Vector dual morphological operators

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.