A Generative Theory of Shape: 2145 (Lecture Notes in Computer Science, 2145) - Softcover

Leyton, Michael

Softcover

ISBN 10: 3540427171 ISBN 13: 9783540427179

Publisher: Springer, 2001

Synopsis

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.

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Review

From the reviews:

"This book is intended for a general scientifically interested audience a ] . The author develops a generative theory of shape along two principles fundamental to intelligence a" maximization of transfer and maximization of recoverability. He proceeds by using an algebraically flavoured approach characterizing features as symmetry groups while the addition of features corresponds to group extension. a ] The generative theory is used in several application areas like visual perception, robotics and computer-aided geometric design." (GA1/4nter Landsman, Zentralblatt MATH, Vol. 1012, 2003)

Synopsis

In this book, the author develops a generative theory of shape with two properties fundamental to intelligence: maximizing transfer of structure, and maximizing recoverability of generative operations. The theory is applied in considerable detail to CAD, perception, and robotics. A significant aspect of this book is the development of an object-oriented theory of geometry. This includes a group-theoretic formulation of object-oriented inheritance. In particular, a class of groups is developed called "unfolding groups", which define any complex shape as unfolded from a maximally collapsed version of itself called an "alignment kernel". The group is decomposed into levels corresponding to the inheritance hierarchy within the complex object. This achieves one of the main goals of the theory - the conversion of complexity into understandability. The advantages of the theory are demonstrated with lengthy studies of robot manipulators, perceptual organization, constructive solid geometry, assembly planning, architectural CAD, and mechanical CAD/CAM.

Edition details

• Publisher: Springer
• Publication date: 2001
• Language: English
• ISBN 10: 3540427171
• ISBN 13: 9783540427179
• Binding: Paperback
• Number of pages: 564