Dynamic Skeletonization Via Variational Medial Axis Sampling

We present a novel method for computing a discrete skeleton from a shape represented by a point cloud or triangle mesh. Inspired by variational shape approximation, our approach optimizes the partitioning of the input shape by minimizing an error metric defined between medial axis samples (medial spheres) and their corresponding clusters. The metric combines plane-sphere and point-sphere distance terms and the balance between these two terms enables coarse skeletons to capture the main geometric features while denser skeletons achieve a uniform distribution of medial axis samples. The sampling of the medial axis is progressively refined through an automatic process that splits medial spheres with the highest errors. Our method’s efficiency also allows users to dynamically add or remove medial axis samples locally while the optimization process continuously updates the underlying partition. Skeleton connectivity is efficiently constructed by computing the dual of the optimized shape partition. Unlike previous approaches, our method does not rely on a predefined set of candidate spheres or an initial medial axis representation.