Skeletonization using an extended Euclidean distance transform

A standard method to perform skeletonisation is to use a distance transform. Unfortunately such an approach has the drawback that only the Symmetric axis transform can be computed and not the more practical smoothed local symmetries or the more general symmetry set. Using singularity theory we introduce an extended distance transform which may be used to capture more of the symmetries of a shape. We describe the relationship of this extended distance transform to the skeletal shape descriptors themselves and other geometric phenomema related to the boundary of the curve. We then show how the extended distance transform can be used to derive skeletal descriptions of an object.