Scale filtered Euclidean medial axis and its hierarchy

We propose an Euclidean medial axis filtering method which generates subsets of the Euclidean medial axis, where 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 the scale axis: the scale axis is not, in general, a subset of the Euclidean medial axis. It is even not necessarily a subset of the original shape. Moreover we propose a new method for the generation of a hierarchy of scale filtered Euclidean medial axes. We prove the correctness of the method. The methods and their properties are presented in 2D space but they can be easily extended to any dimension. Moreover, we propose a new methodology for the experimental comparison of medial axis filtering algorithms, based on five different quality criteria. This methodology allows one to compare algorithms independently on the meaning of their filtering parameter, which ensures a fair confrontation. The results of this confrontation with related previously introduced methods are included and discussed.