Using polyballs to approximate shapes and skeletons

This paper presents an approach to approximate the skeleton of continuous shapes either in 2D or 3D space. The data required is a sampling of the boundary of the shape. The authors call polyball any finite union of balls. A preliminary work on polyballs shows that their skeletons consist of simple components (line segments in 2D and polygons in 3D). To construct these components, only the computation of a Voronoi graph is required. Previous papers have proposed to approximate the skeleton of continuous shapes using the Voronoi graph of boundary points. An original reformulation of these methods is presented here, using polyballs. It allows one to build a hierarchy of simplified skeletons. An application in the frame of a European project in the field of medicine and biology is also presented. The skeleton by influence zones is computed in real time, which validates the authors' approach.