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Reconstruction of Discrete Sets from Three or More X-Rays

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Algorithms and Complexity (CIAC 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1767))

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Abstract

The problem of reconstructing a discrete set from its X-rays in a finite number of prescribed directions is NP-complete when the number of prescribed directions is greater than two. In this paper, we consider an interesting subclass of discrete sets having some connectivity and convexity properties and we provide a polynomial-time algorithm for reconstructing a discrete set of this class from its X-rays in directions (1, 0), (0, 1) and (1, 1). This algorithm can be easily extended to contexts having more than three X-rays.

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Author information

Authors and Affiliations

  1. Dipartimento di Sistemi e Informatica, Università di Firenze, Via Lombroso 6/17, 50134, Firenze, Italy

    Elena Barcucci & Sara Brunetti

  2. Dipartimento di Matematica, Università di Siena, Via del Capitano 15, 53100, Siena, Italy

    Alberto Del Lungo

  3. LIAFA, Institut Blaise Pascal, Université “Denis Diderot”, 2 Place Jussieu 75251, Paris Cedex 05, France

    Maurice Nivat

Authors
  1. Elena Barcucci
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  2. Sara Brunetti
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  3. Alberto Del Lungo
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  4. Maurice Nivat
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rome “La Sapienza”, Via Salaria 113, 00198, Rome, Italy

    Giancarlo Bongiovanni  & Rossella Petreschi  & 

  2. Department of Mathematics, University of Rome “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Rome, Italy

    Giorgio Gambosi

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© 2000 Springer-Verlag Berlin Heidelberg

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Barcucci, E., Brunetti, S., Del Lungo, A., Nivat, M. (2000). Reconstruction of Discrete Sets from Three or More X-Rays. In: Bongiovanni, G., Petreschi, R., Gambosi, G. (eds) Algorithms and Complexity. CIAC 2000. Lecture Notes in Computer Science, vol 1767. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46521-9_17

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  • DOI: https://doi.org/10.1007/3-540-46521-9_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67159-6

  • Online ISBN: 978-3-540-46521-8

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