Skip to main content
SpringerLink
Log in

Smoothing Filters in the DART Algorithm

  • Conference paper
Combinatorial Image Analysis (IWCIA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8466))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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. Batenburg, K., Sijbers, J.: Dart: A practical reconstruction algorithm for discrete tomography. IEEE Transactions on Image Processing 20(9), 2542–2553 (2011)

    Article  MathSciNet  Google Scholar 

  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. 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)

    Article  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

  8. Herman, G.T.: Fundamentals of Computerized Tomography: Image Reconstruction from Projections, 2nd edn. Springer Publishing Company, Incorporated (2009)

    Google Scholar 

  9. Herman, G.T., Kuba, A.: Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis). Birkhauser (2007)

    Google Scholar 

  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. 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)

    Article  MathSciNet  Google Scholar 

  12. Nagy, A., Kuba, A.: Reconstruction of binary matrices from fan-beam projections. Acta Cybernetica 17(2), 359–385 (2005)

    MATH  MathSciNet  Google Scholar 

  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. 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)

    Article  MATH  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

  1. Department of Image Processing and Computer Graphics, University of Szeged, Hungary

    Antal Nagy

Authors
  1. Antal Nagy
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer and Information Sciences, State University of New York at Fredonia, 280 Central Ave, 14063, Fredonia, NY, USA

    Reneta P. Barneva

  2. Mathematics Department, SUNY Buffalo State College, 14222, Buffalo, NY, USA

    Valentin E. Brimkov

  3. Department of Mathematics, Brno University of Technology, 616 69, Brno, Czech Republic

    Josef Šlapal

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Nagy, A. (2014). Smoothing Filters in the DART Algorithm. In: Barneva, R.P., Brimkov, V.E., Šlapal, J. (eds) Combinatorial Image Analysis. IWCIA 2014. Lecture Notes in Computer Science, vol 8466. Springer, Cham. https://doi.org/10.1007/978-3-319-07148-0_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-07148-0_20

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07147-3

  • Online ISBN: 978-3-319-07148-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation