000			04049nam a22005895i 4500
001			978-3-540-45488-5
003			DE-He213
005			20160624102003.0
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	_aTA1637-1638
050		4	_aTA1637-1638
072		7	_aUYT _2bicssc
072		7	_aUYQV _2bicssc
072		7	_aCOM012000 _2bisacsh
072		7	_aCOM016000 _2bisacsh
082	0	4	_a006.6 _223
082	0	4	_a006.37 _223
245	1	2	_aA Generative Theory of Shape _h[electronic resource].
260		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2001.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _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, _x0302-9743 ; _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 science.
650		0	_aComputer graphics.
650		0	_aComputer vision.
650		0	_aComputer aided design.
650		0	_aGroup theory.
650		0	_aGeometry.
650	1	4	_aComputer Science.
650	2	4	_aImage Processing and Computer Vision.
650	2	4	_aComputer Graphics.
650	2	4	_aGeometry.
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 eBooks
776	0	8	_iPrinted edition: _z9783540427179
786			_dSpringer
830		0	_aLecture Notes in Computer Science, _x0302-9743 ; _v2145
856	4	0	_uhttp://dx.doi.org/10.1007/3-540-45488-8
942			_2EBK5405 _cEBK
999			_c34699 _d34699