Color-Dependent Diffusion Equations Based on Quaternion Algebra

Based on quaternion algebra, this paper proposes two new smoothing models called colordependent 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.