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

Overview

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...

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Paperback (Softcover reprint of the original 1st ed. 2001)
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Overview

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.

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Editorial Reviews

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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)

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Product Details

  • ISBN-13: 9781461265351
  • Publisher: Springer New York
  • Publication date: 12/31/2013
  • Edition description: Softcover reprint of the original 1st ed. 2001
  • Pages: 235
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.54 (d)

Table of Contents

Preface
Pt. I Fundamental Concepts
1 Mathematical Preliminaries 3
2 Kinematics of the 2D and 3D Spaces 19
3 Lie Algebras and Algebra of Incidence Using the Null Cone and Affine Plane 39
4 Geometric Algebra of Computer Vision 67
Pt. II Practical Applications
5 Computing the Kinematics of Robot Manipulators 95
6 Image Processing 115
7 Applications in Computer Vision 137
8 Rigid Motion Estimation Using Line Observations 169
9 Geometric Neuralcomputing 201
References 225
Index 231
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