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| -rw-r--r-- | biblio/bibliography.bib | 15 | ||||
| -rw-r--r-- | biblio/how_to_cite_gudhi.bib | 9 |
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diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib index 9fc01a5d..4940ec78 100644 --- a/biblio/bibliography.bib +++ b/biblio/bibliography.bib @@ -306,6 +306,21 @@ language={English}, bibsource = {DBLP, http://dblp.uni-trier.de} } +%------------------------------------------------------------------ +@article{tangentialcomplex2014, +author="Boissonnat, Jean-Daniel and Ghosh, Arijit", +title="Manifold Reconstruction Using Tangential Delaunay Complexes", +journal="Discrete {\&} Computational Geometry", +year="2014", +volume="51", +number="1", +pages="221--267", +abstract="We give a provably correct algorithm to reconstruct a k-dimensional smooth manifold embedded in d-dimensional Euclidean space. The 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 Boissonnat and Fl{\"o}totto (Comput. Aided Des. 36:161--174, 2004), Fl{\"o}totto (A coordinate system associated to a point cloud issued from a manifold: definition, properties and applications. Ph.D. thesis, 2003), Freedman (IEEE Trans. Pattern Anal. Mach. Intell. 24(10), 2002), and the technique of sliver removal by weighting the sample points (Cheng et al. in J. ACM 47:883--904, 2000). Differently from previous methods, we do not construct any subdivision of the d-dimensional ambient 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.", +issn="1432-0444", +doi="10.1007/s00454-013-9557-2", +url="http://dx.doi.org/10.1007/s00454-013-9557-2" +} + %BOOKS %------------------------------------------------------------------ @book{DBLP:tibkat_237559129, diff --git a/biblio/how_to_cite_gudhi.bib b/biblio/how_to_cite_gudhi.bib index 9a143487..7e1eac4f 100644 --- a/biblio/how_to_cite_gudhi.bib +++ b/biblio/how_to_cite_gudhi.bib @@ -85,4 +85,13 @@ , booktitle = "{GUDHI} User and Reference Manual" , url = "http://gudhi.gforge.inria.fr/doc/latest/group__spatial__searching.html" , year = 2016 +} + +@incollection{gudhi:Tangential complex +, author = "Cl\'ement Jamin" +, title = "Tangential complex" +, publisher = "{GUDHI Editorial Board}" +, booktitle = "{GUDHI} User and Reference Manual" +, url = "http://gudhi.gforge.inria.fr/doc/latest/group__tangential__complex.html" +, year = 2016 }
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