000 | 04258nam a22006255i 4500 | ||
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001 | 978-3-540-45488-5 | ||
003 | DE-He213 | ||
005 | 20240423132601.0 | ||
007 | cr nn 008mamaa | ||
008 | 121227s2001 gw | s |||| 0|eng d | ||
020 |
_a9783540454885 _9978-3-540-45488-5 |
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024 | 7 |
_a10.1007/3-540-45488-8 _2doi |
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050 | 4 | _aTA1634 | |
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_aUYQV _2bicssc |
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_aCOM016000 _2bisacsh |
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_aUYQV _2thema |
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082 | 0 | 4 |
_a006.37 _223 |
100 | 1 |
_aLeyton, Michael. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 2 |
_aA Generative Theory of Shape _h[electronic resource] / _cby Michael Leyton. |
250 | _a1st ed. 2001. | ||
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2001. |
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300 |
_aXV, 549 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Computer Science, _x1611-3349 ; _v2145 |
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505 | 0 | _aTransfer -- 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. | |
520 | _aThe 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. | ||
650 | 0 | _aComputer vision. | |
650 | 0 | _aGeometry. | |
650 | 0 | _aApplication software. | |
650 | 0 | _aComputer graphics. | |
650 | 0 | _aGroup theory. | |
650 | 0 | _aComputer-aided engineering. | |
650 | 1 | 4 | _aComputer Vision. |
650 | 2 | 4 | _aGeometry. |
650 | 2 | 4 | _aComputer and Information Systems Applications. |
650 | 2 | 4 | _aComputer Graphics. |
650 | 2 | 4 | _aGroup Theory and Generalizations. |
650 | 2 | 4 | _aComputer-Aided Engineering (CAD, CAE) and Design. |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer Nature eBook | |
776 | 0 | 8 |
_iPrinted edition: _z9783540427179 |
776 | 0 | 8 |
_iPrinted edition: _z9783662207628 |
830 | 0 |
_aLecture Notes in Computer Science, _x1611-3349 ; _v2145 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/3-540-45488-8 |
912 | _aZDB-2-SCS | ||
912 | _aZDB-2-SXCS | ||
912 | _aZDB-2-LNC | ||
912 | _aZDB-2-BAE | ||
942 | _cSPRINGER | ||
999 |
_c189388 _d189388 |