Stability and Computation of Medial Axes: a State-of-the-Art Report

Dominique Attali (1) , Jean-Daniel Boissonnat (2) , Herbert Edelsbrunner (3)

1 GIPSA-GPIG - GIPSA - Géométrie, Perception, Images, Geste
2 GEOMETRICA - Geometric computing
3 Department of Computer Science

The medial axis of a geometric shape captures its connectivity. In spite of its inherent instability, it has found applications in a number of areas that deal with shapes. In this survey paper, we focus on results that shed light on this instability and use the new insights to generate simplified and stable modifications of the medial axis.

Domaines: Géométrie algorithmique [cs.CG]

Dominique Attali, Jean-Daniel Boissonnat, Herbert Edelsbrunner. Stability and Computation of Medial Axes: a State-of-the-Art Report. T. M\"{o}ller and B. Hamann and R. Russell. Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration, Springer-Verlag, pp.109-125, 2009, Mathematics and Visualization. ⟨hal-00468690⟩