Stable Medial-Axis estimation under regularity conditions

C Aaron (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

The medial axis of a geometrical set S ∈ R d carries a lot of information on the shape of S and is a popular tool in image analysis. The aim of this paper is to stably estimate the medial axis using only a finite sub-sample of S. We are going to prove that, under some regularity conditions, it can be done using only one pruning parameter. A general deterministic result will be given, then applied to three different cases. Firstly these is the usual one where the information is given by a finite sub-sample of ∂S. Secondly, these is the classical one where the set is given by its pixelated image. Finally, we can also apply the general theorem to the case where the information is given by a randomly drawn sample of S. In this more challenging case we also detail the algorithm, the choice of the parameter and give some simulation results as illustration.

Mots clés: Manifold Learning; Geometric Inference; Skeleton

Domaines: Statistiques [math.ST]

C Aaron. Stable Medial-Axis estimation under regularity conditions. 2017. ⟨hal-01558392v1⟩