Scale filtered Euclidean medial axis and its hierarchy

• We propose a new methodology for Euclidean medial axis filtering.
• We propose a new methodology for generation of full hierarchy of scale medial axes.
• We propose a new methodology which allows for a fair comparison of medial axis filtering algorithms.
• Series of experiments show that our algorithm gives better or similar results, compared to the best related methods.

We propose an Euclidean medial axis filtering method which generates subsets of the Euclidean medial axis in discrete grids, 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. There is an important difference between the axis produced by our method and the scale axis. Contrarily to ours, 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. In addition, 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.