The Visual Computer

, Volume 33, Issue 3, pp 331–342 | Cite as

Volume enhancement with externally controlled anisotropic diffusion

  • László Szirmay-KalosEmail author
  • Milán Magdics
  • Balázs Tóth
Original Article


This paper proposes a method to enhance volumetric data using anisotropic diffusion controlled by another voxel array representing the same object with different physical quantities. The main application of this approach is to enhance volumetric functional data (obtained e.g. with PET or SPECT) based on anatomic (e.g. CT or MRI) information. Enhancement includes noise removal, sharpening and resolution upsampling. As different modalities measure different physical quantities that may or may not be correlated, enhancement must be carefully designed not to introduce spurious features that are present only in one modality. Forward diffusion working with non-negative diffusivity guarantees this kind of causality but also limits the potential of enhancement. To allow the preservation or even the increase of the dynamic range, diffusion should also go backwards. Therefore, we propose a forward–backward diffusion scheme for the enhancement where stability and the avoidance of spurious features are provided by the automatic determination of parameters controlling the diffusion process.


Medical imaging Upsampling Noise filtering Sharpening Anisotropic diffusion 


  1. 1.
    Bini, A.A., Bhat, M.S.: A nonlinear level set model for image deblurring and denoising. Vis. Comput. 30(3), 311–325 (2014)CrossRefGoogle Scholar
  2. 2.
    Chan, C., Fulton, R., Feng, D.D., Meikle, S.: Regularized image reconstruction with an anatomically adaptive prior for positron emission tomography. Phys. Med. Biol. 54, 7379–7400 (2009)CrossRefGoogle Scholar
  3. 3.
    Catt, F., Lions, P.-L., Morel, J.-M., Coll, Tomeu: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29(1), 182–193 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Crank, J., Nicolson, P.: A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Adv. Compu. Math. 6(1), 207–226 (1996)CrossRefzbMATHGoogle Scholar
  5. 5.
    Erlandsson, K., Buvat, I., Pretorius, P.H., Thomas, B.A.: A review of partial volume correction techniques for emission tomography and their applications in neurology, cardiology and oncology. Phys. Med. Biol. 57, 119–159 (2012)CrossRefGoogle Scholar
  6. 6.
    Magdics, M. et al.: TeraTomo project: a fully 3D GPU based reconstruction code for exploiting the imaging capability of the NanoPET/CT system. In World Molecular Imaging Congress (2010)Google Scholar
  7. 7.
    Fei, B.: An MR image-guided, voxel-based partial volume correction method for PET images. Med. Phys. 39(1), 179194 (2012)Google Scholar
  8. 8.
    Gilboa, Guy, Sochen, Nir, Zeevi, Yehoshua Y.: Forward-and-backward diffusion processes for adaptive image enhancement and denoising. IEEE Trans. Image Process. 11, 119–159 (2002)CrossRefGoogle Scholar
  9. 9.
    Jung, Younhyun, Kim, Jinman, Eberl, Stefan, Fulham, Micheal, Feng, DavidDagan: Visibility-driven pet-ct visualisation with region of interest (roi) segmentation. Vis. Comput. 29(6–8), 805–815 (2013)CrossRefGoogle Scholar
  10. 10.
    Kopf, Johannes., Cohen, Michael F., Lischinski, Dani., Uyttendaele, Matt.: Joint bilateral upsampling. ACM Trans. Graph. 26(3), 96:1–96:5 (2007)Google Scholar
  11. 11.
    Márta, Zsolt: Partial volume effect correction on the GPU. In Proceedings of the 16th central European seminar on computer graphics (CESCG) (2012)Google Scholar
  12. 12.
    Márta, Zsolt., Szirmay-Kalos, László.: Partial volume effect correction using anisotropic backward diffusion. In: KEPAF ’13, pp. 144–157 (2013)Google Scholar
  13. 13.
    Papp, László., Jakab, Gábor., Tóth, Balázs., Szirmay-Kalos, László.: Adaptive bilateral filtering for pet. In: IEEE Nuclear science symposium and medical imaging conference, pp. M18–104 (2014)Google Scholar
  14. 14.
    Perona, Pietro, Malik, Jitendra: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Image Process. 12, 629–639 (1990)Google Scholar
  15. 15.
    Richardt, Christian, Stoll, Carsten, Dodgson, Neil A., Seidel, Hans-Peter, Theobalt, Christian: Coherent spatiotemporal filtering, upsampling and rendering of rgbz videos. Comput. Graph. Forum (Proc. Eurogr.) 31(2pt1), 247–256 (2012)CrossRefGoogle Scholar
  16. 16.
    Rousset, Olivier, Rahmim, Arman, Alavi, Abass, Zaidi, Habib: Partial volume correction strategies in PET. PET Clin. 2(2), 235–249 (2007)CrossRefGoogle Scholar
  17. 17.
    Salvado, Olivier., Wilson, David L.: A new anisotropic diffusion method, application to partial volume effect reduction. In: Proceedings SPIE 6144, Medical Imaging 2006: Image Processing, 614464, (2006)Google Scholar
  18. 18.
    Skretting, Arne: Intensity diffusion is a better description than partial volume effect. Eur. J. Nucl. Med. Mol. Imaging 36, 536–537 (2009)CrossRefGoogle Scholar
  19. 19.
    Soret, Marine, Bacharach, S.L., Buvat, I.: Partial-volume effect in PET tumor imaging. J. Nucl. Med. 48, 932–945 (2007)CrossRefGoogle Scholar
  20. 20.
    Suri, J.S., Wu, Dee., Gao, J., Singh, S., Laxminarayan, S.: A comparison of state-of-the-art diffusion imaging techniques for smoothing medical/non-medical image data. In: Proceedings of the 16th international conference on pattern recognition, volume 1, pp. 508–511 vol. 1 (2002)Google Scholar
  21. 21.
    Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In Proceedings of the Sixth International Conference on Computer Vision, ICCV ’98, pages 839, Washington, DC, USA, 1998. IEEE Computer SocietyGoogle Scholar
  22. 22.
    Weickert, Joachim: Anisotropic Diffusion in Image Processing. B.G. Teubner, Stuttgart (1998)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • László Szirmay-Kalos
    • 1
    Email author
  • Milán Magdics
    • 1
  • Balázs Tóth
    • 1
  1. 1.Budapest University of Technology and EconomicsBudapestHungary

Personalised recommendations