A classical morphological approach to color image filtering based on space filling curves

In the last decade, nonlinear image processing algorithms have been developed for noise removing. With respect to linear methods, they present the advantage of minimizing distortions of informative characteristics. Morphological filters are a class of nonlinear techniques that have been successfully applied in filtering monochromatic images, but their extension to vectorial -valued images encountered great difficulties, cause of the value-ordering step necessary for implementing them. This paper presents a new class of morphological operators for multivalued images. The problem of ordering the vectorial values is solved by the introduction of a vectorial-into-scalar transformation, based on the concept of Space Filling Curves: such a transformation allows one to preserve module information and also to take into account angle information.