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.
Domaines
Informatique [cs]Origine | Fichiers produits par l'(les) auteur(s) |
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