The choice of a suitable colour space representation is still a challenging task in the processing and analysis of colour images. Starting with the recently proposed family of polar coordinate systems LSH (improving the standard HLS) which have suitable properties for quantitative image processing, the derivation of two bivariate histograms: hist^r;HS (putting together the Hue component and the Saturation component) and hist_LS (Luminance and Saturation components) associated to these colour spaces is presented. A method for the morphological clustering of the points in the bivariates histograms is shown, relying on the watershed transformation. Then, by back projecting on the space of the initial colour image, two partitions (chromatic and achromatic) are obtained. A saturation-based combination of the two partitions yields an interesting method for segmenting colour images.