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Communication Dans Un Congrès Année : 2014

Digital Geometry from a Geometric Algebra Perspective

Lilian Aveneau
SIC
Fuchs Laurent
  • Fonction : Auteur
SIC
Andres Eric
SIC

Résumé

To model Euclidean spaces in computerized geometric calcu- lations, the Geometric Algebra framework is becoming popular in com- puter 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 Ge- ometric 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.
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Dates et versions

hal-01155357 , version 1 (26-05-2015)

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  • HAL Id : hal-01155357 , version 1

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Lilian Aveneau, Fuchs Laurent, Andres Eric. Digital Geometry from a Geometric Algebra Perspective. 18th IAPR International Conference on Discrete Geometry for Computer Imagery, Sep 2014, Siena, Italy. ⟨hal-01155357⟩
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