Morphological like operators for color images

Primarily based on Serra´s framework [5], mathematical morphology has become one of the most used nonlinear processing and analysis techniques. Later work extended the initially set operators to functions, in a general algebraic definition [4] for multidimensional scalar signals. The case of vector valued images (or signals) is not included in this theory. The extension of mathematical morphology to color images is equivalent to the definition of an ordering relation in a vector space. In this paper we will investigate several ordering relations in the color space, each of them yielding to the definition of morphological operations. The performance of the filtering based on these operations is evaluated in terms of Normalized Mean Square Error (NMSE), Mean Chromaticity Error (MCRE), space topology preservation and visual subjective perception of image quality.