Multiscale Discrete Geometry

Mouhammad Said (1) , Jacques-Olivier Lachaud (1) , F. Feschet (2)

1 LAMA - Laboratoire de Mathématiques
2 LLAIC1 - Laboratoire de Logique, Algorithmique et Informatique

This paper presents a first step in analyzing how digital shapes behave with respect to multiresolution. We first present an analysis of the covering of a standard digital straight line by a multi-resolution grid. We then study the multi-resolution of Digital Straight Segments (DSS): we provide a sublinear algorithm computing the exact characteristics of a DSS whenever it is a subset of a known standard line. We finally deduce an algorithm for computing a multiscale representation of a digital shape, based only on a DSS decomposition of its boundary.

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]; Traitement des images [eess.IV]; Mathématique discrète [cs.DM]

Mouhammad Said, Jacques-Olivier Lachaud, F. Feschet. Multiscale Discrete Geometry. International Conference on Discrete Geometry for Computer Imagery, Sep 2009, Montréal, Québec, Canada. Accepted. To appear. ⟨hal-00413681⟩