矢量自对偶形态学滤波算子

自对偶形态学算子不依赖形态学腐蚀、膨胀算子的先后次序, 是一种等同处理图像背景和前景的形态学算子. 而将自对偶形态学算子拓展到多通道图像处理是一个难题. 为了解决该问题, 提出了基于极值约束的矢量自对偶形态学滤波算子(EC-VSDMF). 首先根据对称矢量排序算法构建满足对偶性的矢量形态学算子, 然后依据形态学算子中的极值原理优化矢量集合, 从而有效抑制矢量集合中包含单通道极值的矢量作为输出结果, 最终实现了具有约束功能的矢量自对偶形态学滤波算子(VSDMF). 实验结果表明, EC-VSDMF继承了传统自对偶形态学滤波算子的性质, 将其应用于彩色图像滤波可以改善现有矢量形态学滤波算子导致滤波后图像亮度和色度发生偏移的问题. 滤波后的图像在有效抑制噪声的同时较好地保留了图像细节, 滤波性能甚至超过了多种现有的矢量中值滤波算子.

Vector Self-dual Morphological Filtering Operators

Self-dual morphological filtering operators do not rely on the order of the sequence of erosion or dilation. They treat the foreground and background of an image identically. However, it is difficult to apply self-dual morphological operators to multi-channel images. To overcome the problem, vector self-dual morphological filtering operators based on extremum constraint (EC-VSDMF) is proposed in this paper. Firstly, a symmetric vector ordering is introduced to construct vector morphological operators with duality. Besides, vector sets are optical according to the extremum principle of morphological theory. And thus vectors including opposite extrema in single channels are suppressed. Finally, EC-VSDMF is constructed and applied to color image filtering. Experimental results show that the proposed EC-VSDMF inherits the properties of classic self-dual morphological operators. The problem that the brightness, saturation and hue of the filtered image turn to larger or smaller compared to the original image is also addressed. Moreover, EC-VSDMF can suppress noises efficiently while maintaining the image detail, even it can provide better results compared with the various vector median filtering operators.