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Communication Dans Un Congrès Année : 2024

The Ultimate Frontier: An Optimality Construction for Homotopy Inference (Media Exposition)

Résumé

In our companion paper “Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds” we gave optimal bounds (in terms of the two one-sided Hausdorff distances) on a sample P of an input shape S (either manifold or general set with positive reach) such that one can infer the homotopy of S from the union of balls with some radius centred at P , both in Euclidean space and in a Riemannian manifold of bounded curvature. The construction showing the optimality of the bounds is not straightforward. The purpose of this video is to visualize and thus elucidate said construction in the Euclidean setting.
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hal-04628855 , version 1 (28-06-2024)

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Dominique Attali, Hana Dal Poz Kouřimská, Christopher Fillmore, Ishika Ghosh, André Lieutier, et al.. The Ultimate Frontier: An Optimality Construction for Homotopy Inference (Media Exposition). SoCG 2024 - 40th International Symposium on Computational Geometry, Jun 2024, Athènes, Greece. pp.87:1-87:6, ⟨10.4230/LIPIcs.SoCG.2024.87⟩. ⟨hal-04628855⟩
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