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@ARTICLE{Kahra:1046459,
      author       = {Kahra, Marvin and Breuß, Michael and Kleefeld, Andreas and
                      Welk, Martin},
      title        = {{M}atrix-{V}alued {L}og{S}um{E}xp {A}pproximation for
                      {C}olour {M}orphology},
      journal      = {Journal of mathematical imaging and vision},
      volume       = {67},
      number       = {5},
      issn         = {0924-9907},
      address      = {Dordrecht [u.a.]},
      publisher    = {Springer Science + Business Media B.V},
      reportid     = {FZJ-2025-03812},
      pages        = {52},
      year         = {2025},
      abstract     = {Mathematical morphology is a part of image processing that
                      employs a moving window to modify pixel values through the
                      application of specific operations. The supremum and infimum
                      are pivotal concepts, yet defining them in a general sense
                      for high-dimensional data such as colour is a challenging
                      endeavour. As a result, a number of different approaches
                      have been taken to try to find a solution, with certain
                      compromises being made along the way. In this paper, we
                      present an analysis of a novel approach that replaces the
                      supremum within a morphological operation with the LogExp
                      approximation of the maximum for matrix-valued colours. This
                      approach has the advantage of extending the associativity of
                      dilation from the one-dimensional to the higher-dimensional
                      case. Furthermore, the minimality property is investigated
                      and a relaxation specified to ensure that the approach is
                      continuously dependent on the input data.},
      cin          = {JSC},
      ddc          = {510},
      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)16},
      UT           = {WOS:001574657700001},
      doi          = {10.1007/s10851-025-01267-5},
      url          = {https://juser.fz-juelich.de/record/1046459},
}