A Generative Theory of Shape

Michael Leyton (Autor)

Buch | Softcover

XV, 549 Seiten

2001 | 2001
Springer Berlin (Verlag)
978-3-540-42717-9 (ISBN)

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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.

Professor Michael Leytonlehrt an der Fakultät des Center for Discrete Mathematics and Theoretical Computer Science an der Universität Rutgers. Er ist Vorsitzender der International Society for Mathematical and Computational Aesthetics und lebt in Manhattan.

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.

Erscheint lt. Verlag	26.10.2001
Reihe/Serie	Lecture Notes in Computer Science
Zusatzinfo	XV, 549 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 233 mm
Gewicht	822 g
Themenwelt	Informatik ► Grafik / Design ► Digitale Bildverarbeitung
Themenwelt	Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
Schlagworte	Bildverarbeitung • Complexity • Complex Shape • Computergrafik • computer vision • Editing • Erlanger Program • Geometric Invariants • Geometric Objects • Geometric Shape • Geometric Structure • Geometrie • group theory • Hardcover, Softcover / Informatik, EDV/Informatik • HC/Informatik, EDV/Informatik • Kinematics • Machine vision • robot • Robotics • Robot Navigation • Shape generation • Shape Theory • visual perception • Wreath Products
ISBN-10	3-540-42717-1 / 3540427171
ISBN-13	978-3-540-42717-9 / 9783540427179
Zustand	Neuware