Non-linear color image processing by color to plane polygon association

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 operators based on the reduced ordering of colors, with respect to scalars computed as geometrical shape invariants of a plane, polygonal representation of colors.