Reconstruction and Enumeration of hv-Convex Polyominoes with Given Horizontal Projection

  • Norbert Hantos
  • Péter Balázs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8258)


Enumeration and reconstruction of certain types of polyominoes, according to several parameters, are frequently studied problems in combinatorial image processing. Polyominoes with fixed projections play an important role in discrete tomography. In this paper, we provide a linear-time algorithm for reconstructing hv-convex polyominoes with minimal number of columns satisfying a given horizontal projection. The method can be easily modified to get solutions with any given number of columns. We also describe a direct formula for calculating the number of solutions with any number of columns, and a recursive formula for fixed number of columns.


discrete tomography reconstruction enumeration polyomino hv-convexity 


  1. 1.
    Anagnostopoulos, C.-N.E., Anagnostopoulos, I.E., Psoroulas, I.D., Loumos, V., Kayafas, E.: License plate recognition from still images and video sequences: A survey. IEEE Trans. on Intelligent Transportation Systems 9(3), 377–391 (2008)CrossRefGoogle Scholar
  2. 2.
    Barcucci, E., Del Lungo, A., Nivat, M., Pinzani, R.: Medians of polyominoes: A property for the reconstruction. Int. J. Imaging Syst. and Techn. 9, 69–77 (1998)CrossRefGoogle Scholar
  3. 3.
    Del Lungo, A.: Polyominoes defined by two vectors. Theor. Comput. Sci. 127, 187–198 (1994)CrossRefzbMATHGoogle Scholar
  4. 4.
    Del Lungo, A., Duchi, E., Frosini, A., Rinaldi, S.: Enumeration of convex polyominoes using the ECO method. In: Discrete Mathematics and Theoretical Computer Science, Proceedings, pp. 103–116 (2003)Google Scholar
  5. 5.
    Del Lungo, A., Nivat, M., Pinzani, R.: The number of convex polyominoes recostructible from their orthogonal projections. Discrete Math. 157, 65–78 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Gessel, I.: On the number of convex polyominoes. Ann. Sci. Math. Québec 24, 63–66 (2000)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Golomb, S.W.: Polyominoes. Charles Scriber’s Sons, New York (1965)Google Scholar
  8. 8.
    Herman, G.T., Kuba, A. (eds.): Discrete Tomography: Foundations, Algorithms and Applications. Birkhäuser, Boston (1999)zbMATHGoogle Scholar
  9. 9.
    Herman, G.T., Kuba, A. (eds.): Advances in Discrete Tomography and its Applications. Birkhäuser, Boston (2007)zbMATHGoogle Scholar
  10. 10.
    dos Santos, R.P., Clemente, G.S., Ren, T.I., Calvalcanti, G.D.C.: Text line segmentation based on morphology and histogram projection. In: Proceedings of the 10th International Conference on Document Analysis and Recognition, pp. 651–655 (2009)Google Scholar
  11. 11.
    Vezzani, R., Baltieri, D., Cucchiara, R.: HMM based action recognition with projection histogram features. In: Ünay, D., Çataltepe, Z., Aksoy, S. (eds.) ICPR 2010. LNCS, vol. 6388, pp. 286–293. Springer, Heidelberg (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Norbert Hantos
    • 1
  • Péter Balázs
    • 1
  1. 1.Department of Image Processing and Computer GraphicsUniversity of SzegedSzegedHungary

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