How to specify or identify the most accurate multispectral distance function for mathematical morphology?

We developed a distance-based formalism adapted to colour mathematical morphology. To extend the morphological operators to multispectral domain, a suitable distance function between two spectra has to be specified and selected. In order to compare the behaviour of different distance functions, we apply linear transformations on basic spectrum. Then we compare the impact of the distance function choice during morphological process on real spectral images.