Skip to content
DraconiticResearch
Search Sources API
201,683 studies31 sourcesUpdated 38 min ago
PreprintCC BY 4.0arXiv

Strong Convergence of Continuous Median Filter Scheme

  • Fabius Krämer
  • Tim Laux
Open at sourcePDFDOICite

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.

Related

  1. Convergence of a multi-fluid scheme for the Vlasov--Poisson system
    Mehdi Badsi, Nicolas Crouseilles, Daniel Han-Kwan
    HALPreprintCC BY 4.0Full textAnalysis & PDEsNumerical analysis & scientific computingHALarXiv
  2. Unconditional optimal convergence of a relaxation Crank-Nicolson difference scheme for 2D space-fractional NLS
    Lisen Ding, Dongling Wang
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingarXiv
  3. Consistency and Convergence of the Backward-Euler Scheme for Stochastic Functional Differential Equations Driven by Fractional Brownian Motion
    Alexander Abreu, Lisandro Fermin, Ernesto Mordecki +1
    HALPreprintCC BY-NC-ND 4.0Full textNumerical analysis & scientific computingProbabilityHALarXiv
  4. A new convergence proof for an iterative scheme for elliptic Cauchy problems based on alternating orthogonal projections
    Abhijit Guchhait, Adrian Muntean, Martin Lind
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsNumerical analysis & scientific computingarXiv
  5. Rate of convergence of a fully discrete structure-preserving midpoint scheme for the stochastic Landau--Lifshitz--Gilbert equation
    Agus L. Soenjaya
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsNumerical analysis & scientific computingarXiv

Cite

BibTeXRIS
BibTeX
@misc{kramer2026strong,
  title = {{Strong Convergence of Continuous Median Filter Scheme}},
  author = {Fabius Krämer and Tim Laux},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08484},
  eprint = {2610.08484},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08484},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Strong Convergence of Continuous Median Filter Scheme
AU  - Fabius Krämer
AU  - Tim Laux
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08484
UR  - https://arxiv.org/abs/2610.08484
AB  - 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.
ER  -