The mathematical morphology for colour images faces the delicate issue of defining a total order in a vectorial space. There are various approaches based on partial or total orders defined for color images. We propose a probabilistic approach, that uses principal component analysis (PCA), for the computation of the convergence colours, i.e. the extrema of a set. Then we define two pseudo-morphological operations, the dilation and the erosion, applying the Chebyshev's inequality on the first eigenvector of the image colour data. As an application, we use our approach to extract the Beucher colour gradient. We discuss the advantages and disadvantages of our approach, we comment our results and then we conclude this paper.
Mihai Ivanovici, Alexandru Căliman, Noël Richard, Christine Fernandez-Maloigne, "Towards a Multivariate Probabilistic Morphology for Colour Images" in Proc. IS&T CGIV 2012 6th European Conf. on Colour in Graphics, Imaging, and Vision, 2012, pp 189 - 193, https://doi.org/10.2352/CGIV.2012.6.1.art00034