A Voronoi based Labeling Approach to Curve Reconstruction and Medial Axis Approximation

In this paper, we present a Voronoi based algorithm for closed curve reconstruction and medial axis approximation from planar points. In principle, the algorithm estimates one of the poles (farthest Voronoi vertices of a Voronoi cell) and hence the normals at each sample point by drawing an analogy between a residential water distribution system and Voronoi diagram of input samples. The algorithm then labels Voronoi vertices as either inner or outer with respect to the original curve and subsequently construct a piece-wise linear approximation to the boundary and the interior medial axis of the original curve for a class of curves having bi-tangent neighborhood convergence (BNC). The proposed algorithm has been evaluated for its usefulness using various test data. Results indicate that, even sparsely and non-uniformly sampled curves with sharp corners, outliers or collection of curves are faithfully reconstructed by the proposed algorithm.