000 04258nam a22006255i 4500
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
024 7 _a10.1007/3-540-45488-8
_2doi
050 4 _aTA1634
072 7 _aUYQV
_2bicssc
072 7 _aCOM016000
_2bisacsh
072 7 _aUYQV
_2thema
082 0 4 _a006.37
_223
100 1 _aLeyton, Michael.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
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.
300 _aXV, 549 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Computer Science,
_x1611-3349 ;
_v2145
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