New Algorithm for Medial Axis Transform of Plane Domain

In this paper, we present a new approximate algorithm for medial axis transform of a plane domain. The underlying philosophy of our approach is the localization idea based on the Domain Decomposition Lemma, which enables us to break up the complicated domain into smaller and simpler pieces. We then develop tree data structure and various operations on it to keep track of the information produced by the domain decomposition procedure. This strategy enables us to isolate various important points such as branch points and terminal points. Because our data structure guarantees the existence of such important points—in fact, our data structure is devised with this in mind—we can zoom in on those points. This makes our algorithm efficient. Our algorithm is a “from within” approach, whereas traditional methods use a “from-the-boundary” approach. This “from within” nature of our algorithm and the localization scheme help mitigate various instability phenomena, thereby making our algorithm reasonably robust.