中文摘要：

为了提高图像的对比度，提出一种基于Caputo定义的分数阶对比度增强算法．首先给出分数阶Caputo定义的分数阶方向微分和数值计算方法，并推导了8个方向的分数阶微分模板；用8个方向的微分均值替换该点原像素值，得到增强后的图像；最后证明了二阶Laplacian算子是文中方法的一个特例．实验结果表明，该方法能明显地改善图像的对比度，突出图像的细节信息，增强后的图像具有较好的视觉效果．

英文摘要：

In order to improve the contrast of an image, a Caputo-based fractional differential contrast enhancement algorithm is proposed in this paper. First, the fractional directional derivative and its numerical methods are deduced according to Caputo definition. Then, a fractional differential mask in 8 directions is drawn. The image is enhanced by replacing the pixel value with the mean value of the fractional differentials of the 8 directions. The mathematic proof shows that the second-order Laplacian operator is a special case of the proposed algorithm. The experimental results and analysis show that the proposed algorithm not only can heighten the contrast of images, but also obviously strengthen the textural details and edges of the images. The enhanced images have better visual quality than before.