Stable and Topology-Preserving Extraction of Medial Axes

The paper presents a simple method for extracting global medial axes in a stable manner. A new index, called the normalized boundary distance, is introduced in order to measure the degree of importance of a point on the conventional medial axis. This index has a remarkable property that the set of points whose index values are greater than an arbitrarily chosen threshold is topologically equivalent to the original figure. In the proposed method, first the boundary of a given figure is replaced with a dense set of points, next the Voronoi diagram for these points is constructed, then the approximation of the medial axis is extracted from the Voronoi diagram, and finally the global medial axis is constructed by pruning the branches according to the new index. The performance of the proposed method is also shown by examples.