The medial axis of closed bounded sets is Lipschitz stable with respect to the Hausdorff distance under ambient diffeomorphisms - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2023

The medial axis of closed bounded sets is Lipschitz stable with respect to the Hausdorff distance under ambient diffeomorphisms

Abstract

We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let S ⊆ R d be a fixed closed set that contains a bounding sphere. Consider the space of C 1,1 diffeomorphisms of R d 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 R d (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 C 2 manifolds under C 2 ambient diffeomorphisms.
Fichier principal
Vignette du fichier
springerFormat.pdf (1.26 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04297370 , version 1 (21-11-2023)

Identifiers

  • HAL Id : hal-04297370 , version 1

Cite

Hana Dal Poz Kouřimská, André Lieutier, Mathijs Wintraecken. The medial axis of closed bounded sets is Lipschitz stable with respect to the Hausdorff distance under ambient diffeomorphisms. 2023. ⟨hal-04297370⟩
16 View
10 Download

Share

Gmail Mastodon Facebook X LinkedIn More