9 citations · 9 across the 7 of their papers we have counts for
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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,…
Flat Delaunay Complexes for Homeomorphic Manifold Reconstruction
Dominique Attali, André Lieutier
Given a smooth submanifold of the Euclidean space, a finite point cloud and a scale parameter, we introduce a construction which we call the flat Delaunay complex (FDC). This is a…
Delaunay-like Triangulation of Smooth Orientable Submanifolds by L1-Norm Minimization
Dominique Attali, André Lieutier
In this paper, we study the shape reconstruction problem, when the shape we wish to reconstruct is an orientable smooth d-dimensional submanifold of the Euclidean space. Assuming w…