Efficient and Robust Computation of an Approximated Medial Axis

Abstract

The medial axis can be viewed as a compact representation for an arbitrary model; it is an essential geometric structure in many applications. A number of practical algorithms for its computation have been aimed at speeding up its computation and at addressing its instabilities. In this paper we propose a new algorithm to compute the medial axis with arbitrary precision. It exhibits several desirable properties not previously combined in a practical and ef cient algorithm. First, it allows for a tradeoff between computation time and accuracy, making it well-suited for applications in which an approximation of the medial axis suf ces, but computational ef ciency is of particular concern. Second, it is output sensitive: the computation complexity of the algorithm does not depend on the size of the representation of a model, but on the size of the representation of the resulting medial axis. Third, the densities of the approximated medial axis points in different areas are adaptive to local free space volumes, based on the assumption that a coarser approximation in wide open area can still suf ce the requirements of the applications. We present theoretical results, bounding the error introduced by the approximation process. The algorithm has been implemented and experimental results are presented that illustrate its computational ef ciency and robustness.