Grey Level Estimation for Discrete Tomography

  • K. J. Batenburg
  • W. van Aarle
  • J. Sijbers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)


Discrete tomography is a powerful approach for reconstructing images that contain only a few grey levels from their projections. Most theory and reconstruction algorithms for discrete tomography assume that the values of these grey levels are known in advance. In many practical applications, however, the grey levels are unknown and difficult to estimate. In this paper, we propose a semi-automatic approach for grey level estimation that can be used as a preprocessing step before applying discrete tomography algorithms. We present experimental results on its accuracy in simulation experiments.


Grey Level Penalty Function Reconstruction Algorithm Projection Data Projection Angle 
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.


  1. 1.
    Herman, G.T., Kuba, A. (eds.): Discrete Tomography: Foundations, Algorithms and Applications. Birkhäuser, Boston (1999)zbMATHGoogle Scholar
  2. 2.
    Herman, G.T., Kuba, A. (eds.): Advances in Discrete Tomography and its Applications. Birkhäuser, Boston (2007)Google Scholar
  3. 3.
    Schüle, T., Schnörr, C., Weber, S., Hornegger, J.: Discrete tomography by convex-concave regularization and d.c. programming. Discr. Appl. Math. 151, 229–243 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Batenburg, K.J.: A network flow algorithm for reconstructing binary images from continuous X-rays. J. Math. Im. Vision 30(3), 231–248 (2008)MathSciNetGoogle Scholar
  5. 5.
    Liao, H.Y., Herman, G.T.: A coordinate ascent approach to tomographic reconstruction of label images from a few projections. Discr. Appl. Math. 151, 184–197 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Alpers, A., Poulsen, H.F., Knudsen, E., Herman, G.T.: A discrete tomography algorithm for improving the quality of 3DXRD grain maps. J. Appl. Crystall. 39, 582–588 (2006)CrossRefGoogle Scholar
  7. 7.
    Batenburg, K., Bals, S., Sijbers, J., et al.: 3D imaging of nanomaterials by discrete tomography. Ultramicroscopy 109, 730–740 (2009)CrossRefGoogle Scholar
  8. 8.
    Gilbert, P.: Iterative methods for the three-dimensional reconstruction of an object from projections. J. Theoret. Biol. 36, 105–117 (1972)CrossRefGoogle Scholar
  9. 9.
    Gregor, J., Benson, T.: Computational analysis and improvement of SIRT. IEEE Trans. Medical Imaging 27(7), 918–924 (2008)CrossRefGoogle Scholar
  10. 10.
    Brent, R.P.: Algorithms for minimization without derivatives. Prentice-Hall, Englewood Cliffs (1973)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • K. J. Batenburg
    • 1
  • W. van Aarle
    • 1
  • J. Sijbers
    • 1
  1. 1.IBBT - Vision LabUniversity of AntwerpBelgium

Personalised recommendations