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| HAL: hal-00487884, version 1 |
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| Symposium on Computational Geometry, Snowbird : United States (2010) |
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| Geometric Tomography With Topological Guarantees |
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| Omid Amini 1, 2Jean-Daniel Boissonnat 1, 2 |
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| (2010-06-14) |
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| 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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| 1: | Département de Mathématiques et Applications (DMA) |
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CNRS : UMR8553 – Ecole Normale Supérieure de Paris - ENS Paris |
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| 2: | GEOMETRICA (INRIA Sophia Antipolis / INRIA Saclay - Ile de France) |
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INRIA |
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| Subject | : | Computer Science/Computational Geometry |
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| Computational geometry – Computational topology – surface reconstruction – geometric tomography |
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| hal-00487884, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00487884/en/ | |
| oai:hal.archives-ouvertes.fr:hal-00487884 | |
| From: Jean-Daniel Boissonnat | |
| Submitted on: Monday, 31 May 2010 14:12:08 | |
| Updated on: Monday, 31 May 2010 15:28:46 | |
