4 papers
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…
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…