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COMPGEOM
2010
ACM

Manifold reconstruction using tangential Delaunay complexes

13 years 7 months ago
Manifold reconstruction using tangential Delaunay complexes
We give a provably correct algorithm to reconstruct a kdimensional 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 defined in [6, 19, 20], and the technique of sliver removal by weighting the sample points [13]. 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 ma...
Jean-Daniel Boissonnat, Arijit Ghosh
Added 15 Aug 2010
Updated 15 Aug 2010
Type Conference
Year 2010
Where COMPGEOM
Authors Jean-Daniel Boissonnat, Arijit Ghosh
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