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Geometric Computing with Clifford Algebras

Theoretical Foundations and Applications in Computer Vision and Robotics

  • Gerald Sommer

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. A Unified Algebraic Approach for Classical Geometries

    1. Front Matter
      Pages 1-1
    2. David Hestenes, Hongbo Li, Alyn Rockwood
      Pages 3-26
    3. Hongbo Li, David Hestenes, Alyn Rockwood
      Pages 27-59
    4. Hongbo Li, David Hestenes, Alyn Rockwood
      Pages 61-75
    5. Ambjörn Naeve, Lars Svensson
      Pages 105-126
  3. Algebraic Embedding of Signal Theory and Neural Computation

    1. Front Matter
      Pages 153-153
    2. Ekaterina Rundblad-Labunets, Valeri Labunets
      Pages 155-184
    3. Thomas Bülow, Michael Felsberg, Gerald Sommer
      Pages 187-207
    4. Michael Felsberg, Thomas Bülow, Gerald Sommer
      Pages 209-229
    5. Michael Felsberg, Thomas Bülow, Gerald Sommer, Vladimir M. Chernov
      Pages 231-254
    6. Thomas Bülow, Gerald Sommer
      Pages 255-289
    7. Sven Buchholz, Gerald Sommer
      Pages 291-314
    8. Sven Buchholz, Gerald Sommer
      Pages 315-334
  4. Geometric Algebra for Computer Vision and Robotics

    1. Front Matter
      Pages 335-335
    2. Christian B. U. Perwass, Joan Lasenby
      Pages 337-369
    3. Christian B. U. Perwass, Joan Lasenby
      Pages 371-392
    4. Eduardo Bayro-Corrochano, Bodo Rosenhahn
      Pages 393-414
    5. Hongbo Li, Gerald Sommer
      Pages 415-454
    6. Eduardo Bayro-Corrochano
      Pages 455-470
    7. Eduardo Bayro-Corrochano, Detlef Kähler
      Pages 471-488
    8. Yiwen Zhang, Gerald Sommer, Eduardo Bayro-Corrochano
      Pages 501-528
  5. Back Matter
    Pages 531-551

About this book

Introduction

Clifford algebra, then called geometric algebra, was introduced more than a cenetury ago by William K. Clifford, building on work by Grassmann and Hamilton. 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 powerfull algebraic framework for an elegant and coherent representation of various problems occuring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics. This monograph-like anthology introduces the concepts and framework of Clifford algebra and provides computer scientists, engineers, physicists, and mathematicians with a rich source of examples of how to work with this formalism.

Keywords

Algebra Algebraic Expressions Algebraic Geometry Clifford Algebras Computational Geometry Computer Computer Vision Geometric Computing Geometric Languages Neural Computation algorithms image processing robot robotics signal processing

Editors and affiliations

  • Gerald Sommer
    • 1
  1. 1.Institut für Informatik, Lehrstuhl für Kognitive SystemeChristian-Albrechts-Universität zu KielKielGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04621-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2001
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07442-4
  • Online ISBN 978-3-662-04621-0
  • Buy this book on publisher's site