HAL : hal-00023030, version 1

DOI : 10.1016/j.tcs.2004.10.001

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Theoretical Computer Science 332 (2005) 19-45

Determination of Q-convex sets by X-rays

Alain Daurat 1

(2005)

In this paper, the problem of the determination of lattice sets from X-rays is studied. We define the class of Q-convex sets along a set D of directions which generalizes classical lattice convexity and we prove that for any D, the X-rays along D determine all the convex sets if and only if it determines all the Q-convex sets along D. As a consequence, any algorithm which reconstructs Q-convex sets from X-rays can be used to reconstruct convex lattice sets from X-rays along directions which provide uniqueness. This gives a constructive answer to the discrete version of Hammer's X-ray problem.

1 :	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 : Discrete tomography – Convexity – Lattice sets – X-rays

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Contributeur : Alain Daurat <>

Soumis le : Mercredi 19 Avril 2006, 11:39:54

Dernière modification le : Mercredi 19 Avril 2006, 11:47:49