An Algorithm for Reconstructing Special Lattice Sets from Their Approximate X-Rays
نویسندگان
چکیده
We study the problem of reconstructing finite subsets of the integer lattice Z from their approximate X-rays in a finite number of prescribed lattice directions. We provide a polynomial-time algorithm for reconstructing Q-convex sets from their “approximate” X-rays. A Qconvex set is a special subset of Z having some convexity properties. This algorithm can be used for reconstructing convex subsets of Z from their exact X-rays in some sets of four prescribed lattice directions, or in any set of seven prescribed mutually nonparallel lattice directions.
منابع مشابه
Approximate X-rays reconstruction of special lattice sets
Sometimes the inaccuracy of the measurements of the X-rays can give rise to an inconsistent reconstruction problem. In this paper we address the problem of reconstructing special lattice sets in Z from their approximate X-rays in a finite number of prescribed lattice directions. The class of “strongly Q-convex sets” is taken into consideration and a polynomial time algorithm for reconstructing ...
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تاریخ انتشار 2000