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@INPROCEEDINGS{Kahra:1025193,
      author       = {Kahra, Marvin and Breuß, Michael and Kleefeld, Andreas and
                      Welk, Martin},
      title        = {{A}n {A}pproach to {C}olour {M}orphological {S}upremum
                      {F}ormation {U}sing the {L}og{S}um{E}xp {A}pproximation},
      volume       = {14605},
      address      = {Cham},
      publisher    = {Springer},
      reportid     = {FZJ-2024-02761},
      isbn         = {978-3-031-57792-5 (print)},
      series       = {Lecture Notes in Computer Science},
      pages        = {325-337},
      year         = {2024},
      comment      = {Discrete Geometry and Mathematical Morphology},
      booktitle     = {Discrete Geometry and Mathematical
                       Morphology},
      abstract     = {Mathematical morphology is a part of image processing that
                      has proven to be fruitful for numerous applications. Two
                      main operations in mathematical morphology are dilation and
                      erosion. These are based on the construction of a supremum
                      or infimum with respect to an order over the tonal range in
                      a certain section of the image. The tonal ordering can
                      easily be realised in grey-scale morphology, and some
                      morphological methods have been proposed for colour
                      morphology. However, all of these have certain
                      limitations.In this paper we present a novel approach to
                      colour morphology extending upon previous work in the field
                      based on the Loewner order. We propose to consider an
                      approximation of the supremum by means of a log-sum
                      exponentiation introduced by Maslov. We apply this to the
                      embedding of an RGB image in a field of symmetric
                      2x2matrices. In this way we obtain nearly isotropic matrices
                      representing colours and the structural advantage of
                      transitivity. In numerical experiments we highlight some
                      remarkable properties of the proposed approach.},
      month         = {Apr},
      date          = {2024-04-15},
      organization  = {IAPR Third International Conference on
                       Discrete Geometry and Mathematical
                       Morphology, Florence (Italy), 15 Apr
                       2024 - 18 Apr 2024},
      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},
      UT           = {WOS:001280284700025},
      doi          = {10.1007/978-3-031-57793-2_25},
      url          = {https://juser.fz-juelich.de/record/1025193},
}