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.
Brunetti, S., Daurat, A., Del Lungo, A. (2000). An Algorithm for Reconstructing Special Lattice Sets from Their Approximate X-rays. In Discrete Geometry for Computer Imagery (pp. 113-125).
An Algorithm for Reconstructing Special Lattice Sets from Their Approximate X-rays
BRUNETTI, SARA;
2000-01-01
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.
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https://hdl.handle.net/11365/26554
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