Topological maps and robust hierarchical Euclidean skeletons in cubical complexes

Skeletons are notoriously sensitive to contour noise, and an effective filtering scheme is needed in any practical situation, where skeletons are involved. In this article, we introduce a new discrete framework that allows us to define and compute families of filtered Euclidean skeletons, in 2D as well as in 3D or higher dimensions. We prove several properties of our skeletonization scheme, in particular the preservation of topological characteristics and the stability with respect to parameter changes.