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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References
Angulo, J.: Geometric algebra colour image representations and derived total orderings for morphological operators Part I: Colour quaternions. J. Vis. Commun. Image R. 21(1), 33–48 (2010)
Aptoula, E., Lefèvre, S.: A comparative study on multivariate mathematical morphology. Pattern Recognition 40(11), 2914–2929 (2007)
Astola, J., Haavisto, P., Neuvo, Y.: Vector median filters. Proceedings of the IEEE 78(4), 678–689 (1990)
Christensen, O.: Frames and Bases: An Introductory Course. Birkhäuser, Springer e-books (2008)
Goutsias, J., Heijmans, H.J.A.M., Sivakumar, K.: Morphological Operators for Image Sequences. Comput. Vis. Image Und. 62(3), 326–346 (1995)
van de Gronde, J.J., Roerdink, J.B.T.M.: Group-invariant colour morphology based on frames. IEEE Transactions on Image Processing (submitted)
Mausfeld, R., Heyer, D. (eds.): Colour Perception: Mind and the physical world. Oxford University Press (November 2003)
Serra, J.: Anamorphoses and function lattices. Image Algebra and Morphological Image Processing IV 2030(1), 2–11 (1993)
Serra, J.: The “False Colour” Problem. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds.) ISMM 2009. LNCS, vol. 5720, pp. 13–23. Springer, Heidelberg (2009)
Talbot, H., Evans, C., Jones, R.: Complete Ordering and Multivariate Mathematical Morphology. In: Heijmans, H.J.A.M., Roerdink, J.B.T.M. (eds.) Mathematical Morphology and its Applications to Image and Signal Processing, pp. 27–34. Kluwer Academic Publishers (1998)
Velasco-Forero, S., Angulo, J.: Mathematical Morphology for Vector Images Using Statistical Depth. In: Soille, P., Pesaresi, M., Ouzounis, G.K. (eds.) ISMM 2011. LNCS, vol. 6671, pp. 355–366. Springer, Heidelberg (2011)
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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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