Abstract: This paper presents a novel segmentation method to assist the rigging of articulated bodies. The method computes a coarse-to-fine hierarchy of segments ordered by the level of detail. The results are invariant to deformations, and numerically robust to noise, irregular tessellations, and topological short-circuits. The segmentation is based on two key ideas. First, it exploits the multiscale properties of the diffusion distance on surfaces, and then it introduces a new definition of medial structures, composing a bijection between medial structures and segments. Our method computes this bijection through a simple and fast iterative approach, and applies it to triangulated meshes.