REDEFINING MORPHOLOGICAL OPERATORS FOR COLOR IMAGE CONTRAST ENHANCEMENT AND SEGMENTATION

摘要

Mathematical morphology is based on two infimum- and, respectively, supremum-commuting operations (the erosion and the dilation). In the scalar case, these operations are obviously the minimum and the maximum. In the vector-valued case, minimum and maximum cannot be easily defined. Pixels within color images are described by three-component vectors, and thus the mathematical morphology is difficult to introduce for colors. So, the necessary conditions, represented by the complete lattice structure induced by an ordering relation, cannot be accomplished. Instead, we propose in this paper a pseudo-morphology based on reduced ordering of colors (associate a scalar to each color, order the scalars and impose their ranking to their corresponding colors). This approach uses geometrical shape invariants computed from equivalent two-dimensional 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 an equivalence relation). In the last section some experiments based on pseudo-morphology are presented: color image enhancement, color image segmentation and color classification system for domestic objects.