HAL : hal-00023033, version 1

DOI : 10.1016/S0304-3975(03)00050-1

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Theoretical Computer Science 304 (2003) 35-57

An algorithm reconstructing convex lattice sets

Sara Brunetti 1, Alain Daurat 2, 3

(2003)

In this paper, we study the problem of reconstructing special lattice sets from X-rays in a finite set of prescribed directions. We present the class of "Q-convex" sets which is a new class of subsets of Z2 having a certain kind of weak connectedness. The main result of this paper is a polynomial-time algorithm solving the reconstruction problem for the "Q-convex" sets. These sets are uniquely determined by certain finite sets of directions. As a result, this algorithm can be used for reconstructing convex subsets of Z2 from their X-rays in some suitable sets of four lattice directions or in any set of seven mutually non parallel lattice directions.

1 :	Department of Mathematics and Computer Science / Dipartimento di Scienze Matematiche e Informatiche "Roberto Magari" (DSMI)
	Università degli studi di Siena – University of Siena
2 :	Laboratoire de Logique, Algorithmique et Informatique (LLAIC1)
	Université d'Auvergne - Clermont-Ferrand I
3 :	Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection (LSIIT)
	CNRS : UMR7005 – Université Louis Pasteur - Strasbourg I

Domaine

:

Informatique/Mathématique discrète

Mots Clés : algorithms – combinatorial problems – convexity – discrete tomography – lattice sets

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Contributeur : Alain Daurat <>

Soumis le : Mercredi 19 Avril 2006, 12:39:52

Dernière modification le : Mardi 23 Mars 2010, 12:22:40