# Manifold Reconstruction using Tangential Delaunay Complexes

* Auteur correspondant
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We give a provably correct algorithm to reconstruct a $k$-dimensional manifold embedded in $d$-dimensional Euclidean space. Input to our algorithm is a point sample coming from an unknown manifold. Our approach is based on two main ideas~: the notion of tangential Delaunay complex, and the technique of sliver removal by weighting the sample points. Differently from previous methods, we do not construct any subdivision of the embedding $d$-dimensional space. As a result, the running time of our algorithm depends only linearly on the extrinsic dimension $d$ while it depends quadratically on the size of the input sample, and exponentially on the intrinsic dimension $k$. To the best of our knowledge, this is the first certified algorithm for manifold reconstruction whose complexity depends linearly on the ambient dimension. We also prove that for a dense enough sample the output of our algorithm is isotopic to the manifold and a close geometric approximation of the manifold.
Keywords :
Type de document :
Rapport
[Research Report] RR-7142, INRIA. 2009

Littérature citée [42 références]

https://hal.inria.fr/inria-00440337
Contributeur : Arijit Ghosh <>
Soumis le : vendredi 16 septembre 2011 - 14:56:24
Dernière modification le : samedi 27 janvier 2018 - 01:31:33
Document(s) archivé(s) le : dimanche 4 décembre 2016 - 20:20:16

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Reconstruction-report.pdf
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• HAL Id : inria-00440337, version 2

### Citation

Jean-Daniel Boissonnat, Arijit Ghosh. Manifold Reconstruction using Tangential Delaunay Complexes. [Research Report] RR-7142, INRIA. 2009. 〈inria-00440337v2〉

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