Crust and Skeleton Approximation from Samples

Samples of shape boundary carry the information of the shape for a sufficiently dense sampling. There is not any connectivity information between sample points and the geometry or topology of the original shape is not known. These samples are used for crust and skeleton approximation. In this article, we focus on the Voronoi-based methods which the shape is defined by a set of sample points on the shape boundary and then the shape and its skeleton is approximated with the Voronoi diagram of these points. These methods are extremely sensitive to noise and boundary perturbation. To overcome the problems of crust and skeleton extraction, we propose a new method by labeling the sample points. The conceptual structure and the results illustrate that our method are stable, easy to implement, robust and able to handle sharp corners and open curves, even in the presence of significant noise and perturbations.