Fractional differential algorithms for rock fracture images

Abstract

It is a new research topic that fractional differential theory is used into image processing. This paper presents a new type of algorithms to improve the fractional differential Tiansi operator, which can significantly enhance the edge detection result. The studied algorithms are based on the enhancement ability of fractional differential to image details, and they can be used to analyse the properties of fractional differential. The general procedure of the algorithms is as follows: firstly, Tiansi template is divided into eight sub-templates with different directions around the detecting pixel, and then the eight weight sum values for the eight sub-templates are obtained. Furthermore, those eight weights are classified into different groups. In this way, the three improved algorithms with different enhancing ranges are obtained. Finally, the experiments of edge detection show that the improved algorithms can obtain edge information more effectively and can show much more detailed information than traditional edge detection operators especially for the images of fine edges such as complicated rock fracture images.