Abstract
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.
This research is funded by the Dutch National Science Foundation (NWO), project no. 612.001.001.
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van de Gronde, J.J., Roerdink, J.B.T.M. (2013). Group-Invariant Frames for Colour Morphology. In: Hendriks, C.L.L., Borgefors, G., Strand, R. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2013. Lecture Notes in Computer Science, vol 7883. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38294-9_23
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DOI: https://doi.org/10.1007/978-3-642-38294-9_23
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