Advertisement

Smoothing Filters in the DART Algorithm

  • Antal Nagy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8466)

Abstract

We propose new variants of the Discrete Algebraic Reconstruction Technique (DART) with a combined filtering technique. We also set up a test framework to investigate the influence of the filters for different number of sources and noise level in case of various parameters. Our results are produced by performing numerous reconstructions on the test data set. The reconstructed images were evaluated by locally using relatives mean error (RME) and globally by an ordered ranking system. The achievements are subjected and discussed. Finally we also suggest a filter parameter combination which gives a way to improve the quality of the DART reconstruction algorithm.

Keywords

Discrete tomography Reconstruction quality DART Filtering Non-destructive testing 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alpers, A., Poulsen, H.F., Knudsen, E., Herman, G.T.: A discrete tomography algorithm for improving the quality of three-dimensional X-ray diffraction grain maps. Journal of Applied Crystallography 39(4), 582–588 (2006)CrossRefGoogle Scholar
  2. 2.
    Batenburg, K.J.: A network flow algorithm for reconstructing binary images from continuous x-rays. Journal of Mathematical Imaging and Vision 30(3), 231–248 (2008)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Batenburg, K.J., Sijbers, J.: Dart: A fast heuristic algebraic reconstruction algorithm for discrete tomography. In: IEEE International Conference on Image Processing, ICIP 2007, vol. 4, pp. IV–133–IV–136 (2007)Google Scholar
  4. 4.
    Batenburg, K., Sijbers, J.: Dart: A practical reconstruction algorithm for discrete tomography. IEEE Transactions on Image Processing 20(9), 2542–2553 (2011)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Chaudhury, K.N.: Acceleration of the shiftable O(1) algorithm for bilateral filtering and non-local means. CoRR abs/1203.5128 (2012)Google Scholar
  6. 6.
    Chaudhury, K., Sage, D., Unser, M.: Fast O(1) bilateral filtering using trigonometric range kernels. IEEE Transactions on Image Processing 20(12), 3376–3382 (2011)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Hantos, N., Balázs, P.: Image enhancement by median filters in algebraic reconstruction methods: An experimental study. In: Bebis, G., et al. (eds.) ISVC 2010, Part III. LNCS, vol. 6455, pp. 339–348. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  8. 8.
    Herman, G.T.: Fundamentals of Computerized Tomography: Image Reconstruction from Projections, 2nd edn. Springer Publishing Company, Incorporated (2009)Google Scholar
  9. 9.
    Herman, G.T., Kuba, A.: Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis). Birkhauser (2007)Google Scholar
  10. 10.
    Kuba, A., Herman, G.T., Matej, S., Todd-Pokropek, A.: Medical applications of discrete tomography. In: Discrete Mathematical Problems with Medical Applications, DIMACS Workshop, DIMACS Center, Princeton, NJ, USA, December 8-10, 2000, pp. 195–208. AMS, American Mathematical Society, Providence (2000)Google Scholar
  11. 11.
    Maestre-Deusto, F., Scavello, G., Pizarro, J., Galindo, P.: Adart: An adaptive algebraic reconstruction algorithm for discrete tomography. IEEE Transactions on Image Processing 20(8), 2146–2152 (2011)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Nagy, A., Kuba, A.: Reconstruction of binary matrices from fan-beam projections. Acta Cybernetica 17(2), 359–385 (2005)MATHMathSciNetGoogle Scholar
  13. 13.
    Pereira, L.F.A., Roelandts, T., Sijbers, J.: Inline 3d x-ray inspection of food using discrete tomography. In: InsideFood Symposium, Leuven, Belgium (2013)Google Scholar
  14. 14.
    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)CrossRefMATHGoogle Scholar
  15. 15.
    Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: Proceedings of the Sixth International Conference on Computer Vision, ICCV 1998, pp. 836–846. IEEE Computer Society, Washington (1998)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Antal Nagy
    • 1
  1. 1.Department of Image Processing and Computer GraphicsUniversity of SzegedHungary

Personalised recommendations