A Generative Theory of Shape

2001
ISBN: 978-3-540-42717-9
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 2145, 549 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 1760 g

Reihe: Lecture Notes in Computer Science

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.

Zielgruppe

Research

Autoren/Hrsg.

Leyton, Michael

Fachgebiete

• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Fotobeabeitung und Bildbearbeitung
• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning
• Mathematik | Informatik EDV | Informatik Informatik Bildsignalverarbeitung
• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Robotik
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Grafikprogrammierung
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.