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pro vyhledávání: '"Lieutier, André"'
Given a finite set of points $P$ sampling an unknown smooth surface $\mathcal{M} \subseteq \mathbb{R}^3$, our goal is to triangulate $\mathcal{M}$ based solely on $P$. Assuming $\mathcal{M}$ is a smooth orientable submanifold of codimension 1 in $\ma
Externí odkaz:
http://arxiv.org/abs/2411.10388
Autor:
Lieutier, André, Wintraecken, Mathijs
In this paper we introduce a pruning of the medial axis called the $(\lambda,\alpha)$-medial axis ($\textrm{ax}_\lambda^\alpha $). We prove that the $(\lambda,\alpha)$-medial axis of a set $K$ is stable in a Gromov-Hausdorff sense under weak assumpti
Externí odkaz:
http://arxiv.org/abs/2303.04014
We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let $\mathcal{S} \subseteq \mathbb{R}^d$ be (fixed) closed set (that contains a bounding sphere). Consider the space of $C^{1,1}$ diffeomorphisms of $\mathbb{R}^
Externí odkaz:
http://arxiv.org/abs/2212.01118
Autor:
Attali, Dominique, Kouřimská, Hana Dal Poz, Fillmore, Christopher, Ghosh, Ishika, Lieutier, André, Stephenson, Elizabeth, Wintraecken, Mathijs
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, Niyogi, Smale, and Weinberger studied samples of $C^2$ manifolds with
Externí odkaz:
http://arxiv.org/abs/2206.10485
Autor:
Attali, Dominique, Lieutier, André
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 we have as input a simplicial complex K that approximates the submanifo
Externí odkaz:
http://arxiv.org/abs/2203.06008
Autor:
Attali, Dominique, Lieutier, André
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 variant of the tangential Delaunay complex (TDC) introduced by Boisson
Externí odkaz:
http://arxiv.org/abs/2203.05943
Autor:
Attali, Dominique, Lieutier, André
Publikováno v:
Discrete & Computational Geometry: Volume 54, Issue 4 (2015), Page 798-825
Given a set of points that sample a shape, the Rips complex of the data points is often used in machine-learning to provide an approximation of the shape easily-computed. It has been proved recently that the Rips complex captures the homotopy type of
Externí odkaz:
http://arxiv.org/abs/1304.3680
We address the problem of curvature estimation from sampled compact sets. The main contribution is a stability result: we show that the gaussian, mean or anisotropic curvature measures of the offset of a compact set K with positive $\mu$-reach can be
Externí odkaz:
http://arxiv.org/abs/0812.1390
Akademický článek
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Publikováno v:
In Computational Geometry: Theory and Applications September 2015 48(8):606-621
