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, ECVSDMF 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.