Quaternion Diffusion for Color Image Filtering

How to combine color and multiscale information is a fundamental question for computer vision, and quite a few color diffusion techniques have been presented. Most of these proposed techniques do not consider the direct interactions between color channel pairs. In this paper, a new method of color diffusion considering these effects is presented, which is based on quaternion diffusion (QD) equation. In addition to showing the solution to linear QD and its analysis, one form of nonlinear QD is discussed. Compared with other color diffusion techniques, considering the interactions between channel pairs, QD has the following advantages: 1) staircasing effect is avoided; 2) as diffusion tensor, the image derivative is regularized without requiring additional convolution; 3) less time is needed. Experimental results demonstrate the effectiveness of linear and nonlinear QD applied to natural color images for denoising by both visual and quantitative evaluations.