Geometric Tomography With Topological Guarantees

Omid Amini; Jean-Daniel Boissonnat; Pooran Memari

hal-00487884, version 1

Geometric Tomography With Topological Guarantees

Omid Amini () ^1, 2, Jean-Daniel Boissonnat () ^1, 2, Pooran Memari () ^1, 2

Symposium on Computational Geometry (2010) 200

Résumé : 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.

1 : Département de Mathématiques et Applications (DMA)
CNRS : UMR8553 – Ecole normale supérieure de Paris - ENS Paris
2 : GEOMETRICA (INRIA Sophia Antipolis / INRIA Saclay - Ile de France)
INRIA

hal-00487884, version 1
http://hal.archives-ouvertes.fr/hal-00487884
oai:hal.archives-ouvertes.fr:hal-00487884
Contributeur : Jean-Daniel Boissonnat <>
Soumis le : Lundi 31 Mai 2010, 14:12:08
Dernière modification le : Lundi 31 Mai 2010, 15:28:46

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