Only distances are required to reconstruct submanifolds - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Computational Geometry Year : 2017

Only distances are required to reconstruct submanifolds

Jean-Daniel Boissonnat
  • Function : Author
  • PersonId : 935453
Ramsay Dyer
  • Function : Author
  • PersonId : 962563
Steve Y. Oudot
  • Function : Author
  • PersonId : 845393

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.
Vignette du fichier
only-distances-fig.png (94.31 Ko) Télécharger le fichier Fichier principal
Vignette du fichier
only-distances.pdf (895.98 Ko) Télécharger le fichier
Vignette du fichier
only-distances-fig.jpg (41.14 Ko) Télécharger le fichier
Format : Figure, Image
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Format : Figure, Image
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01583086 , version 1 (06-09-2017)

Identifiers

Cite

Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh, Steve Y. Oudot. Only distances are required to reconstruct submanifolds. Computational Geometry, 2017, 66, pp.32 - 67. ⟨10.1016/j.comgeo.2017.08.001⟩. ⟨hal-01583086⟩
165 View
253 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More