Computing and Simplifying 2D and 3D Continuous Skeletons

摘要

Skeletons provide a synthetic and thin representation of objects. Therefore, they are useful for shape description. Recent papers have proposed to approximate the skeleton of continuous shapes using the Voronoi graph of boundary points. An original formulation is presented here, using the notion of polyballs (we call polyball any finite union of balls). A preliminary work shows that their skeletons consist of simple components (line segments in 2D and polygons in 3D). An efficient method for simplifying 3D continuous skeletons is also presented. The originality of our approach consists in simplifying the shape without modifying its topology and in including these modifications on the skeleton. Depending on the desired result, we propose two strategies which lead to either surfacical skeletons or wireframe skeletons. Two angular criteria are proposed that allow us to build a size-invariant hierarchy of simplified skeletons.