Image Enhancement Based on Quaternion Fractional Directional Differentiation
基于四元数分数阶方向微分的图像增强

In this paper, according to the developed fractional differentiation and its applications in modern signal processing, we extend it to the quaternion body and put forward a novel concept: quaternion fractional directional differentiation, for image enhancement. We first use a quaternion function to color image and give the definition and calculation method of the quaternion fractional directional derivative. Then, we deduce their numerical calculation templates along eight directions. According to the fractional directional differentiation along the eight directions, the maximum of the norm of quaternion fractional directional differentiation for every point in the image plane is found, then this maximum as the pixel value of this point is viewed, and the enhanced image is obtained. Experimental results show that our method can greatly increase high frequency, reinforce medium frequency, and non-linearly preserve low frequency of signals, hence it is superior to those based on the traditional methods of differentiation in visual effects.