| A Generative Theory of Shape 2001 Edition Contributor(s): Leyton, Michael (Author) |
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ISBN: 3540427171 ISBN-13: 9783540427179 Publisher: Springer OUR PRICE: $104.49 Product Type: Paperback - Other Formats Published: October 2001 |
| Additional Information |
| BISAC Categories: - Mathematics | Group Theory - Mathematics | Geometry - General - Computers | Cad-cam |
| Dewey: 516 |
| LCCN: 2001049819 |
| Series: Lecture Notes in Computer Science |
| Physical Information: 1.17" H x 6.14" W x 9.21" (1.75 lbs) 549 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |