Multivariate self-dual morphological operators

Self-dual morphological operators (SDMO) do not rely on whether one starts the sequence with erosion or dilation, they treat the image foreground and background identically. Nevertheless, it is difficult to extend SDMO to multi-channel images. Based on the self-duality property of traditional morphological operators and the theory of extremum constraint, this paper gives a complete characterization for the construction of multivariate SDMO. We introduce a pair of symmetric vector orderings (SVO) to construct multivariate dual morphological operators. Utilizing extremum constraint to optimize multivariate morphological operators, we further establish methods for the construction of multivariate SDMO. Finally, we illustrate the importance and effectiveness of the multivariate SDMO by an application of noise removal in color images. The experimental results show that the proposed multivariate SDMO provide better results, they can suppress noises efficiently while maintaining image details compared with other operators.