Very few linear vector filters are known for color images and this may be due to the lack of a mathematical framework. This paper explores some possible mathematical approaches to linear vector filtering, including hypercomplex numbers, and dot and cross products. It also considers the fundamental pixel level operations that must exist to make linear vector filtering possible.
S. J. Sangwine, "Mathematical Approaches to Linear Vector Filtering of Color Images" in Proc. IS&T CGIV 2002 First European Conf. on Colour in Graphics, Imaging, and Vision, 2002, pp 348 - 351, https://doi.org/10.2352/CGIV.2002.1.1.art00073