An algorithm reconstructing convex lattice sets

Sara Brunetti (1) , Alain Daurat (2, 3)

1 DSMI - Department of Mathematics and Computer Science / Dipartimento di Scienze Matematiche e Informatiche "Roberto Magari"
2 LLAIC1 - Laboratoire de Logique, Algorithmique et Informatique
3 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection

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.

Mots clés: algorithms; combinatorial problems; convexity; discrete tomography; lattice sets

Domaines: Mathématique discrète [cs.DM]

Sara Brunetti, Alain Daurat. An algorithm reconstructing convex lattice sets. Theoretical Computer Science, 2003, 304, pp.35-57. ⟨10.1016/S0304-3975(03)00050-1⟩. ⟨hal-00023033⟩