Duality is one of the most important properties of morphological operators

and it has important applications in image processing.Since the existing vector morphological operators are unable to meet the duality

it is difficult to develop vector morphological theory and applications.In order to address the issue

we studied the properties of the existing vector morphological operators

and then found color spaces and vector ordering algorithms are two important factors which directly determine whether vector morphological operators are dual or not.In this paper

the symmetric color space and the symmetric vector distance are chosen and used to define the novel vector morphological operators with duality.Moreover

the novel vector morphological filters

gradient operators are also proposed and applied to color image corrupted by noise.Experimental results show that the proposed vector morphological operators can provide better results than the existing approaches for color image filtering and edge detection.