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.