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.
Domaines
Informatique [cs]
Fichier principal
LIPIcs.SoCG.2024.87.pdf (3.34 Mo)
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SoCGVideosupplement.pdf (15.78 Mo)
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Origine | Fichiers produits par l'(les) auteur(s) |
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Commentaire | Supplementary material |
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