中文摘要：

对偶性是形态学算子的重要性质之一,且具有重要应用.现有的矢量形态学算子均难以满足对偶性,从而限制了矢量数学形态学理论的发展及应用.为了解决该问题,研究了现有矢量形态学算子的性质,发现彩色空间和矢量排序算法是导致矢量形态学算子难以满足对偶性的两个关键因素.通过选用对称彩色空间,利用矢量对称距离实现了具有对偶特性的矢量形态学算子.为了验证矢量对偶形态学算子的性能,给出了满足对偶特性的矢量形态学滤波及梯度算子,并将其应用到彩色图像滤波及边缘检测中.实验结果表明,矢量对偶形态学算子较传统的矢量形态学算子具有更好的对称性,对噪声条件下的图像进行滤波及边缘检测,均获得了更好的处理效果.

英文摘要：

Duality is one of the most important properties of morphological operators,and it has important applica-tions 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.Exper-imental results show that the proposed vector morphological operators can provide better results than the existing approaches for color image filtering and edge detection.