9 citations · 9 across the 7 of their papers we have counts for
10 papers
Manifolds of positive reach, differentiability, tangent variation, and attaining the reach
André Lieutier, Mathijs Wintraecken
This paper contains three main results. Firstly, we give an elementary proof of the following statement: Let be a (closed, in both the geometrical and topological sense of the…
A free lunch: manifolds of positive reach can be smoothed without decreasing the reach
Hana Dal Poz Kouřimská, André Lieutier, Mathijs Wintraecken
Assumptions on the reach are crucial for ensuring the correctness of many geometric and topological algorithms, including triangulation, manifold reconstruction and learning, homot…
When alpha-complexes collapse onto codimension-1 submanifolds
Dominique Attali, Mattéo Clémot, Bianca B. Dornelas +1
Given a finite set of points sampling an unknown smooth surface , our goal is to triangulate based solely on . Assuming $\m…
Hausdorff and Gromov-Hausdorff stable subsets of the medial axis
André Lieutier, Mathijs Wintraecken
In this paper we introduce a pruning of the medial axis called the -medial axis (). We prove that the -medial axis of a set is stable in a Gromov…
The medial axis of closed bounded sets is Lipschitz stable with respect to the Hausdorff distance under ambient diffeomorphisms
Hana Dal Poz Kouřimská, André Lieutier, Mathijs Wintraecken
We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let be (fixed) closed set (that contains a bounding sp…
Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds
Dominique Attali, Hana Dal Poz Kouřimská, Christopher Fillmore +4
In this article we extend and strengthen the seminal work by Niyogi, Smale, and Weinberger on the learning of the homotopy type from a sample of an underlying space. In their work,…