In theory, there is no problem generalizing morphological operators to colour images. In practice, it has proved quite tricky to define a generalization that “makes sense”. This could be because many generalizations violate our implicit assumptions about what kind of transformations should not matter. Or in other words, to what transformations operators should be invariant. As a possible solution, we propose using frames to explicitly construct operators invariant to a given group of transformations. We show how to create saturation- and rotation-invariant frames, and demonstrate how group-invariant frames can improve results.


colour morphology group invariance frames 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jasper J. van de Gronde
    • 1
  • Jos B. T. M. Roerdink
    • 1
  1. 1.Johann Bernoulli Institute for Mathematics and Computer ScienceUniversity of GroningenGroningenThe Netherlands

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