A conditionally invariant mathematical morphological framework for color images

It is difficult to extend a grayscale morphological approach to color images because total vector ordering is required for color pixels. To address this issue, we developed a kind of vector ordering method based on linear transformations from RGB to other color spaces (i.e., YUV, YIQ and YCbCr) and principal component analysis (PCA). Additionally, we propose a conditionally invariant morphological framework based on the proposed vector ordering. We also define elementary multivariate morphological operators (e.g., multivariate erosion, dilation, opening and closing), and investigate their properties with a focus on duality. The proposed framework guarantees some important properties of classical mathematical morphology, such as translation-invariance, conditional increasingness, and duality. Therefore, it is easy to extend existing grayscale morphological approaches to color images in terms f the proposed multivariate morphological framework (MMF). Simulation results show the potential abilities of MMF in color image processing, such as image filtering, reconstruction, and segmentation.