Continuous skeleton computation by Voronoi diagram

The skeleton of a continuous shape can be approximated from the Voronoi diagram of points sampled along the shape boundary. To bound the error of this approximation, one must relate the spatial complexity of the shape to the boundary sampling density. The regular set model of mathematical morphology provides a practical basis to establish such a relationship. Given a binary image shape, we exhibit a corresponding continuous, regular shape such that the sequence of points describing its boundary constitutes a sufficiently dense sampling for an accurate skeleton approximation. Additionally, we bound the regeneration error from the sampling density and the regularity parameter. This approach opens significant new possibilities for shape analysis by the exact, Euclidean skeleton. As a simple example, we describe how the skeleton can be refined by pruning, without introducing significant error in the regenerated image.