Mathematical morphology extension to colour or multi/hyperspectral domain in image processing is not straightforward. Most approaches have focused on the mathematical translation of the operators without taking into account the physical or perceptual sense of colour/spectral information. The developed tools in this work are part of a new generic formalism based on a distance function. This construction allows using morphological operators in colour or multi/hyperspectral domain by adapting the distance function. Moreover, the distance function choice validates the operators in the perceptual or physical sense. In front of the increasing number of existing approaches, selection criteria are developed in order to compare the different mathematical morphology constructions. These criteria are based on the validation of the theoretical properties of operators, on the metrological properties and the computational efficiency. With a formalism taking into account the perceptual information of colour and integrating a valid definition of non-flat structuring elements, two kinds of highest level operators are defined. The first is a spatial-colorimetric object detector through the definition of a vectorial and spacial template. The second is the computation of vectorial texture spectra. The spectral extension for both tools is made and opens new scientific questions.
