Reconstruction of Q-Convex Lattice Sets
We study the reconstruction of special lattice sets from X-rays when some convexity constraints are imposed on the sets. Two aspects are relevant for a satisfactory reconstruction: the unique determination of the set by its X-rays and the existence of a polynomial-time algorithm reconstructing the set from its X-rays. For this purpose we present the notion of Q-convex lattice sets for which there are unique determination by X-rays in suitable directions, and a polynomial-time reconstruction algorithm. After discussing these results, we show that many reconstructions of sets with convexity and connectivity constraints can be seen as particular cases of the algorithm reconstructing Q-convex lattice sets.
KeywordsPolynomial Time Lattice Direction Boolean Variable Regular Polygon Reconstruction Problem
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