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| HAL : hal-00023034, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Pure Mathematics and Applications 11 (2000) 409-425 |
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| Approximate X-rays reconstruction of special lattice sets |
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| Sara Brunetti 1Alain Daurat 2 |
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| (2000) |
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| Sometimes the inaccuracy of the measurements of the X-rays can give rise to an inconsistent reconstruction problem. In this paper we address the problem of reconstructing special lattice sets in Z2 from their approximate X-rays in a finite number of prescribed lattice directions. The class of "strongly Q-convex sets" is taken into consideration and a polynomial time algorithm for reconstructing members of that class with line sums having possibly some bounded differences with the given X-ray values is provided. In particular, when these differences are zero, the algorithm exactly reconstructs any set. As a result, this algorithm can also be used to reconstruct convex subsets of Z2 from their exact X-rays in a finite set of suitable prescribed lattice directions. |
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| 1 : | Dipartimento di Sistemi e Informatica |
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Università degli studi di Firenze |
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| 2 : | Laboratoire de Logique, Algorithmique et Informatique (LLAIC1) |
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Université d'Auvergne - Clermont-Ferrand I |
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| 3 : | Dipartimento di Matematica |
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Università degli studi di Siena |
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| Domaine | : | Informatique/Mathématique discrète |
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| algorithms – combinatorial problems – discrete tomography – lattice sets – convexity – X-rays |
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| hal-00023034, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00023034/fr/ | |
| oai:hal.archives-ouvertes.fr:hal-00023034_v1 | |
| Contributeur : Alain Daurat | |
| Soumis le : Mercredi 19 Avril 2006, 13:30:22 | |
| Dernière modification le : Mercredi 19 Avril 2006, 13:53:33 | |
