Scale Filtered Euclidean Medial Axis

Abstract

Abstract. We propose an Euclidean medial axis filtering method which generates subsets of Euclidean medial axis were filtering rate is controlled by one parameter. The method is inspired by Miklos', Giesen's and Pauly's scale axis method which preserves important features of an input object from shape understanding point of view even if they are at different scales. Our method overcomes the most important drawback of scale axis: scale axis is not, in general, a subset of Euclidean medial axis. It is even not necessarily a subset of the original shape. The method and its properties are presented in 2D space but it can be easily extended to any dimension. Experimental verification and comparison with a few previously introduced methods are also included.

Scale filtered Euclidean medial axis and its hierarchy

“…This article extends the paper [21], which was limited to the algorithm that computes a single filtered medial axis. Additionally, we introduce here a method for the generation of full medial axes hierarchies, we prove its correctness, we propose a new methodology for comparison of medial axis filtering algorithms, we report more experiments and discuss some properties of our new methods.…”