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Clifford algebraic calculus for geometric reasoning

with application to computer vision
  • Dongming Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1360)

Abstract

In this paper we report on our recent study of Clifford algebra for geometric reasoning and its application to problems in computer vision. A general framework is presented for construction and representation of geometric objects with selected rewrite rules for simplification. It provides a mechanism suitable for devising methods and software tools for geometric reasoning and computation. The feasibility and efficiency of the approach are demonstrated by our preliminary experiments on automated theorem proving in plane Euclidean geometry. We also explain how non-commutative Gröbner bases can be applied to geometric theorem proving. In addition to several well-known geometric theorems, two application examples from computer vision are given to illustrate the practical value of our approach.

Keywords

Theorem Prove Clifford Algebra Outer Product Geometric Reasoning Grassmann Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Dongming Wang
    • 1
  1. 1.LEIBNIZ-IMAGGrenoble CedexFrance

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