Pareto-Morphology for Color Image Processing

This paper presents an approach to the generalization of grayscale morphology to color images. Attaining such a generalization is strongly related to the issues of multivariate ranking and to the Pareto sets of multiobjective optimization. Some ranking schemes for multivariate data are recalled. For color morphology, the most important underlying ranking scheme is reduced ordering (also referred to as total ordering). Also, there is the partial ordering, which gives the important class of Pareto-Morphologies. Since partial ordering by Pareto sets commutes with reduced ordering, a so-called Pareto-Morphology is defined as a generalized multivariate morphology, for which the results will not change, when its computations are restricted to the Pareto set of the (local) neighborhood of a pixel. By further applying the concept of fuzzy subsethood to color values, a Pareto-Morphology can be designed, which is not based on reduced ordering, hence providing a manner for native color treatment. The properties of this newly-proposed Fuzzy-Pareto-Morphology and examples of its application for the processing of color textile