An algorithm reconstructing convex lattice sets
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 Z(2) 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 Z(2) from their X-rays in some suitable sets of four lattice directions or in any set of seven mutually nonparallel lattice directions. (C) 2003 Elsevier B.V. All rights reserved.
algorithms convexity lattice sets combinatorial problems discrete tomography