The Medial Axis of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms - Archive ouverte HAL
Communication Dans Un Congrès Année : 2024

The Medial Axis of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms

Résumé

We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let S ⊆ Rd be a fixed closed set that contains a bounding sphere. That is, the bounding sphere is part of the set S. Consider the space of C1,1 diffeomorphisms of Rd to itself, which keep the bounding sphere invariant. The map from this space of diffeomorphisms (endowed with a Banach norm) to the space of closed subsets of Rd (endowed with the Hausdorff distance), mapping a diffeomorphism F to the closure of the medial axis of F (S), is Lipschitz. This extends a previous stability result of Chazal and Soufflet on the stability of the medial axis of C2 manifolds under C2 ambient diffeomorphisms.
Fichier principal
Vignette du fichier
LIPIcs.SoCG.2024.69.pdf (1.54 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04628829 , version 1 (28-06-2024)

Identifiants

Citer

Hana Dal Poz Kouřimská, André Lieutier, Mathijs Wintraecken. The Medial Axis of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms. SoCG 2024 - 40th International Symposium on Computational Geometry, Jun 2024, Athens, Greece. ⟨10.4230/LIPIcs.SoCG.2024.69⟩. ⟨hal-04628829⟩
20 Consultations
16 Téléchargements

Altmetric

Partager

More