Strong Convergence of Continuous Median Filter Scheme

Fabius Krämer; Tim Laux

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arXiv · 2610.08484

Strong Convergence of Continuous Median Filter Scheme

Fabius Krämer·Tim Laux

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Abstract

We introduce a continuous-time counterpart of the median filter that gradually denoises a given image. In the limit of vanishing stencil size, our results show that the evolution converges to level-set mean curvature flow. Surprisingly, and for the first time for any median-type filter scheme, we can prove the convergence of energies in this limit. Such strong convergence results are of major interest as they often have to be assumed in the literature to prove convergence of related schemes. Moreover, this result carries crucial geometric information, namely the unit multiplicity of interfaces. The proof relies on a compensated compactness argument inspired by the work of Evans and Spruck.

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Fabius Krämer, Tim Laux. 2026-10-06. Strong Convergence of Continuous Median Filter Scheme. https://arxiv.org/abs/2610.08484

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