Abstract: In view of the problem that the traditional integer order differential image is blurred and affected by noise, the algorithm starts with the improvement of the traditional integer order differential Sobel operator. The fractional differential Sobel operator is derived with the fractional differential theory. The algorithm is combined with edge detection method of Sobel operator. The integer order differential Sobel operator is used as a filter and convolution operation with fractional order differential Sobel operator. The algorithm improves integer order differential Sobel operator. Fractional differential Sobel operator by integer order differential filtering solves the problems of low accuracy and poor noise resistance of the traditional edge detection operators successfully. Theoretical research and experimental results show that the edge detection operator is more precise and robust to image edge details, which is better than the commonly used integer order differential edge detection operator and the algorithm has good edge detection effect.

Key words: Sobel operator, integer differential, filter, fractional differential, edge detection

摘要： 针对传统的整数阶微分图像边缘检测算子存在的边缘模糊不清、受噪声影响大等问题，该算法从改进传统的整数阶微分Sobel算子入手，以分数阶微分理论为基础推导出了分数阶微分Sobel算子，结合Sobel算子边缘检测方法，将整数阶微分Sobel算子作为滤波器与分数阶微分Sobel算子作卷积运算，改进了整数阶微分Sobel算子。整数阶微分滤波后的分数阶微分Sobel算子成功地解决了传统的边缘检测算子存在的准确性低、抗噪性差等问题。理论研究与实验结果表明，该边缘检测算子对图像的边缘细节特征刻画得更精细，抗噪性更强，优于常用的整数阶微分边缘检测算子，边缘检测效果很好。

关键词: Sobel算子, 整数阶微分, 滤波器, 分数阶微分, 边缘检测