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

  • Sara Brunetti
  • Alain Daurat
  • Alberto Del Lungo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1953)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Sara Brunetti
    • 1
  • Alain Daurat
    • 2
  • Alberto Del Lungo
    • 3
  1. 1.Dipartimento di Sistemi e InformaticaFirenzeItaly
  2. 2.Laboratoire de Logique et d’Informatique de Clermont-1 (LLAIC1)Ensemble Universitaire des CézeauxAubière CedexFrance
  3. 3.Dipartimento di MatematicaSienaItaly

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