Only distances are required to reconstruct submanifolds

Jean-Daniel Boissonnat 1 Ramsay Dyer 1 Arijit Ghosh 2 Steve Oudot 1
1 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : In this paper, we give the first algorithm that outputs a faithful reconstruction of a subman-ifold of Euclidean space without maintaining or even constructing complicated data structures such as Voronoi diagrams or Delaunay complexes. Our algorithm uses the witness complex and relies on the stability of power protection, a notion introduced in this paper. The complexity of the algorithm depends exponentially on the intrinsic dimension of the manifold, rather than the dimension of ambient space, and linearly on the dimension of the ambient space. Another interesting feature of this work is that no explicit coordinates of the points in the point sample is needed. The algorithm only needs the distance matrix as input, i.e., only distance between points in the point sample as input.
Type de document :
Article dans une revue
Computational Geometry, Elsevier, 2017, 66, pp.32 - 67. <10.1016/j.comgeo.2017.08.001>
Liste complète des métadonnées



https://hal.inria.fr/hal-01583086
Contributeur : Jean-Daniel Boissonnat <>
Soumis le : mercredi 6 septembre 2017 - 16:48:31
Dernière modification le : samedi 9 septembre 2017 - 01:07:02

Fichiers

only-distances.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh, Steve Oudot. Only distances are required to reconstruct submanifolds. Computational Geometry, Elsevier, 2017, 66, pp.32 - 67. <10.1016/j.comgeo.2017.08.001>. <hal-01583086>

Partager

Métriques

Consultations de
la notice

33

Téléchargements du document

11