Analysis of Morphology-like Operators Used in Color Image Contrast Enhancement

Mathematical morphology is difficult to introduce for color images because in the color vector space, minimum and maximum cannot be easily defined. So, the necessary conditions, represented by the complete lattice structure induced by an ordering relation, cannot be accomplished. Instead, we can build a pseudo-morphology based on reduced color ordering. This approach uses geometrical shape invariants computed from equivalent twodimensional star glyphs (triangles) associated to the RGB colors. It does not fulfill the exact conditions but we can, at least, define pseudo-morphological or morphological-like erosion and dilation. The color image processing applications presented in this paper indicate that the shape descriptors used for the triangle color representation (star glyph) insures an increased independence with respect to luminance changes, while preserving essential hue information. The comparative analysis of different geometric shape descriptors is based upon the study of the equivalency class set induced onto the color vectors set (or factor set induced by the equivalence relation).