中文摘要：

分数阶微分理论用于图像处理是近期一个新的研究课题．文中从分数阶微分对图像细微细节的增强能力出发，对分数阶微分的机理进行分析，且根据分数阶微分Tiansi算子的作用特点，提出一种可大幅增强边缘信息值的改进Tiansi算子方法．具体的做法是将Tiansi模板分解为8个不同方向的小模板，得到像素点周围8个方向的加权求和值．然后将8个值进行不同的分组，得到增强幅度不同的3种改进方法．最后通过增强的实验表明，对于岩石节理裂隙图像而言，改进方法可有效增强边缘并且比传统算子得到更丰富的细节信息．

英文摘要：

Applying the fractional differential theory to image processing is a new research topic. According to the functional characteristics of fractional differential Tiansi operator, an algorithm is proposed to improve Tiansi operator. The algorithm significantly enhances the edge information value. It is based on the enhancement ability of fractional differential to image details and the mechanism analysis of fractional differential. 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. Next, the eight weights are divided into different groups. Consequently, three improved algorithms with different enhancing ranges are gained. Finally, the experimental results of edge enhancement show that the improve algorithm enhances edge information effectively and reveals more detailed information than traditional operators for rock fracture images.