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Geometric Algebra Computing

in Engineering and Computer Science

By Eduardo Bayro-Corrochano , Gerik Scheuermann

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This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Its accessible style is enhanced by examples, figures and experimental analysis.

Full Description

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  • ISBN13: 978-1-8499-6107-3
  • 552 Pages
  • User Level: Science
  • Publication Date: May 19, 2010
  • Available eBook Formats: PDF
Full Description
This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. 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; explores new developments in the domain of Clifford Fourier Transforms and Clifford Wavelet Transform; 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.
Table of Contents

Table of Contents

  1. Part I: Geometric Algebra.
  2. New Tools for Computational Geometry and Rejuvenation of Screw Theory.
  3. Tutorial: Structure Preserving Representation of Euclidean Motions through Conformal Geometric Algebra.
  4. Engineering Graphics in Geometric Algebra.
  5. Parametrization of 3D Conformal Transformations in Conformal Geometric Algebra.
  6. Part II: Clifford Fourier Transform.
  7. Two
  8. Dimensional Clifford Windowed Fourier Transform.
  9. The Cylindrical Fourier Transform.
  10. Analyzing Real Vector Fields with Clifford Convolution and Clifford Fourier Transform.
  11. Clifford Fourier Transform for Color Image Processing.
  12. Hilbert Transforms in Clifford Analysis.
  13. Part III: Image Processing, Wavelets and Neurocomputing.
  14. Geometric Neural Computing for 2D Contour and 3D Surface Reconstruction.
  15. Geometric Associative Memories and their Applications to Pattern Classification.
  16. Classification and Clustering of Spatial Patterns with Geometric Algebra.
  17. QWT: Retrospective and New Applications.
  18. Part IV: Computer Vision.
  19. Image Sensor Model using Geometric Algebra: from Calibration to Motion Estimation.
  20. Model
  21. Based Visual Self
  22. Localization Using Gaussian Spheres.
  23. Part V: Conformal Mapping and Fluid Analysis.
  24. Geometric Characterization of M
  25. conformal Mappings.
  26. Fluid Flow Problems with Quaternionic Analysis: An Alternative Conception.
  27. Part VI: Cristalography, Holography and Complexity.
  28. Interactive 3D Space Group Visualization with CLUCalc and Crystallographic Subperiodic Groups in Geometric Algebra.
  29. Geometric Algebra Model of Distributed Representations.
  30. Computational Complexity Reductions using Clifford Algebras.
  31. Part VII: Efficient Computing with Clifford (Geometric) Algebra.
  32. Efficient Algorithms for Factorization and Join of Blades.
  33. Gaalop
  34. High Performance Parallel Computing based on Conformal Geometric Algebra.
  35. Some Applications of Gröbner Bases in Robotics and Engineering.

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