Exploring Non-linear Difusion: The Difusion Echo

  • Erik Dam
  • Mads Nielsen
Conference paper
Part of the Lecture Notes in Computer Science 2106 book series (LNCS, volume 2106)


The Gaussian serves as Green’s function for the linear diffusion equation and as a source for intuitive understanding of the linear difusion process. In general, non-linear difusion equations have no known closed formsolu tions and thereby no equally simple description. This article introduces a simple, intuitive description of these processes in terms of the Difusion Echo. The Difusion Echo offers intuitive visualisations for non-linear difusion processes.

In addition, the Difusion Echo has potential for o?ering simple formulations for grouping problems. Furthermore, the Difusion Echo can be considered a deep structure summary and thereby offers an alternative to multi-scale linking and ?ooding techniques.


Intuitive Understanding Segmentation Task Watershed Segmentation Soft Threshold Intuitive Description 
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.


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  1. 1.
    The internet brain segmentation repository, 1999. MR brain data set 788⁃6⁃m and its manual segmentation was provided by the Center for Morphometric Analysis at MGH,
  2. 2.
    F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll. Image selective smoothing and edge detection by nonlinear difusion. SIAM J. of Num. An., 29:182–193, 1992.zbMATHCrossRefGoogle Scholar
  3. 3.
    Erik Dam. Evaluation of difusion schemes for watershed segmentation. Master#x2019;s thesis, University of Copenhagen, 2000. Technical report 2000/1 on
  4. 4.
    Erik Dam and Mads Nielsen. Non-linear difusion for interactive multi-scale watershed segmentation. MICCAI 2000, vol 1935 of LNCS, 216–225. Springer, 2000.Google Scholar
  5. 5.
    Jan J. Koenderink. The structure of images. Biol. Cybern., 50:363–370, 1984.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Tony Lindeberg. Scale-Space Theory in Computer Vision. Kluwer, 1994.Google Scholar
  7. 7.
    Pietro Perona and Jitendra Malik. Scale-space and edge detection using anisotropic difusion. IEEE PAMI, 12(7):629–639, July 1990.CrossRefGoogle Scholar
  8. 8.
    H. Scharr and J. Weickert. An anisotropic difusion algorithmwit h optimized rotation invariance. Mustererkennung 2000, DAGM, pp 460–467. Springer, 2000.Google Scholar
  9. 9.
    Joachim W eickert. Anisotropic Difusion in Image Processing. Teubner, 1998.Google Scholar
  10. 10.
    Andrew P. Witkin. Scale-space filtering. In Proceedings of International Joint Conference on Artificial Intelligence, pages 1019–1022, Karlsruhe, Germany, 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Erik Dam
    • 1
  • Mads Nielsen
    • 1
  1. 1.The IT UniversityCopenhagenDenmark

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