03475nmm a2200409 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002000139245007700159250001700236260006300253300003100316505059100347653002200938653004100960653001701001653003701018653002201055653005301077653002501130653003101155653001301186653002601199653001301225653002801238710003401266041001901300989003801319490003801357856006801395082001101463082001001474520158101484EB000656527EBX0100000000000000050960900000000000000.0cr|||||||||||||||||||||140122 ||| eng a97835404548851 aLeyton, Michael00aA Generative Theory of ShapehElektronische Ressourcecby Michael Leyton a1st ed. 2001 aBerlin, HeidelbergbSpringer Berlin Heidelbergc2001, 2001 aXV, 549 pbonline resource0 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 aComputer graphics aImage Processing and Computer Vision aGroup theory aGroup Theory and Generalizations aComputer Graphics aComputer-Aided Engineering (CAD, CAE) and Design aApplication software aComputer-aided engineering aGeometry aComputer Applications aGeometry aOptical data processing2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aLecture Notes in Computer Science uhttps://doi.org/10.1007/3-540-45488-8?nosfx=yxVerlag3Volltext0 a006.370 a006.6 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