A complete scheme for colour morphology with perceptual integration

Abstract

Mathematical morphology is a powerful tool for filtering, segmentation and texture analysis, extended to multivariate signal in the last years. The major limitations of applying it to colour image reside in the non-linear behavior of the Human Visual System to the perception of colour. So a direct extension of the multivariate approach to colour image is not appropriate and the existing approaches can not offer generic solutions from a perceptual point of view. To overcome this limit, we present a coherent solution for the addition/subtraction parts of the colour dilatation/erosion specification, which didn't limit the structural element to the flat ones. By combination of two perceptual colour spaces, we define a partial order, specified by a perceptual colour distance. By this way, we solve lot of problems induced by all methods based on bit mixing or lexicographical strategies. In addition, we define unic supremum and infimum in the colour space allowing classical developments for filtering or segmentation and colour texture analysis without colour artefacts. In this paper, we will discuss about the colour spaces and their specificities, then we present the possible colour ordering schemes for mathematical morphology. In a second time, we develop our specific approach, beginning by the discussion about an adapted colour space, following with the extrema extraction formulation in this adapted colour space, by distance computation. Then we propose the colour addition expression needed in the complete formulation of supremum and infimum. Finally, we show the first results in colour textured image filtering and we conclude with perspectives.