Advertisement

A New Numerical Scheme for Anisotropic Diffusion

  • Hongwen Yi
  • Peter H. Gregson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3211)

Abstract

Automatically stopping the diffusion process is a challenging task in anisotropic diffusion (AD). Without a preset number of iterations, over-smoothing of semantically meaningful features occurs very easily with current discrete version of AD (DAD). We address this problem by considering the difference in the behavior of DAD and its continuous counterpart. A new numerical scheme is proposed in this paper in which the non-negative part of the derivative of flux is employed for the first time to control the smoothing strength. Our proposed algorithm implements the desired AD operation with over-smoothing prevented.

Keywords

Numerical Scheme Edge Preservation Preset Number Continuous Counterpart Selective Smoothing 
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.
    Black, M., Sapiro, G., Marimont, D., Heeger, D.: Robust anisotropic diffusion. IEEE Trans. IP. 7, 421–432 (1998)Google Scholar
  2. 2.
    Catte, F., Lions, P., Morel, J., Coil, T.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Num. Anal. 29, 182–193 (1992)zbMATHCrossRefGoogle Scholar
  3. 3.
    Dautray, R., Lions, J.-L.: Mathematical Analysis and Numerical Methods for Science and Technology, vol. 11(6). Springer, Berlin (1988)Google Scholar
  4. 4.
    Esedoglu, S.: An analysis of Perona-Malik scheme. Comm. Pure Appl. Math. 1442–1487 (2001)Google Scholar
  5. 5.
    Gilboa, G., Sochen, N., Zeevi, Y.Y.: Forward-and-backward diffusion processes for adaptive image enhancement and denoising. IEEE Trans. IP 11, 689–703 (2002)Google Scholar
  6. 6.
    Jin, J.S., Wang, Y., Hiller, J.: An adaptive nonlinear diffusion algorithm for filtering medical images. IEEE Trans. Inform. Technol. Biomed. 4, 298–305 (2000)CrossRefGoogle Scholar
  7. 7.
    Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. PAMI, 629–639 (1990)Google Scholar
  8. 8.
    Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. In: IEEE Computer Society Workshop on Computer Vision - Miami, pp. 16–22 (1987)Google Scholar
  9. 9.
    Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)zbMATHCrossRefGoogle Scholar
  10. 10.
    Saint-Marc, P., Chen, J.S., Medioni, G.: Adaptive smoothing: a general tool for early vision. PAMI 13, 514–529 (1991)Google Scholar
  11. 11.
    Segall, C.A., Acton, S.T.: Morphological anisotropic diffusion. In: Int. Conf. on IP vol. 3, pp. 348–351 (1997)Google Scholar
  12. 12.
    Solo, V.: A fast automatic stopping criterion for anisotropic diffusion. In: IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, pp. 1661–1664 (2002)Google Scholar
  13. 13.
    Torkamani-Azar, F., Tait, K.E.: Image recovery using the anisotropic diffusion equation. IEEE Trans. IP 5, 1573–1578 (1996)Google Scholar
  14. 14.
    Weickert, J.A.: Applications of nonlinear diffusion in image processing and computer vision. Acta Mathematica Universitatis Comenianae 70, 33–50 (2001)zbMATHMathSciNetGoogle Scholar
  15. 15.
    Weickert, J.A., Romeny, B.H., Florack, L., Koenderink, J.: Viergever: A review of nonlinear diffusion filtering, pp. 3–28. Springer, Berlin (1997) Invited paperGoogle Scholar
  16. 16.
    Yi, H., Gregson, P.H.: Behavioral analysis of anisotropic diffusion for image processing. IEEE Trans. Image Processing (2004) (submitted )Google Scholar
  17. 17.
    You, Y., Kaveh, M.: Differences in the behaviors of continuous and discrete anisotropic diffusion equations for image processing. In: ICIP 1998, pp. 249–253 (1998)Google Scholar
  18. 18.
    You, Y., Xu, W., Tannenbaum, A., Kaveh, M.: Behavioral analysis of anisotropic diffusion in image processing. IEEE Trans. IP 5, 1539–1553 (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Hongwen Yi
    • 1
  • Peter H. Gregson
    • 2
  1. 1.Postdoctoral follow, iDLabDalhousie UniversityHalifaxCanada
  2. 2.NSERC Chair in Design Innovation, Director of iDLabDalhousie UniversityHalifaxCanada

Personalised recommendations