A Caputo Fractional Differential Approach to Image Enhancement

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.