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Record Nr. |
UNISA996466018303316 |
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Autore |
Leyton Michael |
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Titolo |
A Generative Theory of Shape [[electronic resource] /] / by Michael Leyton |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2001 |
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ISBN |
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Edizione |
[1st ed. 2001.] |
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Descrizione fisica |
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1 online resource (XV, 549 p.) |
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Collana |
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Lecture Notes in Computer Science, , 0302-9743 ; ; 2145 |
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Disciplina |
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Soggetti |
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Optical data processing |
Geometry |
Application software |
Computer graphics |
Group theory |
Computer-aided engineering |
Image Processing and Computer Vision |
Computer Applications |
Computer Graphics |
Group Theory and Generalizations |
Computer-Aided Engineering (CAD, CAE) and Design |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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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Sommario/riassunto |
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The purpose of this book is to develop a generative theory of shape that has two properties we regard as fundamental to intelligence –(1) |
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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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