Digital Geometry from a Geometric Algebra Perspective

Lilian Aveneau (1) , Fuchs Laurent (1) , Andres Eric (1)

1 XLIM-SIC - SIC

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.

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]

Lilian Aveneau, Fuchs Laurent, Andres Eric. Digital Geometry from a Geometric Algebra Perspective: 18th IAPR International Conference, DGCI 2014, Siena, Italy, September 10-12, 2014. Proceedings. Discrete Geometry for Computer Imagery, 8668, Springer, pp.358-369, 2014, Lecture Notes in Computer Science, 978-3-319-09954-5. ⟨10.1007/978-3-319-09955-2_30⟩. ⟨hal-01155364⟩