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Reconstruction of Q-Convex Lattice Sets

  • S. Brunetti
  • A. Daurat
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

We study the reconstruction of special lattice sets from X-rays when some convexity constraints are imposed on the sets. Two aspects are relevant for a satisfactory reconstruction: the unique determination of the set by its X-rays and the existence of a polynomial-time algorithm reconstructing the set from its X-rays. For this purpose we present the notion of Q-convex lattice sets for which there are unique determination by X-rays in suitable directions, and a polynomial-time reconstruction algorithm. After discussing these results, we show that many reconstructions of sets with convexity and connectivity constraints can be seen as particular cases of the algorithm reconstructing Q-convex lattice sets.

Keywords

Polynomial Time Lattice Direction Boolean Variable Regular Polygon Reconstruction Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • S. Brunetti
    • 1
  • A. Daurat
    • 2
  1. 1.Dipartimento di Scienze Matematiche e InformaticheUniversità di SienaSienaItaly
  2. 2.LSIIT UMR 7005 CNRS, Pöle API, Université Louis Pasteur (Strasbourg 1)Illkirch-GraffenstadenFrance

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