Local beta-Crusts for Simple Curves Reconstruction

Sébastien Bougleux (1) , Mahmoud Melkemi (2) , Abderrahim Elmoataz (1)

1 Equipe Image - Laboratoire GREYC - UMR6072
2 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]

We consider the problem of curve reconstruction from a finite planar set of points. To solve this problem, we propose to use a family of neighborhood graphs included in the Gabriel graph. The neighborhood that we use is the β-neighborhood, initially defined in the context of circle-based β-skeletons, but applied to edges of the Voronoi diagram. This family of graphs includes the local crust. This formulation enables us to design effective algorithms to reconstruct curves, by using as a prior knowledge that the curves to be reconstructed are without intersections. We show, through several examples, that the proposed algorithms improve the results obtained with the local crust, when the set of points is of low density.

Mots clés: Voronoi diagram; Delaunay triangulation; curve reconstruction; greedy algorithms; local-crust

Domaines: Géométrie algorithmique [cs.CG]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Sébastien Bougleux, Mahmoud Melkemi, Abderrahim Elmoataz. Local beta-Crusts for Simple Curves Reconstruction. 4th International Symposium on Voronoi Diagrams in Science and Engineering, Jul 2007, Pontypridd, United Kingdom. pp.48-57, ⟨10.1109/ISVD.2007.29⟩. ⟨hal-00250489⟩