Probing convex polygons with X-rays
SIAM Journal on Computing
On the computational complexity of reconstructing lattice sets from their x-rays
Discrete Mathematics
Determination of Q-convex sets by X-rays
Theoretical Computer Science
Characterization of Binary Patterns and Their Projections
IEEE Transactions on Computers
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
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We deal with the question of uniqueness, namely to decide when an unknown finite set of points in Z^2 is uniquely determined by its X-rays corresponding to a given set S of lattice directions. In Hajdu (2005) [11] proved that for any fixed rectangle A in Z^2 there exists a non trivial set S of four lattice directions, depending only on the size of A, such that any two subsets of A can be distinguished by means of their X-rays taken in the directions in S. The proof was given by explicitly constructing a suitable set S in any possible case. We improve this result by showing that in fact whole families of suitable sets of four directions can be found, for which we provide a complete characterization. This permits us to easily solve some related problems and the computational aspects.