Pseudo multivariate morphological operators based on α-trimmed lexicographical extrema

The extension of mathematical morphology to color and more generally to multivariate image data is still an open problem. The definition of multivariate morphological operators requires the introduction of a complete lattice structure on the image data, hence vectorial extrema computation methods are necessary. In this paper, we propose a lexicographical approach with this end, based on the principle of a-trimming, that leads to flexible, but nevertheless pseudo-morphological operators, in the sense that there is no underlying binary ordering relation among the vectors. Moreover a possible solution to this problem is presented as well as a way of automatically computing the parameter a based on statistical measures. The results of a series of color noise reduction experiments are also included, illustrating the superior performance of the proposed approach against uncorrelated Gaussian noise, with respect to state-of-the-art vector ordering schemes.