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A graph approach to color mathematical morphology

The processing of color images has become a major field of interest, however the direct extension of their gray scale counterparts is not always possible since there is no natural ordering of color vectors. Mathematical morphology has to face with this problem since it needs a complete lattice which is generally based on a conditional ordering. We propose another approach based on a graph decimation of a given structuring element to find the supremum and the infimum of a color vector set. The effects of the proposed graph approach are studied on several morphological operators (erosion, dilatation, watershed) and compared with the conditional ordering