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Geometric Algebra Applications Vol. I

Computer Vision, Graphics and Neurocomputing

  • Eduardo Bayro-Corrochano

Table of contents

  1. Front Matter
    Pages i-xxxiii
  2. Fundamentals of Geometric Algebra

    1. Front Matter
      Pages 19-19
    2. Eduardo Bayro-Corrochano
      Pages 21-53
    3. Eduardo Bayro-Corrochano
      Pages 89-112
    4. Eduardo Bayro-Corrochano
      Pages 113-180
  3. Euclidean, Pseudo-Euclidean Geometric Algebras, Incidence Algebra, Conformal and Projective Geometric Algebras

    1. Front Matter
      Pages 181-181
    2. Eduardo Bayro-Corrochano
      Pages 183-207
    3. Eduardo Bayro-Corrochano
      Pages 209-231
    4. Eduardo Bayro-Corrochano
      Pages 233-267
    5. Eduardo Bayro-Corrochano
      Pages 269-292
    6. Eduardo Bayro-Corrochano
      Pages 293-301
  4. Image Processing and Computer Vision

    1. Front Matter
      Pages 303-303
    2. Eduardo Bayro-Corrochano
      Pages 305-358
    3. Eduardo Bayro-Corrochano
      Pages 359-413
  5. Machine Learning

    1. Front Matter
      Pages 415-415
    2. Eduardo Bayro-Corrochano
      Pages 417-486
  6. Applications of GA in Image Processing, Graphics and Computer Vision

  7. Applications of GA in Machine Learning

    1. Front Matter
      Pages 629-629
    2. Eduardo Bayro-Corrochano
      Pages 631-657
    3. Eduardo Bayro-Corrochano
      Pages 659-675
    4. Eduardo Bayro-Corrochano
      Pages 677-697
  8. Back Matter
    Pages 699-742

About this book

Introduction

The goal of the Volume I Geometric Algebra for Computer Vision, Graphics  and Neural Computing is to present a unified mathematical treatment of diverse problems in the general domain of artificial intelligence and associated fields using Clifford, or geometric, algebra.

Geometric algebra provides a rich and general mathematical framework for Geometric Cybernetics in order to develop solutions, concepts and computer algorithms without losing geometric insight of the problem in question. Current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra for instance: multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras and conformal geometry.

By treating a wide spectrum of problems in a common language, this Volume I offers both new insights and new solutions that should be useful to scientists, and engineers working in different areas related with the development and building of intelligent machines. Each chapter is written in accessible terms accompanied by numerous examples, figures and a complementary appendix on Clifford algebras, all to clarify the theory and the crucial aspects of the application of geometric algebra to problems in graphics engineering, image processing, pattern recognition, computer vision, machine learning, neural computing and cognitive systems.

Keywords

Computer Vision Geometric Algebra Geometric Neural Computing Graphics Machine Learning

Authors and affiliations

  • Eduardo Bayro-Corrochano
    • 1
  1. 1.Electrical Engineering and Computer Science DepartmentCINVESTAV, Campus GuadalajaraJaliscoMexico

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