Abstract: The present edge detection algorithms are sensitive to noise, they may not get ideal effect on image edge detection and result in unclear image edges. To overcome these shortages, a new edge detection model is proposed, which is based on the theory of fractional differential and combines with the image edge detection method of Sobel operator. Both theoretical researches and simulation results show that compared with existing methods, the new model is able to extract the characteristics of image edge better, and has better inhibitory effect on image noise. Especially, for images with more texture details, it is better than existing integer order differential methods since it can detect more texture information. Therefore, it is an effective edge detection method.

Key words: edge detection, fractional differential, Sobel operator, texture details

摘要： 现有的边缘检测算法对噪声敏感，检测到的图像边缘效果不够理想，得到的图像边缘有可能模糊不清。为了克服这些不足，以分数阶微分理论为基础，结合Sobel算子边缘检测方法，提出了一种基于分数阶微分和Sobel算子的边缘检测新模型。理论研究和实验结果表明，与现有方法相比较，该模型不仅能较好地提取图像边缘特征，而且对噪声具有一定的抑制作用；特别地，对于纹理细节较丰富的图像而言，该模型能够检测出更多的纹理细节信息，优于常用的整数阶微分方法，是一种有效的边缘检测方法。

关键词: 边缘检测, 分数阶微分, Sobel算子, 纹理细节