A new pruning method for medial axis of planar free-form shape

Abstract

The medial axis (or a topological skeleton) is a thinner version of a geometric object. The medial axis was first introduced by Blum as a description of shape. Its classical definitions include grass-fire model and maximal disk model The grass-fire model means that an object's boundary is taken as an initial fire front that propagates within the object's interior region. Points where the fire front folds or interacts with itself are retained as the skeleton points. The maximal disk model means that the medial axis of a planar domain is the locus of the center of a maximal disc, which touches the boundary in at least two points. The medial axis has been used within various scientific and engineering areas, including geographical information systems, face recognition, path-finding, image processing, computer vision, collision detection, mesh-generation, and machining applications, etc. Usually, because of the noise on the boundary contours of a shape, the traditional algorithms of constructing medial axis produce the redundant branches of medial axis. This paper analyses the reason for the redundant branches of medial axis using the circumcenter method based on constraint Delaunay triangulation, and then presents a new method to prune the redundant branches of the medial axis. Several experiments demonstrate that the proposed method can remove the redundant medial axis branches effectively and efficiently. Obviously this method is an optimization for the circumcenter method based on constraint Delaunay triangulation. On the one hand, it makes medial axis more accurate; on the other hand, it can eliminate the byproduct-medial axis branches.