Towards surface regularization via medial axis transitions

The reconstruction of objects from data in practical ap-plications often leads to surfaces with small perturbations and other artifacts which make the detection of their ridges and generalized axes difficult. We propose an approach to smoothing small structures while preserving ridges which is based on the medial axis structure of the surface. The medial axis of the surface is organized as a graph struc-ture and the closeness of the medial axis graph to points of instability (transitions) is used to identify those structures which are most likely due to perturbations. The removal of these structures is our approach to regularizing both the medial axis and the surface. This paper focuses on a sub-set of medial transitions arising from protrusions and the method is illustrated for a few synthetic and real images.