Skip to main content

Volume enhancement with externally controlled anisotropic diffusion

Abstract

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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

References

  1. Bini, A.A., Bhat, M.S.: A nonlinear level set model for image deblurring and denoising. Vis. Comput. 30(3), 311–325 (2014)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    MathSciNet  Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  10. Kopf, Johannes., Cohen, Michael F., Lischinski, Dani., Uyttendaele, Matt.: Joint bilateral upsampling. ACM Trans. Graph. 26(3), 96:1–96:5 (2007)

  11. Márta, Zsolt: Partial volume effect correction on the GPU. In Proceedings of the 16th central European seminar on computer graphics (CESCG) (2012)

  12. Márta, Zsolt., Szirmay-Kalos, László.: Partial volume effect correction using anisotropic backward diffusion. In: KEPAF ’13, pp. 144–157 (2013)

  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)

  14. Perona, Pietro, Malik, Jitendra: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Image Process. 12, 629–639 (1990)

    Google Scholar 

  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)

    Article  Google Scholar 

  16. Rousset, Olivier, Rahmim, Arman, Alavi, Abass, Zaidi, Habib: Partial volume correction strategies in PET. PET Clin. 2(2), 235–249 (2007)

    Article  Google Scholar 

  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)

  18. Skretting, Arne: Intensity diffusion is a better description than partial volume effect. Eur. J. Nucl. Med. Mol. Imaging 36, 536–537 (2009)

    Article  Google Scholar 

  19. Soret, Marine, Bacharach, S.L., Buvat, I.: Partial-volume effect in PET tumor imaging. J. Nucl. Med. 48, 932–945 (2007)

    Article  Google Scholar 

  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)

  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 Society

  22. Weickert, Joachim: Anisotropic Diffusion in Image Processing. B.G. Teubner, Stuttgart (1998)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to László Szirmay-Kalos.

Additional information

This work has been supported by OTKA K-104476 and VKSZ-14 PET/MRI 7T projects.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Szirmay-Kalos, L., Magdics, M. & Tóth, B. Volume enhancement with externally controlled anisotropic diffusion. Vis Comput 33, 331–342 (2017). https://doi.org/10.1007/s00371-015-1203-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-015-1203-y

Keywords

  • Medical imaging
  • Upsampling
  • Noise filtering
  • Sharpening
  • Anisotropic diffusion