Color morphology-like operators based on color geometric shape characteristics

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 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. We propose 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). The approach has been widely investigated, by proposing different scalars (usually the same scalars as used for distance-based color image filtering). We propose the use of scalars issued as geometrical shape invariants for a triangle-representation of colors.