Hierarchic Euclidean skeletons in cubical complexes
Résumé
In the 90s, several authors introduced the notion of a hierarchic family of 2D Euclidean skeletons, evolving smoothly under the control of a filtering parameter. We provide in this paper a discrete framework which formalizes and generalizes this notion, in particular to higher dimensions. This framework allows us to propose a new skeletonization scheme and to prove several important properties, such as topology preservation and stability w.r.t. parameter changes.