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Geometric Tomography with Topological Guarantees

Omid Amini 1, 2 Jean-Daniel Boissonnat 1, 2 Pooran Memari 1, 2
2 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We consider the problem of reconstructing a compact 3-manifold (with boundary) embedded in R3 from its cross- sections with a given set of cutting planes having arbitrary orientations. Under appropriate sampling conditions that are satisfied when the set of cutting planes is dense enough, we prove that the algorithm presented by Liu et al. preserves the homotopy type of the original object. Using the homotopy equivalence, we also show that the reconstructed object is homeomorphic (and isotopic) to the original object. This is the first time that shape reconstruction from cross-sections comes with such theoretical guarantees.
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https://hal.archives-ouvertes.fr/hal-00921910
Contributor : Jean-Daniel Boissonnat <>
Submitted on : Sunday, December 22, 2013 - 6:12:46 PM
Last modification on : Tuesday, September 22, 2020 - 3:53:35 AM

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Omid Amini, Jean-Daniel Boissonnat, Pooran Memari. Geometric Tomography with Topological Guarantees. Discrete and Computational Geometry, Springer Verlag, 2013, 50 (4), pp.821-856. ⟨10.1007/s00454-013-9531-z⟩. ⟨hal-00921910⟩

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