Progressive medial axis filtration

The Scale Axis Transform provides a parametric simplification of the Medial Axis of a 3D shape which can be seen as a hierarchical description. However, this powerful shape analysis method has a significant computational cost, requiring several minutes for a single scale on a mesh of few thousands vertices. Moreover, the scale axis can be artificially complexified at large scales, introducing new topological structures in the simplified model. In this paper, we propose a progressive medial axis simplification method inspired from surface optimization techniques which retains the geometric intuition of the scale axis transform. We compute a hierarchy of simplified medial axes by means of successive edge-collapses of the input medial axis. These operations prevent the creation of artificial tunnels that can occur in the original scale axis transform. As a result, our progressive simplification approach allows to compute the complete hierarchy of scales in a few seconds on typical input medial axes. We show how this variation of the scale axis transform impacts the resulting medial structure.