Non-linear color image filtering by color to planar shape mapping

Non-linear rank-order-based filtering of color images is difficult to implement; the multivariate nature of colors does not allow the introduction of a mathematically-correct and topology-preserving ordering relation. The most widely investigated approach is based on the use of reduced ordering relations introduced according to different scalars. We propose pseudo-morphologic and median operators based on reduced ordering of colors, with respect to scalars computed as geometrical shape invariants of a triangle representation of colors. The same color representation allows the introduction of a luminance invariant inter-color distance, used with good results in distance-based color filters.