Constructing Area Voronoi Diagram Based on Direct Calculation of the Freeman Code of Expanded Contours

A Voronoi diagram of image elements provides an intuitive and appealing definition of proximity, which has been suggested as an effective tool for the description of relations among the neighboring objects in a digital image. In this paper, an implementation algorithm based on direct calculation of the Freeman code of expanded contours is proposed for generating area Voronoi diagram of connected components. A closed convex polygon is utilized to bound each connected component, as an approximate representation, and the contour is represented using Freeman chain coding, from which we can compute the corresponding Freeman chain coding of its expanded contour directly, without recourse to the operation on pixels. While the contours iteratively expand outwards, the Voronoi diagram is constructed by the intersections of the expanded contours from different connected components. The experimental results show that our proposed approach significantly improves the speed of constructing area Voronoi diagram in digital images.