关键词: 边缘检测, 纹理图像, Sobel算子, 非整数步长, 分数阶微分

Abstract: In response to the relatively low edge detection precision of the role played by fractional order edge extraction operator in images containing a large number of smooth regions as well as those with abundant texture, relevant improvement has been made in Gruwald-Letnikov（G-L） fractional differential integer step size and the traditional Sobel operator. Besides, a new fractional differential mask template is structured by means of Gaussian weighted Lagrange’s interpolation for a definite gray value of a non-integral point. Theoretical research and experimental analysis indicate that the model can be adopted for detecting images containing a large number of smooth regions as well as those with abundant texture, precision and clarity significantly improved.

Key words: edge detection, texture image, Sobel operator, non-integer step , fractional derivative