REFS : Generative Theory of Shape
Vision List Digest:
Article 12,
Volume 21, Issue 14
From: "James Johnson"
Post-Followup: submission@VISLIST.com
The following book has just appeared in Springer-Verlag.
A Generative Theory of Shape
Michael Leyton
Springer-Verlag, 550 pages
The purpose of the book is to develop a generative theory of shape that
has two properties regarded as fundamental to intelligence - maximizing
transfer of structure and maximizing recoverability of the generative
operations. These two properties are particularly important in the
representation of complex shape - which is the main concern of the book.
The primary goal of the theory is the conversion of complexity into
understandability. For this purpose, a mathematical theory is presented
of how understandability is created in a structure. This is achieved by
developing a group-theoretic approach to formalizing transfer and
recoverability. To handle complex shape, a new class of groups is
developed, called unfolding groups. These unfold structure from a
maximally collapsed version of that structure. A principal aspect of the
theory is that it develops a group-theoretic formalization of major
object-oriented concepts such as inheritance. The result is an
object-oriented theory of geometry.
The algebraic theory is applied in detail to CAD, perception, and
robotics. In CAD, lengthy chapters are presented on mechanical and
architectural design. For example, using the theory of unfolding groups,
the book works in detail through the main stages of mechanical CAD/CAM:
part-design, assembly and machining. And within part-design, an
extensive algebraic analysis is given of sketching, alignment,
dimensioning, resolution, editing, sweeping, feature-addition, and
intent-management. The equivalent analysis is also done for
architectural design. In perception, extensive theories are given for
grouping and the main Gestalt motion phenomena (induced motion,
separation of systems, the Johannson relative/absolute motion effects);
as well as orientation and form. In robotics, several levels of analysis
are developed for manipulator structure, using the author's algebraic
theory of object-oriented structure.
This book can be viewed electronically at the following site:
http://link.springer.de/link/service/series/0558/tocs/t2145.htm
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