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.
This work is partially supported by MURST project: Modelli di calcolo innovativi: metodi sintattici e combinatori. and by the University Siena project: Problemi Inversi Discreti: Tomografia Discreta
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Brunetti, S., Daurat, A., Del Lungo, A. (2000). An Algorithm for Reconstructing Special Lattice Sets from Their Approximate X-Rays. In: Borgefors, G., Nyström, I., di Baja, G.S. (eds) Discrete Geometry for Computer Imagery. DGCI 2000. Lecture Notes in Computer Science, vol 1953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44438-6_10
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