Geometric Algebra with Applications in Science and Engineering

Overview

"This book is a resource for a broad audience of professionals researchers and practitioners, computer scientists, engineers, applied physicists, and applied mathematicians. The book contains many examples that clarify the importance of geometric algebra in signal and image processing for the techniques of geometric filtering and also in neural computing, computer vision, robotics, and physics. This book will help the reader to gain a better understanding of the potential of geometric algebra for the design and implementation of real-time
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Paperback (Softcover reprint of the original 1st ed. 2001)
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Overview

"This book is a resource for a broad audience of professionals researchers and practitioners, computer scientists, engineers, applied physicists, and applied mathematicians. The book contains many examples that clarify the importance of geometric algebra in signal and image processing for the techniques of geometric filtering and also in neural computing, computer vision, robotics, and physics. This book will help the reader to gain a better understanding of the potential of geometric algebra for the design and implementation of real-time artificial systems."--BOOK JACKET.
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Product Details

  • ISBN-13: 9781461266396
  • Publisher: Birkhauser Verlag
  • Publication date: 12/31/2013
  • Edition description: Softcover reprint of the original 1st ed. 2001
  • Pages: 592
  • Product dimensions: 6.14 (w) x 9.21 (h) x 1.26 (d)

Table of Contents

Preface
Contributors
I Advances in Geometric Algebra 1
1 Old Wine in New Bottles: A New Algebraic Framework for Computational Geometry 3
2 Universal Geometric Algebra 18
3 Realizations of the Conformal Group 42
4 Hyperbolic Geometry 61
II Theorem Proving 87
5 Geometric Reasoning With Geometric Algebra 89
6 Automated Theorem Proving 110
III Computer Vision 121
7 The Geometry Algebra of Computer Vision 123
8 Using Geometric Algebra for Optical Motion Capture 147
9 Bayesian Inference and Geometric Algebra: An Application to Camera Localization 170
10 Projective Reconstruction of Shape and Motion Using Invariant Theory 190
IV Robotics 209
11 Robot Kinematics and Flags 211
12 The Clifford Algebra and the Optimization of Robot Design 235
13 Applications of Lie Algebras and the Algebra of Incidence 252
V Quantum and Neural Computing, and Wavelets 279
14 Geometric Algebra in Quantum Information Processing by Nuclear Magnetic Resonance 281
15 Geometric Feedforward Neural Networks and Support Multivector Machines 309
16 Image Analysis Using Quaternion Wavelets 326
VI Applications to Engineering and Physics 347
17 Objects in Contact: Boundary Collisions as Geometric Wave Propagation 349
18 Modern Geometric Calculations in Crystallography 371
19 Quaternion Optimization Problems in Engineering 387
20 Clifford Algebras in Electrical Engineering 413
21 Applications of Geometric Algebra in Physics and Links With Engineering 430
VII Computational Methods in Clifford Algebras 459
22 Clifford Algebras and Projections of Group Algebras 461
23 Counterexamples for Validation and Discovering of New Theorems 477
24 The Making of GABLE: A Geometric Algebra Learning Environment in Matlab 491
25 Helmstetter Formula and Rigid Motions with CLIFFORD 512
References 535
Index 583
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