Geometric Computing for Perception Action Systems: Concepts, Algorithms, and Scientific Applications

ISBN-13: 9780387951911 / Angielski / Twarda / 2001 / 235 str.

Eduardo Bayro Corrochano

Opis

This book presents a unified mathematical treatment of diverse problems in the fields of cognitive systems using Clifford, or geometric, algebra. Geometric algebra provides a rich general mathematical framework for the development of the ideas of multilinear algebra, projective and affine geometry, calculus on manifolds, the representation of Lie groups and Lie algebras, and many other areas of applications. By treating a wide spectrum of problems in a common geometric language, the book offers both new insights and new solutions that should be useful to scientists and engineers working in different but related areas of artificial intelligence. It looks at building intelligence systems through the construction of Perception Action Cycles; critical to this concept is incorporating representation and learning in a flexible geometric system. Each chapter is written in accessible terms accompanied by numerous examples and figures that clarify the application of geometric algebra to problems in geometric computing, image processing, computer vision, robotics, neural computing and engineering. Topics and features: *Introduces a nonspecialist to Clifford, or geometric, algebra and it shows applications in artificial intelligence *Thorough discussion of several tasks of signal and image processing, computer vision, robotics, neurocomputing and engineering using the geometric algebra framework *Features the computing frameworks of the linear model n-dimensional affine plane and the nonlinear model of Euclidean space known as the horosphere, and addresses the relationship of these models to conformal, affine and projective geometries *Applications of geometric algebra to other related areas: aeronautics, mechatronics, graphics engineering, and speech processing *Exercises and hints for the development of future computer software packages for extensive calculations in geometric algebra The book is an essential resource for computer scientists, AI researchers, and electrical engineers and includes computer programs to clarify and demonstrate the importance of geometric computing for cognitive systems and artificial autonomous systems research.

Recenzje

From the reviews:

MATHEMATICAL REVIEWS

"We are sure that the mathematicians, computer scientists, engineers and physicists will enjoy reading this book."

"For the case of perception action cycles the author of this nice book shows that the Clifford algebra ... of multivectors of an n-dimensional vector space is indeed superior to previous mathematical structures used to deal with this subject. ... We are sure that mathematicians, computer scientists, engineers and physicists will enjoy reading this book." (Waldyr Alves Rodrigues, Jr., Mathematical Reviews, Issue 2003 d)

Spis treści

Mathematical Preliminaries * Lie Algebras and Geometric Algebra for Robotics and Image Analysis * Kinematics of 2-Space and 3-Space * Mathematics of the Human Eye * Image Analysis and Low Level Operations * Theory of Extended Kalman Filter * Geometric Algebra of Computer Vision * Analysis and Computation of Projective Invariants * Geometric Computing of Intrinsic Camera Parameters * Geometric Approach for Computing Shape and Motion * Geometric Neural Computing * Geometric Computing in Robotics