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• catalog abstract "The 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.".
• catalog contributor b12452592.
• catalog created "c2001.".
• catalog date "2001".
• catalog date "c2001.".
• catalog dateCopyrighted "c2001.".
• catalog description "Includes bibliographical references (p. [541]-548) and index.".
• catalog description "The 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.".
• catalog description "Transfer -- 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.".
• catalog extent "xvi, 554 p. :".
• catalog identifier "3540427171 (alk. paper)".
• catalog isPartOf "Lecture notes in computer science ; 2145".
• catalog issued "2001".
• catalog issued "c2001.".
• catalog language "eng".
• catalog publisher "Berlin ; New York : Springer,".
• catalog subject "516 21".
• catalog subject "Computer aided design.".
• catalog subject "Computer graphics.".
• catalog subject "Computer science.".
• catalog subject "Computer vision.".
• catalog subject "Geometric programming.".
• catalog subject "Geometry.".
• catalog subject "Group theory.".
• catalog subject "Shape theory (Topology)".
• catalog subject "T57.825 .L49 2001".
• catalog tableOfContents "Transfer -- 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.".
• catalog title "A generative theory of shape / Michael Leyton.".
• catalog type "text".