Multiscale Importance Metrics for Robust Skeletonization of 2D and 3D Shapes

We present a single generalized method for computing skeletons for arbitrary objects in both 2D and 3D space. We also present a method for computing the multiscale boundary-collapse importance metric for arbitrary 2D shapes in an incremental fashion, the results of which are comparable to the AFMM Star for 2D shapes. Finally, we reveal an approach which potentially allows the same importance metric to be computed for 3D shapes as well to provide results comparable to the Reniers et al.[33] method. The resulting method retains the simple implementation of the AFMM Star while avoiding the computational cost of the 3D boundary-collapse measure as computed by Reniers et al..