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Reconstruction in Different Classes of 2D Discrete Sets

  • Attila Kuba
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1568)

Abstract

The problem of reconstruction of two-dimensional discrete sets from their two projections is considered in different classes. The reconstruction algorithms and complexity results are summarized in the case of hv-convex sets, hv-convex polyominoes, hv-convex 8-connected sets, and directed h-convex sets. We show that the reconstruction algorithms used in the class of hv-convex 4-connected sets (polyominoes) can be used, with small modifications, for reconstructing hv-convex 8-connected sets. Finally, it is shown that the directed h-convex sets are uniquely reconstructible with respect to the row and column sum vectors.

References

  1. 1.
    Barcucci, E., Del Lungo, A., Nivat, M., Pinzani, R.: Reconstructing convex polyominoes from horizontal and vertical projections. Theor. Comput. Sci.155 (1996) 321–347zbMATHCrossRefGoogle Scholar
  2. 2.
    Barcucci, E., Del Lungo, A., Nivat, M., Pinzani, R.: Medians of polyominoes: A property for the reconstruction. Int. J. Imaging Systems and Techn.9 (1998)-Google Scholar
  3. 3.
    Brualdi, R.A.: Matrices of zeros and ones with fixed row and column sum vectors. Lin. Algebra and Its Appl.33 (1980) 159–231zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Brunetti, S., Del Lungo, A., Del Ristoro, F., Kuba, A., Nivat, M.: Reconstruction of 8-and 4-connected convex discrete sets from row and column projections. (1998) submitted for publicationGoogle Scholar
  5. 5.
    Chang, S.-K.: The reconstruction of binary patterns from their projections. Commun. ACM14 (1971) 21–25zbMATHCrossRefGoogle Scholar
  6. 6.
    Chang, S.-K.: Algorithm 445. Binary pattern reconstruction from projections. Commun. ACM 16 (1973) 185–186Google Scholar
  7. 7.
    Chang, S.-K., Shelton, G. L.: Two algorithms for multiple-view binary pattern reconstruction. IEEE Trans. Systems, Man and Cybern. SMC-1 (1971) 90–94Google Scholar
  8. 8.
    Chrobak, M., Dürr, C: Reconstructing hv-convex polyominoes from orthogonal projections. (1998) submitted for publicationGoogle Scholar
  9. 9.
    Crewe, A.V., Crewe, D.A.: Inexact reconstruction: Some improvements. Ultramicroscopy16 (1985) 33–40CrossRefGoogle Scholar
  10. 10.
    Del Lungo, A.: Polyominoes defined by two vectors. Theor. Comput. Sci.127 (1994) 187–198zbMATHCrossRefGoogle Scholar
  11. 11.
    Del Lungo, A., Nivat, M., Pinzani, R.: The number of convex polyominoes reconstructible from their orthogonal projections. Discrete Math. 157 (1996) 65–78zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Golomb, S.W.: Polyominoes. Schribner, New York (1965)Google Scholar
  13. 13.
    Herman, G.T., Kuba, A. (Eds.): Discrete Tomography, Special Issue. Int. J. Imaging Systems and Techn.9 (1998) No. 2/3Google Scholar
  14. 14.
    Huang, L.: The reconstruction of uniquely determined plane sets from two projections in discrete case. Techn. Report, University of Tokyo UTMS 95-29 (1995)Google Scholar
  15. 15.
    Kuba, A.: The reconstruction of two-directionally connected binary patterns from their two orthogonal projections. Comp. Vision, Graphics, and Image Proc.27 (1984) 249–265CrossRefGoogle Scholar
  16. 16.
    Prause, G.M.P., Onnasch, D.G.W.: Binary reconstruction of the heart chambers from biplane angiographic image sequences. IEEE Trans. Medical ImagingMI-15 (1996) 532–546CrossRefGoogle Scholar
  17. 17.
    Ryser, H.J.: Combinatorial properties of matrices of zeros and ones. Canad. J. Math.9 (1957) 371–377zbMATHMathSciNetGoogle Scholar
  18. 18.
    Schilferstein, A.R., Chien, Y.T.: Switching components and the ambiguity problem in the reconstruction of pictures from their projections. Pattern Recognition10 (1978) 327–340CrossRefGoogle Scholar
  19. 19.
    Woeginger, G.W.: The reconstruction of polyominoes from their orthogonal projections. Techn. Report, Technische Universität Graz 65 (1965)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Attila Kuba
    • 1
  1. 1.Department of Applied InformaticsJózsef Attila UniversitySzegedHungary

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