基于四元数表达的模糊矢量形态学算子

Fuzzy vector morphological operators based on quaternion representation

由于经典的形态学算子不能直接拓展到彩色图像处理中,提出一类基于四元数表达的模糊矢量形态学算子.该算子利用四元数表达彩色图像并结合其分解特性,将彩色图像的模值、四元数的垂直分量和角度信息作为词典编纂顺序的3个边缘分量.3个分量一方面去除了彩色图像多通道数据的相关性,另一方面更便于词典编纂顺序等级的划分.并利用模糊数学解决了现有词典编纂顺序存在的等级判定难以深层进入的问题,给出了基于四元数表达的模糊矢量排序算法.与现有的矢量排序算法相比,新的矢量排序算法同时考虑了各分量的作用,并将判定进行到词典编纂顺序的最后一层,实现了矢量的正确排序.基于新的矢量排序规则,定义了矢量形态学算子,并将新的矢量形态学算子应用于彩色图像滤波、分割中.实验结果表明,与现有的矢量形态学算子相比,新的矢量形态学算子在平滑彩色图像噪声的同时保留了图像细节,并能正确地分割多类彩色图像,具有较高的鲁棒性及实用性.

Classical morphological operators cannot be extended directly to color image processing. Therefore, fuzzy vector morphological operators based on a quaternion representation are proposed in this paper. Using a quaternion polar expression combined with its decomposition characteristics, the modulus, the vertical component of the vector and the angular information of a color image are extracted, and they are used to construct the three components for lexicographical ordering. On one hand, the novel three-color components remove the correlation between the multi-channels data; on the other hand, the three components are ranked in the lexicographical ordering facility. ~hlzzy mathematics is therefore introduced to solve the problem where the computation cannot be performed at deeper levels. Unlike the existing vector ordering, the new vector ordering takes the role of each component into account, and the computation arrives at the last layer of the lexicographical ordering. Based on a novel vector ordering rule, some new vector morphological operators are defined, and they are applied to color image filtering and segmentation. Experimental results show that, when compared to the existing vector morphological operators, the new vector morphological operators can smooth the image noise while preserving the image detail, and color images can therefore be segmented correctly with high robustness and practicality.