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Digital Geometry from a Geometric Algebra Perspective

  • Lilian Aveneau
  • Laurent Fuchs
  • Eric Andres
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8668)

Abstract

To model Euclidean spaces in computerized geometric calculations, the Geometric Algebra framework is becoming popular in computer vision, image analysis, etc. Focusing on the Conformal Geometric Algebra, the claim of the paper is that this framework is useful in digital geometry too. To illustrate this, this paper shows how the Conformal Geometric Algebra allow to simplify the description of digital objects, such as k-dimensional circles in any n-dimensional discrete space. Moreover, the notion of duality is an inherent part of the Geometric Algebra. This is particularly useful since many algorithms are based on this notion in digital geometry. We illustrate this important aspect with the definition of k-dimensional spheres.

Keywords

Digital Geometry Geometric Algebra Conformal Model Digital Object 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Lilian Aveneau
    • 1
  • Laurent Fuchs
    • 1
  • Eric Andres
    • 1
  1. 1.Laboratoire XLIM-SIC UMR CNRS 7252, Université de PoitiersFuturoscope Chasseneuil CedexFrance

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