Color Persistent Anisotropic Diffusion of Images

  • Freddie Åström
  • Michael Felsberg
  • Reiner Lenz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6688)


Techniques from the theory of partial differential equations are often used to design filter methods that are locally adapted to the image structure. These techniques are usually used in the investigation of gray-value images. The extension to color images is non-trivial, where the choice of an appropriate color space is crucial. The RGB color space is often used although it is known that the space of human color perception is best described in terms of non-euclidean geometry, which is fundamentally different from the structure of the RGB space. Instead of the standard RGB space, we use a simple color transformation based on the theory of finite groups. It is shown that this transformation reduces the color artifacts originating from the diffusion processes on RGB images. The developed algorithm is evaluated on a set of real-world images, and it is shown that our approach exhibits fewer color artifacts compared to state-of-the-art techniques. Also, our approach preserves details in the image for a larger number of iterations.


non-linear diffusion color image processing perceptual image quality 


  1. 1.
    Black, M.J., Sapiro, G., Marimont, D.H., Heeger, D.: Robust anisotropic diffusion. IEEE Transactions on Image Processing 7(3), 421–432 (1998)CrossRefGoogle Scholar
  2. 2.
    Chambolle, A.: Partial differential equations and image processing. In: Proceedings of the IEEE International Conference Image Processing, ICIP 1994, vol. 1, pp. 16–20 (November 1994)Google Scholar
  3. 3.
    Felsberg, M.: On the relation between anisotropic diffusion and iterated adaptive filtering. In: Rigoll, G. (ed.) DAGM 2008. LNCS, vol. 5096, pp. 436–445. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Felsberg, M.: Autocorrelation-Driven Diffusion Filtering. IEEE Transactions on Image Processing (2011), doi:10.1109/TIP.2011.2107330Google Scholar
  5. 5.
    Kimmel, R., Malladi, R., Sochen, N.: Images as embedded maps and minimal surfaces: Movies, color, texture, and volumetric medical images. International Journal of Computer Vision 39, 111–129 (2000)CrossRefzbMATHGoogle Scholar
  6. 6.
    Larsson, F., Felsberg, M., Forssen, P.E.: Patch contour matching by correlating fourier descriptors. In: Digital Image Computing: Techniques and Applications, DICTA 2009, pp. 40–46 (December 2009)Google Scholar
  7. 7.
    Lenz, R., Carmona, P.L.: Hierarchical s(3)-coding of rgb histograms. In: Selected Papers from VISAPP 2009, vol. 68, pp. 188–200. Springer, Heidelberg (2010)Google Scholar
  8. 8.
    Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12, 629–639 (1990)CrossRefGoogle Scholar
  9. 9.
    Renner, A.I.: Anisotropic Diffusion in Riemannian Colour Space. Ph.D. thesis, Ruprecht-Kars-Universitt, Heidelberg (2003)Google Scholar
  10. 10.
    Scharr, H., Black, M.J., Haussecker, H.W.: Image statistics and anisotropic diffusion. In: Proceedings of the Ninth IEEE International Conference on Computer Vision, pp. 840–847 (October 2003)Google Scholar
  11. 11.
    Sharma, G.: Digital Color Imaging Handbook. CRC Press, Inc., Boca Raton (2002)CrossRefGoogle Scholar
  12. 12.
    Sochen, N., Kimmel, R., Bruckstein, A.: Diffusions and confusions in signal and image processing. Journal of Mathematical Imaging and Vision 14, 195–209 (2001)Google Scholar
  13. 13.
    Sochen, N., Kimmel, R., Malladi, R.: A general framework for low level vision. IEEE Transactions on Image Processing 7(3), 310–318 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Tang, B., Sapiro, G., Caselles, V.: Color image enhancement via chromaticity diffusion. IEEE Transactions on Image Processing 10, 701–707 (2002)CrossRefzbMATHGoogle Scholar
  15. 15.
    Tschumperle, D., Deriche, R.: Diffusion pdes on vector-valued images. IEEE Signal Processing Magazine 19(5), 16–25 (2002)CrossRefzbMATHGoogle Scholar
  16. 16.
    Wang, Z., Bovik, A., Sheikh, H., Simoncelli, E.: Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing 13(4), 600–612 (2004)CrossRefGoogle Scholar
  17. 17.
    Weickert, J.: Anisotropic diffusion in image processing (1996)Google Scholar
  18. 18.
    Weickert, J.: Coherence-enhancing diffusion of colour images. Image and Vision Computing 17(3-4), 201–212 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Freddie Åström
    • 1
  • Michael Felsberg
    • 1
  • Reiner Lenz
    • 1
  1. 1.Linköping UniversityLinköpingSweden

Personalised recommendations