Advertisement

Coherence-Enhancing Shock Filters

  • Joachim Weickert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2781)

Abstract

Shock filters are based in the idea to apply locally either a dilation or an erosion process, depending on whether the pixel belongs to the influence zone of a maximum or a minimum. They create a sharp shock between two influence zones and produce piecewise constant segmentations. In this paper we design specific shock filters for the enhancement of coherent flow-like structures. They are based on the idea to combine shock filtering with the robust orientation estimation by means of the structure tensor. Experiments with greyscale and colour images show that these novel filters may outperform previous shock filters as well as coherence-enhancing diffusion filters.

Keywords

Colour Image Structure Tensor Jacobi Formulation Fingerprint Image Dilation Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alvarez, L., Mazorra, L.: Signal and image restoration using shock filters and anisotropic diffusion. SIAM Journal on Numerical Analysis 31, 590–605 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bigün, J., Granlund, G.H., Wiklund, J.: Multidimensional orientation estimation with applications to texture analysis and optical flow. IEEE Transactions on Pattern Analysis and Machine Intelligence 13(8), 775–790 (1991)CrossRefGoogle Scholar
  3. 3.
    Brockett, R.W., Maragos, P.: Evolution equations for continuous-scale morphology. In: Proc. IEEE International Conference on Acoustics, Speech and Signal Processing, San Francisco, CA, March 1992, vol. 3, pp. 125–128 (1992)Google Scholar
  4. 4.
    Förstner, W., Gülch, E.: A fast operator for detection and precise location of distinct points, corners and centres of circular features. In: Proc. ISPRS Intercommission Conference on Fast Processing of Photogrammetric Data, Interlaken, Switzerland, June 1987, pp. 281–305 (1987)Google Scholar
  5. 5.
    Gilboa, G., Sochen, N.A., Zeevi, Y.Y.: Regularized shock filters and complex diffusion. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2350, pp. 399–413. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Guichard, F., Morel, J.-M.: A note on two classical shock filters and their asymptotics. In: Kerckhove, M. (ed.) Scale-Space 2001. LNCS, vol. 2106, pp. 75–84. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Höcker, C., Fehmers, G.: Fast structural interpretation with structure-oriented filtering. The Leading Edge 21(3), 238–243 (2002)CrossRefGoogle Scholar
  8. 8.
    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(2), 111–129 (2000)zbMATHCrossRefGoogle Scholar
  9. 9.
    Kornprobst, P., Deriche, R., Aubert, G.: Nonlinear operators in image restoration. In: Proc. 1997 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Juan, Puerto Rico, June 1997, pp. 325–330. IEEE Computer Society Press, Los Alamitos (1997)CrossRefGoogle Scholar
  10. 10.
    Kramer, H.P., Bruckner, J.B.: Iterations of a non-linear transformation for enhancement of digital images. Pattern Recognition 7, 53–58 (1975)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Osher, S., Rudin, L.: Shocks and other nonlinear filtering applied to image processing. In: Applications of Digital Image Processing XIV. Proceedings of SPIE, vol. 1567, pp. 414–431. SPIE Press, Bellingham (1991)Google Scholar
  12. 12.
    Osher, S., Rudin, L.I.: Feature-oriented image enhancement using shock filters. SIAM Journal on Numerical Analysis 27, 919–940 (1990)zbMATHCrossRefGoogle Scholar
  13. 13.
    Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton–Jacobi formulations. Journal of Computational Physics 79, 12–49 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    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
  15. 15.
    Preußer, T., Rumpf, M.: Anisotropic nonlinear diffusion in flow visualization. In: Proc. 1999 IEEE Visualization Conference, San Francisco, CA, October 1999, pp. 223–232 (1999)Google Scholar
  16. 16.
    Rao, A.R., Schunck, B.G.: Computing oriented texture fields. In: CVGIP: Graphical Models and Image Processing, vol. 53, pp. 157–185 (1991)Google Scholar
  17. 17.
    Schavemaker, J.G.M., Reinders, M.J.T., Gerbrands, J.J., Backer, E.: Image sharpening by morphological filtering. Pattern Recognition 33, 997–1012 (2000)CrossRefGoogle Scholar
  18. 18.
    Solé, A.F., López, A., Sapiro, G.: Crease enhancement diffusion. Computer Vision and Image Understanding 84, 241–248 (2001)zbMATHCrossRefGoogle Scholar
  19. 19.
    Wahl, F.M.: Digitale Bildsignalverarbeitung. Springer, Berlin (1984)Google Scholar
  20. 20.
    Weickert, J.: Anisotropic Diffusion in Image Processing. Teubner, Stuttgart (1998)zbMATHGoogle Scholar
  21. 21.
    Weickert, J.: Coherence-enhancing diffusion filtering. International Journal of Computer Vision 31(2/3), 111–127 (1999)CrossRefGoogle Scholar
  22. 22.
    Weickert, J.: Coherence-enhancing diffusion of colour images. Image and Vision Computing 17(3–4), 199–210 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Joachim Weickert
    • 1
  1. 1.Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Bldg. 27Saarland UniversitySaarbrückenGermany

Personalised recommendations