Implementation of Geometric Algebra in MATLAB (registered trademark) with Applications

Abstract

Geometric Algebra is the most appropriate unifying mathematical language to describe diverse problems in mathematics, physics, engineering and computer science. In combination with Projective Geometry it provides an efficient framework for computer vision and robotics, where image processing and recognition play the central role. This document addresses a gentle introduction to Geometric Algebra followed by its implementation in MATLAB. The developed fully vectorized code is thoroughly tested. Several applications are presented in the form of unit tests, amongst which are some basic algorithms for the reconstruction of a three-dimensional structure from two-dimensional images.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 2014
Accession Number
ADA615302

Entities

People

  • Leonid K. Antanovskii

Organizations

  • Defence Science and Technology Group

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Australia
  • Base Lines
  • Cartesian Coordinates
  • Complex Numbers
  • Computer Science
  • Computer Vision
  • Coordinate Systems
  • Geometric Forms
  • Geometry
  • Image Processing
  • Mathematics
  • Projective Geometry
  • Three Dimensional
  • Two Dimensional
  • Vector Spaces

Fields of Study

  • Computer science

Readers

  • Computer Vision.
  • Parallel and Distributed Computing.
  • Theoretical Analysis.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms
  • Autonomy
  • Autonomy - Autonomous System Control