Voronoi-based medial axis approximation from samples: Issues and solutions

Abstract

Continuous curves are approximated by sample points, which carry the shape information of the curve. If sampling is sufficiently dense, the sample points can be used to extract the structural properties of the curve (e.g., crust, medial axis, etc.). This article focuses on approximation of medial axis from sample points. Especially, we review the methods that approximate the medial axis using Voronoi diagram. Such methods are extremely sensitive to noise and boundary perturbations. Thus, a pre- or post-processing step is needed to filter irrelevant branches of the medial axis, which are introduced in this article. We, then, propose a new medial axis approximation algorithm that automatically avoids irrelevant branches through labeling sample points. The results indicate that our method is stable, easy to implement, robust and able to handle sharp corners, even in the presence of significant noise and perturbations. © 2013 Springer-Verlag Berlin Heidelberg.