Root Images of Median Filters — Semi-topological Approach

  • Ulrich Eckhardt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2616)


Median filters are frequently used in signal analysis because they are robust edge-preserving smoothing filters. Since median filters are nonlinear filters, the tools of linear theory are not applicable to them. One approach to deal with nonlinear filters consists in investigating their root images (fixed elements or signals transparent to the filter). Whereas for one-dimensional median filters the set of all root signals can be completely characterized, this is not true for higher dimensional filters. Tyan (1981) and Döhler (1989) proposed a method for construction of small root images for two-dimensional median filters. Although the Tyan-Döhler construction is valid for a wide class of median filters, their arguments were not correct and their assertions do not hold universally. In this paper we give a rigorous treatment for the construction of Tyan and Döhler. Moreover, the approach is generalized to the d-dimensional case.


semi-topology median filter rank order filter multi-dimensional filter root image fixed point 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ulrich Eckhardt
    • 1
  1. 1.Fachbereich Mathematik - Optimierung und ApproximationUniversität HamburgHamburg

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