Voronoi diagrams of polygons: A framework for shape representation

Abstract

This paper describes an efficient shape representation framework for planar shapes using Voronoi skeletons. This paper makes the following significant contributions. First a new algorithm for the construction of the Voronoi diagram of a polygon with holes is described. The main features of this algorithm are its robustness in handling the standard degenerate cases (colinearity of more than two points; co-circularity of more than three points), and its ease of implementation. It also features a robust numerical scheme to compute non-linear parabolic edges that avoids having to solve equations of degree greater than two. The algorithm has been fully implemented and tested in a variety of test inputs. Second, the Voronoi diagram of a polygon is used to derive accurate and robust skeletons for planar shapes. The shape representation scheme using Voronoi skeletons possesses the important properties of connectivity as well as Euclidean metrics. Redundant skeletal edges are deleted in a pruning step which guarantees that connectivity of the skeleton will be preserved. The resultant representation is stable with respect to being invariant to perturbations along the boundary of the shape. A number of examples of shapes with and without holes are presented to demonstrate the features of this approach.