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@ARTICLE{Kleefeld:844935,
      author       = {Kleefeld, Andreas and Vorderwülbecke, Sophia and Burgeth,
                      Bernhard},
      title        = {{A}nomalous diffusion, dilation, and erosion in image
                      processing},
      journal      = {International journal of computer mathematics},
      volume       = {95},
      number       = {6-7},
      issn         = {1029-0265},
      address      = {London [u.a.]},
      publisher    = {Taylor and Francis},
      reportid     = {FZJ-2018-02276},
      pages        = {1375 - 1393},
      year         = {2018},
      abstract     = {In this paper, anomalous sub- and super-diffusion arising
                      in image processing is considered and is modelled by a
                      diffusion equation with fractional time derivative. It might
                      serve as a building block for the construction of various
                      filters. The resulting partial differential equation is
                      discretized in space with centred differences and in time
                      with the explicit or implicit Euler method, respectively. A
                      numerical investigation is performed to illustrate new and
                      interesting results. Additionally, the time derivative of
                      the partial differential equation describing dilation and
                      erosion is replaced by a fractional time derivative and then
                      solved numerically. Interesting new questions arise from the
                      presented numerical results. A short summary and outlook
                      conclude this article.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511)},
      pid          = {G:(DE-HGF)POF3-511},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000429600100019},
      doi          = {10.1080/00207160.2017.1423292},
      url          = {https://juser.fz-juelich.de/record/844935},
}