Partial Differential Equations of Bivariate Median Filters

  • Martin WelkEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9087)


Multivariate median filters have been proposed as generalisations of the well-established median filter for grey-value images to multi-channel images. As multivariate median, most of the recent approaches use the \(L^1\) median, i.e. the minimiser of an objective function that is the sum of distances to all input points. Many properties of univariate median filters generalise to such a filter. However, the famous result by Guichard and Morel about approximation of the mean curvature motion PDE by median filtering does not have a comparably simple counterpart for \(L^1\) multivariate median filtering. We discuss the affine equivariant Oja median as an alternative to \(L^1\) median filtering. We derive the PDE approximated by Oja median filtering in the bivariate case, and demonstrate its validity by a numerical experiment.


Steiner Point Bivariate Case Input Data Point Common Intersection Point Multivariate Median 
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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University for Health Sciences, Medical Informatics and Technology (UMIT)Hall/TyrolAustria

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