Complex Difusion Processes for Image Filtering

  • Guy Gilboa
  • Yehoshua Y. Zeevi
  • Nir A. Sochen
Conference paper
Part of the Lecture Notes in Computer Science 2106 book series (LNCS, volume 2106)


A framework that naturally uni?es smoothing and enhancement processes is presented. We generalize the linear and nonlinear scale spaces in the complex domain, by combining the difusion equation with the simpli?ed Schrödinger equation. A fundamental solution for the linear case is developed. Preliminary analysis of the complex difusion shows that the generalized difusion has properties of both forward and inverse difusion. An important observation, supported theoretically and numerically, is that the imaginary part can be regarded as an edge detector (smoothed second derivative), after rescaling by time, when the complex difusion coefficient approaches the real axis. Based on this observation, a nonlinear complex process for ramp preserving denoising is developed.


Scale-space image ?ltering image denoising image enhancement nonlinear difusion complex difusion. 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F. Catte, P.L. Lions, J.M. Morel and T. Coll, “Image selective smoothing and edge detection by nonlinear difusion”, SIAM J. Num. Anal., vol. 29,no. 1, pp. 182–193, 1992.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    J.J. Koenderink, “The structure of images”, Biol. Cybern., 50: 363–370, 1984.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    M. Nagasawa, Schröinger equations and difusion theory, Monographs in mathematics, vol. 86, Birkhäuser Verlag, Basel, Switzerland 1993.Google Scholar
  4. 4.
    P. Perona and J. Malik, “Scale-space and edge detection using anisotropic difusion”, EEE Trans. Pat. Anal. Machine Intel., vol. PAMI-12,no. 7, pp. 629–639, 1990.CrossRefGoogle Scholar
  5. 5.
    B.M ter Haar Romeny Ed., Geometry Driven Diffusion in Computer Vision, Kluwer Academic Publishers, 1994.Google Scholar
  6. 6.
    A.P. Witkin, “Scale space filtering”, Proc. Int. Joint Conf. On Arti.cial Intelligence, pp. 1019–1023, 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Guy Gilboa
    • 1
  • Yehoshua Y. Zeevi
    • 1
  • Nir A. Sochen
    • 1
  1. 1.Department of Electrical EngineeringTechnion - Israel Institute of TechnologyHaifaIsrael

Personalised recommendations