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. (C) 2017 Elsevier Inc. All rights reserved.