A Method for Feature Detection in Binary Tomography

  • Wagner Fortes
  • K. Joost Batenburg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7749)


Binary tomography deals with the problem of reconstructing a binary image from its projections. Depending on properties of the unkown original image, the constraint that the image is binary enables accurate reconstructions from a relatively small number of projection angles. Even in cases when insufficient information is available to compute an accurate reconstruction of the complete image, it may still be possible to determine certain features of it, such as straight boundaries, or homogeneous regions. In this paper, we present a computational technique for discovering the possible presence of such features in the unknown original image. We present numerical experiments, showing that it is often possible to accurately identify the presence of certain features, even without a full reconstruction.


Original Image Binary Tomography Homogeneous Region Feature Detection Probe Image 
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.
    Batenburg, K.J.: A network flow algorithm for reconstructing binary images from continuous X-rays. J. Math. Im. Vision 30(3), 231–248 (2008)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Batenburg, K.J., Sijbers, J.: Dart: a practical reconstruction algorithm for discrete tomography. IEEE Trans. Image Processing 20(9), 2542–2553 (2011)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Herman, G.T.: Fundamentals of Computerized Tomography: Image reconstruction from projections. Springer (2009)Google Scholar
  4. 4.
    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)zbMATHCrossRefGoogle Scholar
  5. 5.
    Alpers, A., Gritzmann, P.: On stability, error correction, and noise compensation in discrete tomography. SIAM Journal on Discrete Mathematics 20(1), 227–239 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Alpers, A., Brunetti, S.: Stability results for the reconstruction of binary pictures from two projections. Image and Vision Computing 25(10), 1599–1608 (2007)CrossRefGoogle Scholar
  7. 7.
    Van Dalen, B.: Stability results for uniquely determined sets from two directions in discrete tomography. Discrete Mathematics 309, 3905–3916 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Hajdu, L., Tijdeman, R.: Algebraic aspects of discrete tomography. J. Reine Angew. Math. 534, 119–128 (2001)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Herman, G.T., Kuba, A. (eds.): Discrete Tomography: Foundations, Algorithms and Applications. Birkhäuser, Boston (1999)zbMATHGoogle Scholar
  10. 10.
    Gara, M., Tasi, T.S., Balazs, P.: Learning connectedness and convexity of binary images from their projections. Pure Math. Appl. 20(1-2), 27–48 (2009)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Helgason, S.: The Radon transform. Birkhäuser, Boston (1980)zbMATHGoogle Scholar
  12. 12.
    Stolk, A., Batenburg, K.J.: An algebraic framework for discrete tomography: Revealing the structure of dependencies. SIAM J. Discrete Math. 24(3), 1056–1079 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Batenburg, K.J., Fortes, W., Hajdu, L., Tijdeman, R.: Bounds on the Difference between Reconstructions in Binary Tomography. In: Debled-Rennesson, I., Domenjoud, E., Kerautret, B., Even, P. (eds.) DGCI 2011. LNCS, vol. 6607, pp. 369–380. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    Kak, A.C., Slaney, M.: Principles of Computerized Tomographic Imaging. SIAM (2001)Google Scholar
  15. 15.
    Björck, Å.: Numerical methods for least square problems. SIAM, Linköping University, Sweden (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Wagner Fortes
    • 1
    • 2
  • K. Joost Batenburg
    • 1
    • 3
  1. 1.Centrum Wiskunde & InformaticaAmsterdamThe Netherlands
  2. 2.Mathematical InstituteLeiden UniversityThe Netherlands
  3. 3.Vision LabUniversity of AntwerpBelgium

Personalised recommendations