An algorithm reconstructing convex lattice sets

Authors:
Sara Brunetti;Alain Daurat
Affiliations:
Dipartimento di Scienze Matematiche ed Informatiche, Università di Siena, Via Del Capitano 15, 53100 Siena, Italy;LLAIC1. I.U.T. Informatique, Ensemble Universitaire des Cézeaux, B.P. no 86, 63172 Aubière Cedex, France
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

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 nonparallel lattice directions.