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@INBOOK{Burgeth:830151,
      author       = {Burgeth, Bernhard and Kleefeld, Andreas},
      title        = {{A} {U}nified {A}pproach to {PDE}-{D}riven {M}orphology for
                      {F}ields of {O}rthogonal and {G}eneralized
                      {D}oubly-{S}tochastic {M}atrices},
      volume       = {10225},
      address      = {Cham},
      publisher    = {Springer International Publishing},
      reportid     = {FZJ-2017-03728},
      isbn         = {978-3-319-57239-0 (print)},
      series       = {Lecture Notes in Computer Science},
      pages        = {284 - 295},
      year         = {2017},
      comment      = {Mathematical Morphology and Its Applications to Signal and
                      Image Processing / Angulo, Jesús (Editor) ; Cham : Springer
                      International Publishing, 2017, Chapter 23 ; ISSN:
                      0302-9743=1611-3349 ; ISBN:
                      978-3-319-57239-0=978-3-319-57240-6},
      booktitle     = {Mathematical Morphology and Its
                       Applications to Signal and Image
                       Processing / Angulo, Jesús (Editor) ;
                       Cham : Springer International
                       Publishing, 2017, Chapter 23 ; ISSN:
                       0302-9743=1611-3349 ; ISBN:
                       978-3-319-57239-0=978-3-319-57240-6},
      abstract     = {In continuous morphology two nonlinear partial differential
                      equations (PDEs) together with specialized numerical
                      solution schemes are employed to mimic the fundamental
                      processes of dilation and erosion on a scalar valued image.
                      Some attempts to tackle in a likewise manner the processing
                      of higher order data, such as color images or even matrix
                      valued images, so-called matrix fields, have been made.
                      However, research has been focused almost exclusively on
                      real symmetric matrices. Fields of non-symmetric matrices,
                      for example rotation matrices, defy a unified approach. That
                      is the goal of this article. First, the framework for
                      symmetric matrices is extended to complex-valued Hermitian
                      matrices. The later offer sufficient degrees of freedom
                      within their structures such that, in principle, any class
                      of real matrices may be mapped in a one-to-one manner onto a
                      suitable subset of Hermitian matrices, where image
                      processing may take place. Second, both the linear mapping
                      and its inverse are provided. However, the non-linearity of
                      dilation and erosion processes requires a backprojection
                      onto the original class of matrices. Restricted by
                      visualization shortcomings, the steps of this procedure are
                      applied to the set of 3D-rotation matrices and the set of
                      generalized doubly-stochastic matrices.},
      month         = {May},
      date          = {2017-05-15},
      organization  = {13th International Symposium on
                       Mathematical Morphology and Its
                       Applications to Signal and Image
                       Processing, Fontainebleau (France), 15
                       May 2017 - 17 May 2017},
      cin          = {JSC},
      ddc          = {004},
      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)8 / PUB:(DE-HGF)7},
      UT           = {WOS:000425356700023},
      doi          = {10.1007/978-3-319-57240-6_23},
      url          = {https://juser.fz-juelich.de/record/830151},
}