Colour morphology with perceptual behaviour and vectorial structuring element
Résumé
Mathematical morphology is a powerful tool for image filtering, segmentation and texture analysis, extended to multivariate signal in the last years. The major limitations of applying it to colour images reside in the non-linear behaviour of the Human Visual System to the perception of colours. So a direct extension of the multivariate approach to colour image is not appropriate and the existing approaches cannot offer generic solutions from a perceptual point of view. To overcome this limitation, we present a coherent solution for the addition/subtraction of the colour dilatation/erosion expression, which does not limit the structuring element to the flat ones. By combination of two perceptual colour spaces, we define a partial order, specified by a perceptual colour distance. In this way, we solve the issues generated by all the methods based on bit mixing or lexicographical strategies. In addition, we define supremum and infimum in the colour space allowing classical developments for filtering or segmentation and colour texture analysis without introduction any colour artefacts. We discuss about the colour spaces and their specificities, and then we present the possible colour ordering schemes for mathematical morphology. Secondly, we develop our specific approach, beginning with the discussion about an adapted colour space, following with the extrema extraction formulation in this adapted colour space, by computing a distance. Then we propose the colour addition/subtraction expressions needed in the complete formulation of supremum and infimum. Finally, we show the some preliminary results for colour image erosion and dilatation.