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Séminaire Calcul Formel

Manifold reconstruction based on Coxeter triangulations of the ambient Euclidean space

by Siargey Kachanovich (Inria Sophia Antipolis)

jeudi 14 juin 2018 de au (Europe/Paris)
at Bâtiment XLIM ( Salle XR203 )
We present an experimental algorithm for manifold reconstruction, which takes as input a point cloud sampled from a manifold with positive reach and outputs a simplicial complex which is homotopy equivalent to the manifold. The time complexity and the space complexity are polynomial in ambient dimension and depend on the intrinsic dimension $k$ of the manifold as $O(2^k)$, which improves the $O(2^{k^2})$ time and space complexities of tangential complex. The algorithm is based on Coxeter triangulations, space-filling triangulations generated by a single simplex via consecutive flips. We have seen in experiments that a series of collapses can be applied to the output of the first algorithm to find a triangulation of the manifold.