Fuzzy mathematical morphology for color images defined by fuzzy preference relations

Abstract

Nowadays, the representation and the treatment of color images are still open problems. Mathematical morphology is the natural area for a rigorous formulation of many problems in image analysis. Moreover, it comprises powerful non-linear techniques for filtering, texture analysis, shape analysis, edge detection or segmentation. A large number of morphological operators have been widely defined and tested to process binary and gray scale images. However, the extension of mathematical morphology operators to multi-valued functions, and in particular to color images, is neither direct nor general due to the vectorial nature of the data. In this paper, basic morphological operators, erosion and dilation, are extended to color images from a new vector ordering scheme based on a fuzzy order in the RGB color space. Experimental results show that the proposed color operators can be efficiently used for color image processing.