEAL-Link
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|a ZDB-2-LNC
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|a Computer Science (Springer-11645)
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