A Stable Voronoi-based Algorithm for Medial Axis Extraction through Labeling Sample Points

Abstract

This paper presents a Voronoi-based algorithm to extract the medial axis through labeling sample points. A major issue of the medial axis is its inherent instability under small perturbations. The medial axis is very sensitive to small changes of the boundary, which produce many irrelevant branches in the medial axis. Filtering extraneous branches is a common solution to handle this issue, It may be applied as a pre-processing step through simplifying (smoothing) the boundary, or as a post-processing step through pruning, which eliminates the irrelevant branches of the extracted medial axis. However, filtering may alter the topological or geometrical structure of the medial axis. This paper proposes a modification to a Voronoi-based medial axis extraction algorithm to automatically avoid appearing irrelevant branches through labeling the sample points. The experimental results indicate that our method is stable, even in the presence of significant noises and perturbations.