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@INPROCEEDINGS{Welk:1047562,
      author       = {Welk, Martin and Kleefeld, Andreas and Breuß, Michael and
                      Burgeth, Bernhard},
      title        = {{M}orphological {PDE}s with {R}otationally {I}nvariant
                      {S}pace-{F}ractional {D}erivatives},
      volume       = {16296},
      address      = {Cham},
      publisher    = {Springer Nature Switzerland},
      reportid     = {FZJ-2025-04388},
      isbn         = {978-3-032-09543-5 (print)},
      series       = {Lecture Notes in Computer Science},
      pages        = {401–414},
      year         = {2025},
      comment      = {Discrete Geometry and Mathematical Morphology},
      booktitle     = {Discrete Geometry and Mathematical
                       Morphology},
      abstract     = {The spatial derivatives in Hamilton-Jacobi partial
                      differential equations for the definition of morphological
                      operations such as dilation and erosion for grey-value
                      images are replaced by fractional derivatives of arbitrary
                      positive order. Focus is laid on geometric invariance with
                      respect to reflections and rotations so that directional
                      bias towards the coordinate directions is avoided.
                      Discretisation of directional fractional derivatives via
                      truncated general power series ultimately leads to an
                      optimisation problem for the advection direction. We
                      numerically compare the proposed fractional morphological
                      operations with conventional counterparts and a simpler
                      fractional-order alternative on grey-value images to show
                      interesting phenomena and gain insights into the effects of
                      the non-local nature of the fractional derivatives which
                      merit further investigation.},
      month         = {Nov},
      date          = {2025-11-03},
      organization  = {Discrete Geometry and Mathematical
                       Morphology, Groningen (Netherlands), 3
                       Nov 2025 - 6 Nov 2025},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs)
                      and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5112},
      typ          = {PUB:(DE-HGF)8 / PUB:(DE-HGF)7},
      doi          = {10.1007/978-3-032-09544-2_29},
      url          = {https://juser.fz-juelich.de/record/1047562},
}