Simultaneous Skeletonization and Topologic Decomposition for Digital Shape Reconstruction

Abstract

Analyzing the structure of 2D shapes has been studied intensively in recent years. It is a key aspect in various computer vision and computer graphics applications. In this paper, a new algorithm is proposed which efficiently computes a skeleton and a corresponding decomposition of an arbitrary shape. Given the Voronoi diagram, the pruning step has linear complexity. The skeleton is a sparse 1D representation which captures the topology as well as the general structure of a shape. Considering the Voronoi diagram of the boundary vertices, the skeleton is extracted as a subset of the Voronoi edges using a simple classification scheme. A parameter allows to control the skeleton’s sensitivity to perturbations in the boundary curve. The dual Delaunay triangulation yields a topological decomposition of the shape that is consistent with the skeleton. Each part can be classified as belonging to one of three base types which have some interesting properties. The method has been successfully implemented and evaluated. The presented concepts can also be applied to manifold surfaces which is particularly useful for digital shape reconstruction as it is shown at the end of this paper.