LEADER 05166nam 22007935 450 001 996466018303316 005 20200706073615.0 010 $a3-540-45488-8 024 7 $a10.1007/3-540-45488-8 035 $a(CKB)1000000000016865 035 $a(SSID)ssj0000323450 035 $a(PQKBManifestationID)11243265 035 $a(PQKBTitleCode)TC0000323450 035 $a(PQKBWorkID)10299609 035 $a(PQKB)10305450 035 $a(DE-He213)978-3-540-45488-5 035 $a(MiAaPQ)EBC3073251 035 $a(PPN)155164236 035 $a(EXLCZ)991000000000016865 100 $a20121227d2001 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 12$aA Generative Theory of Shape$b[electronic resource] /$fby Michael Leyton 205 $a1st ed. 2001. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2001. 215 $a1 online resource (XV, 549 p.) 225 1 $aLecture Notes in Computer Science,$x0302-9743 ;$v2145 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-42717-1 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThe purpose of this book is to develop a generative theory of shape that has two properties we regard as fundamental to intelligence ?(1) maximization of transfer: whenever possible, new structure should be described as the transfer of existing structure; and (2) maximization of recoverability: the generative operations in the theory must allow maximal inferentiability from data sets. We shall show that, if generativity satis?es these two basic criteria of - telligence, then it has a powerful mathematical structure and considerable applicability to the computational disciplines. The requirement of intelligence is particularly important in the gene- tion of complex shape. There are plenty of theories of shape that make the generation of complex shape unintelligible. However, our theory takes the opposite direction: we are concerned with the conversion of complexity into understandability. In this, we will develop a mathematical theory of und- standability. The issue of understandability comes down to the two basic principles of intelligence - maximization of transfer and maximization of recoverability. We shall show how to formulate these conditions group-theoretically. (1) Ma- mization of transfer will be formulated in terms of wreath products. Wreath products are groups in which there is an upper subgroup (which we will call a control group) that transfers a lower subgroup (which we will call a ?ber group) onto copies of itself. (2) maximization of recoverability is insured when the control group is symmetry-breaking with respect to the ?ber group. 410 0$aLecture Notes in Computer Science,$x0302-9743 ;$v2145 606 $aOptical data processing 606 $aGeometry 606 $aApplication software 606 $aComputer graphics 606 $aGroup theory 606 $aComputer-aided engineering 606 $aImage Processing and Computer Vision$3https://scigraph.springernature.com/ontologies/product-market-codes/I22021 606 $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006 606 $aComputer Applications$3https://scigraph.springernature.com/ontologies/product-market-codes/I23001 606 $aComputer Graphics$3https://scigraph.springernature.com/ontologies/product-market-codes/I22013 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 606 $aComputer-Aided Engineering (CAD, CAE) and Design$3https://scigraph.springernature.com/ontologies/product-market-codes/I23044 615 0$aOptical data processing. 615 0$aGeometry. 615 0$aApplication software. 615 0$aComputer graphics. 615 0$aGroup theory. 615 0$aComputer-aided engineering. 615 14$aImage Processing and Computer Vision. 615 24$aGeometry. 615 24$aComputer Applications. 615 24$aComputer Graphics. 615 24$aGroup Theory and Generalizations. 615 24$aComputer-Aided Engineering (CAD, CAE) and Design. 676 $a516 700 $aLeyton$b Michael$4aut$4http://id.loc.gov/vocabulary/relators/aut$0553383 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466018303316 996 $aGenerative theory of shape$9977447 997 $aUNISA