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Characterization of { − 1,0, + 1} Valued Functions in Discrete Tomography under Sets of Four Directions

  • Sara Brunetti
  • Paolo Dulio
  • Carla Peri
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6607)

Abstract

In this paper we use the algebraic approach to Discrete Tomography introduced by Hajdu and Tijdeman to study functions f:ℤ2→{ − 1,0, + 1} which have zero line sums along the lines corresponding to certain sets of four directions.

Keywords

Discrete Tomography X-ray Unique Reconstruction Generating Function 

References

  1. 1.
    Hajdu, L., Tijdeman, R.: Algebraic aspects of discrete tomography. J. Reine Angew. Math. 534, 119–128 (2001)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Hajdu, L.: Unique reconstruction of bounded sets in discrete tomography. Electron. Notes Discrete Math. 20, 15–25 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Kuba, A., Herman, G.T.: Discrete tomography. Appl. Numer. Harmon. Anal. Birkhäuser, Boston (1999)zbMATHGoogle Scholar
  4. 4.
    Kuba, A., Herman, G.T.: Advances in Discrete Tomography and Its Applications. Appl. Numer. Harmon. Anal. Birkhäuser, Boston (2007)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Sara Brunetti
    • 1
  • Paolo Dulio
    • 2
  • Carla Peri
    • 3
  1. 1.Dipartimento di Scienze Matematiche e InformaticheUniversità di SienaSienaItaly
  2. 2.Dipartimento di Matematica “F. Brioschi”Politecnico di MilanoMilanoItaly
  3. 3.Università Cattolica S. C.PiacenzaItaly

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