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International Workshop on Automated Deduction in Geometry

ADG 1996: Automated Deduction in Geometry pp 115–140Cite as

Clifford algebraic calculus for geometric reasoning

with application to computer vision

  • Conference paper
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Part of the book series: Lecture Notes in Computer Science ((LNAI,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.

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Authors and Affiliations

  1. LEIBNIZ-IMAG, 46, avenue Félix Viallet, 38031, Grenoble Cedex, France

    Dongming Wang

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  1. Dongming Wang
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Dongming Wang

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© 1998 Springer-Verlag Berlin Heidelberg

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Wang, D. (1998). Clifford algebraic calculus for geometric reasoning. In: Wang, D. (eds) Automated Deduction in Geometry. ADG 1996. Lecture Notes in Computer Science, vol 1360. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022723

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  • DOI: https://doi.org/10.1007/BFb0022723

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64297-8

  • Online ISBN: 978-3-540-69717-6

  • eBook Packages: Springer Book Archive

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