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

ISBN-13: 9781461265351 / Angielski / Miękka / 2012 / 235 str.

Eduardo Bayro Corrochano

Opis

After an introduction to geometric algebra, and the necessary math concepts that are needed, the book examines a variety of applications in the field of cognitive systems using geometric algebra as the mathematical system. There is strong evidence that geobetric albegra can be used to carry out efficient computations at all levels in the cognitive system. Geometric algebra reduces the complexity of algebraic expressions and as a result, it improves algorithms both in speed and accuracy. The book is addressed to a broad audience of computer scientists, cyberneticists, and engineers. It contains computer programs to clarify and demonstrate the importance of geometric algebra in cognitive systems.

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