Fuzzy-Subsethood based Color Image Processing

This paper presents the exploitation of the concept of fuzzy--subsethood for defining a new class of color image processing operations. By considering a color value as a fuzzy set, the calculus of fuzzy-subsethood becomes applicable to color images. From this, a simple color threshold operation can be defined, which gives a grayvalue image from the degrees of subsethood. Also, mathematical morphology can be extended to color images this way. For doing so, the important class of Pareto--Morphologies is introduced, and fuzzy--subsethood is used to define a new ranking scheme for multivariate data. This gives the Fuzzy-- Pareto--Morphology (FPM), which fulfills basic requirements for a generalized morphology. An extension of the difference image to color images and an operation given by an intermediate result of FPM, the M-image, are presented as new operations. Some examples of frameworks, which employs the newly defined operations, are given. It comes out, that fuzzy--subsethood allows for the definition of a new class of comprehensive color image processing operations