Scale filtered Euclidean medial axis and its hierarchy

Abstract

International audienceWe 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

Cosine-Pruned Medial Axis: A New Method for Isometric Equivariant and Noise-Free Medial Axis Extraction

“…The SAT involves scaling the EDT and computing the medial axis of the original un-scaled shape as the medial axis of the scaled one. However, in [45], the authors show that the SAT is not necessarily a subset of the medial axis of the original shape. In another work, [45] propose the Scale Filtered Euclidean Medial Axis (SFEMA), a solution to the stated problem with the SAT that guarantees a better approximation by including additional constraints on the scaled EDT.…”

“…SAT [54] Scale Axis Transform s: scale factor to resize MAT (Ω). SFEMA [45] Scale Filtered Euclidean Medial Axis s: scale factor to all balls in the MAT (Ω). Poisson skel.…”

“…Many medial axis pruning methods depend on hyperparameters to accurately estimate the medial axis [43]- [45], [54]. These parameters usually have a physical meaning in the context of the object whose medial axis they seek to estimate.…”

Cosine-Pruned Medial Axis: A new method for isometric equivariant and noise-free medial axis extraction

“…The most common methods to extract the medial axis are those based on the distance transform. Within these methods, the medial axis is computed as the ridges of the distance transform inside the object [3,40,2,22,14,35,41]. This interpretation of the medial axis follows definition 1, because the centers of the maximal balls are located on points x along the ridgeline of the distance transform, and the radius of the balls correspond to the distance value at x.…”

“…The SAT involves scaling the distance transform and computing the medial axis of the original un-scaled shape as the medial axis of the scaled one. However, in [35], the authors show that the SAT is not necessarily a subset of the medial axis of the original shape. Instead, they propose a solution that guarantees a better approximation by including additional constraints on the scaled distance transform.…”