Exploiting curvature to compute the medial axis with Constrained Centroidal Voronoi Diagram on discrete data

In this paper, we present a novel method for medial axis approximation based on Constrained Centroidal Voronoi Diagram of discrete data (image, volume). The proposed approach is based on the shape boundary subsampling controled by a clustering approach which generates a Voronoi Diagram well suited for Medial Axis extraction. The resulting Voronoi Diagram is further filtered in order to capture the correct topology of the medial axis. The main contribution of this paper is the integration of both a curvature maps and a distance map for controlling the local variability of Voronoi cells densities. Examples of complex shape processing prove the effectiveness of the proposed approach.