Color-Dependent Diffusion Equations Based on Quaternion Algebra

Based on quaternion algebra, this paper proposes two new smoothing models called color-dependent diffusion equations. One model is designed to only smooth the components in the direction of a chosen color. The other model is designed to only smooth the components perpendicular to the direction of a chosen color. To improve the color selectivity, a weight factor
$W$
is proposed. For example, if we filter the parallel components of the image, greater weight is given to pixels with the color close to the chosen color. Finally, a color-dependent diffusion scheme is presented, which can detect a chosen color edge or low-pass filter a certain color efficiently. Experimental results demonstrate the effectiveness of this scheme applied to natural color images.