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

摘要： 针对现有的分数阶边缘提取算子对于具有大量的平滑区域图像和丰富纹理图像的边缘检测精度较低的情况，对Gruwald-Letnikov（G-L）分数阶微分整数步长和传统的Sobel算子进行了相关的改进，并利用高斯加权的拉格朗日插值方法确定非整数点的灰度值，构造了一个新的分数阶微分掩模模板。理论研究与实验分析表明：该模型可用于检测含有丰富的纹理细节与大量的平滑区域的图像，且检测精度与清晰程度都有显著的提高。

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