An Algorithm for Reconstructing Special Lattice Sets from Their Approximate X-Rays

Authors:
Sara Brunetti;Alain Daurat;Alberto Del Lungo
Affiliations:
-;-;-
Venue:
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Year:
2000

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Abstract

We study the problem of reconstructing finite subsets of the integer lattice Z2 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 Z2 having some convexity properties. This algorithm can be used for reconstructing convex subsets of Z2 from their exact X-rays in some sets of four prescribed lattice directions, or in any set of seven prescribed mutually nonparallel lattice directions.