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Geometric Computing with Clifford Algebra : Theoretical Foundations and Applications in Computer Vision and Robotics :  Theoretical Foundations and Applications in Computer Vision and Robotics - Gerald Sommer

Geometric Computing with Clifford Algebra : Theoretical Foundations and Applications in Computer Vision and Robotics

Theoretical Foundations and Applications in Computer Vision and Robotics

By: Gerald Sommer (Editor)

Hardcover Published: June 2001
ISBN: 9783540411987
Number Of Pages: 551

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This text introduces the concepts and framework of Clifford algebra. It provides a rich source of examples of how to work with this formalism. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "mother algebra" in various subfields of physics and engineering. Recent work outlines that Clifford algebra provides a universal and powerful algebraic framework for an elegant and coherent representation of various problems occurring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics.

From the reviews:





"This monograph-like anthology presents a collection of contributions concerning the problem of solving geometry related problems with suitable algebraic embeddings. It is not only directed at scientists who have already discovered the power of Clifford algebras ... but also at those scientists who are interested in Clifford algebras ... . Therefore, an effort is made to keep this book accessible to newcomers ... while still presenting up to date research and new developments. ... The 21 coherently written chapters cover all relevant issues ... ." (Vasily A. Chernecky, Mathematical Reviews, Issue 2003 m)

"This is a collection of contributions which describe the solution of geometry-related problems by suitable algebraic embeddings, especially into Clifford algebras. ... this book can serve as a reference to the state of the art concerning the use of Clifford algebras as a frame for geometric computing." (H. G. Feichtinger, Monatshefte fur Mathematik, Vol. 140 (4), 2003)

"Clifford Algebras were introduced by W. K. Clifford in 1878. ... The book is a collection of 21 chapters/papers written by experts in the field. These 21 papers are coherently written and the book can be read almost like a monograph. ... The book is clearly written and well structured. It is recommended to mathematicians, physicists, computer scientists, engineers, and ... to graduate students." (K. Gurlebeck, Zeitschrift fur Analysis und ihre Anwendungen, Vol. 21 (4), 2002)

A Unified Algebraic Approach for Classical Geometries
New Algebraic Tools for Classical Geometry
Generalized Homogeneous Coordinates for Computational Geometry
Spherical Conformal Geometry with Geometric Algebra
A Universal Model for Conformal Geometries of Euclidean
Spherical and Double-Hyperbolic Spaces
Geo-MAP Unification
Honing Geometric Algebra for Its Use in the Computer Sciences
Algebraic Embedding for Signal Theory and Neural Computation
Spatial-Color Clifford Algebras for Invariant Image Recognition
Non-commutative Hypbercomplex Fourier Transforms of Multidimensional Signals
Commutative Hypercomplex Fourier Transforms of Mulitdimensional Signals
Fast Algorithms fo Hypercomplex Fourier Transforms
Local Hypercomplex Signal Representations and Applications
Introduction to Neural Computation in Clifford Algebra
Clifford Algebra Mulitlayer Perceptrons, etc
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540411987
ISBN-10: 3540411984
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 551
Published: June 2001
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 24.13 x 16.51  x 1.91
Weight (kg): 0.93