Geometric Algebra Computing

in Engineering and Computer Science

  • Eduardo Bayro-Corrochano
  • Gerik Scheuermann

Table of contents

  1. Front Matter
    Pages I-XXII
  2. Geometric Algebra

  3. Clifford Fourier Transform

    1. Front Matter
      Pages 91-91
    2. Mawardi Bahri, Eckhard M. S. Hitzer, Sriwulan Adji
      Pages 93-106
    3. Fred Brackx, Nele De Schepper, Frank Sommen
      Pages 107-119
    4. Thomas Batard, Michel Berthier, Christophe Saint-Jean
      Pages 135-162
    5. Fred Brackx, Bram De Knock, Hennie De Schepper
      Pages 163-187
  4. Image Processing, Wavelets and Neurocomputing

    1. Front Matter
      Pages 189-189
    2. Jorge Rivera-Rovelo, Eduardo Bayro-Corrochano, Ruediger Dillmann
      Pages 191-209
    3. Benjamin Cruz, Ricardo Barron, Humberto Sossa
      Pages 211-230
    4. Minh Tuan Pham, Kanta Tachibana, Eckhard M. S. Hitzer, Tomohiro Yoshikawa, Takeshi Furuhashi
      Pages 231-247
    5. Yi Xu, Xiaokang Yang, Li Song, Leonardo Traversoni, Wei Lu
      Pages 249-273
  5. Computer Vision

    1. Front Matter
      Pages 275-275
    2. Thibaud Debaecker, Ryad Benosman, Sio H. Ieng
      Pages 277-297
    3. David Gonzalez-Aguirre, Tamim Asfour, Eduardo Bayro-Corrochano, Ruediger Dillmann
      Pages 299-324

About this book

Introduction

Geometric algebra provides a rich and general mathematical framework for the development of solutions, concepts and computer algorithms without losing geometric insight into the problem in question. Many current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra, such as 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.

Geometric Algebra Computing in Engineering and Computer Science presents contributions from an international selection of experts in the field. This useful text/reference offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. The book also provides an introduction to advanced screw theory and conformal geometry. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis.

Topics and features:

  • Provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework
  • Introduces nonspecialists to screw theory in the geometric algebra framework, offering a tutorial on conformal geometric algebra and an overview of recent applications of geometric algebra
  • Explores new developments in the domain of Clifford Fourier Transforms and Clifford Wavelet Transform, including novel applications of Clifford Fourier transforms for 3D visualization and colour image spectral analysis
  • Presents a detailed study of fluid flow problems with quaternionic analysis
  • Examines new algorithms for geometric neural computing and cognitive systems
  • Analyzes computer software packages for extensive calculations in geometric algebra, investigating the algorithmic complexity of key geometric operations and how the program code can be optimized for real-time computations

The book is an essential resource for computer scientists, applied physicists, AI researchers and mechanical and electrical engineers. It will also be of value to graduate students and researchers interested in a modern language for geometric computing.

Prof. Dr. Eng. Eduardo Bayro-Corrochano is a Full Professor of Geometric Computing at Cinvestav, Mexico. He is the author of the Springer titles Geometric Computing for Perception Action Systems, Handbook of Geometric Computing, and Geometric Computing for Wavelet Transforms, Robot Vision, Learning, Control and Action.

Prof. Dr. Gerik Scheuermann is a Full Professor at the University of Leipzig, Germany. He is the author of the Springer title Topology-Based Methods in Visualization II.

Keywords

3D graphics algebra algorithms calibration computer vision construction geometry graphics holography image processing model robot robotics visualization wavelets

Editors and affiliations

  • Eduardo Bayro-Corrochano
    • 1
  • Gerik Scheuermann
    • 2
  1. 1., CINVESTAVUnidad GuadalajaraColonia el Bajío, ZapopanMexico
  2. 2.Inst. InformatikUniversität LeipzigLeipzigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-84996-108-0
  • Copyright Information Springer-Verlag London Limited 2010
  • Publisher Name Springer, London
  • eBook Packages Computer Science
  • Print ISBN 978-1-84996-107-3
  • Online ISBN 978-1-84996-108-0
  • About this book