--- res: bibo_abstract: - In this paper we introduce a pruning of the medial axis called the (λ,α)-medial axis (axλα). We prove that the (λ,α)-medial axis of a set K is stable in a Gromov-Hausdorff sense under weak assumptions. More formally we prove that if K and K′ are close in the Hausdorff (dH) sense then the (λ,α)-medial axes of K and K′ are close as metric spaces, that is the Gromov-Hausdorff distance (dGH) between the two is 1/4-Hölder in the sense that dGH (axλα(K),axλα(K′)) ≲ dH(K,K′)1/4. The Hausdorff distance between the two medial axes is also bounded, by dH (axλα(K),λα(K′)) ≲ dH(K,K′)1/2. These quantified stability results provide guarantees for practical computations of medial axes from approximations. Moreover, they provide key ingredients for studying the computability of the medial axis in the context of computable analysis.@eng bibo_authorlist: - foaf_Person: foaf_givenName: André foaf_name: Lieutier, André foaf_surname: Lieutier - foaf_Person: foaf_givenName: Mathijs foaf_name: Wintraecken, Mathijs foaf_surname: Wintraecken foaf_workInfoHomepage: http://www.librecat.org/personId=307CFBC8-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-7472-2220 bibo_doi: 10.1145/3564246.3585113 dct_date: 2023^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/9781450399135 dct_language: eng dct_publisher: Association for Computing Machinery@ dct_title: Hausdorff and Gromov-Hausdorff stable subsets of the medial axis@ ...