中文摘要：

为了提取出更加精确和细微的边缘信息,同时为了具有更好的抗噪性能,提出了一种新的分数阶微分梯度算子。根据Riemann-Liouville分数阶微积分定义,推导出了非整数步长的分数阶微分方程,并采用拉格朗日插值方法确定非整数步长像素点的灰度值,进而构造出八个方向的微分掩模,实现了图像边缘检测。实验表明,该方法更好地利用了图像的自相关性,比传统的边缘检测算子能更好地提取图像边缘细节,且对噪声具有更好的鲁棒性。

英文摘要：

To extract more accurate and subtle edge information, and also to obtain better anti-noise capability, this paper proposed a new fractional order differential based image edge detection operator. It derived the fractional order differential equation based on non-integer step according to the Riemann-Liouville definition, and used the method of Lagrange interpolation polynomial to get the gray value of non-integer step pixel. It constructed eight directions fractional order differential mask to realize image edge detection. The experimental results show that this method used more advantage of image autocorrelation so it can extract more detail edge information than the classic method of edge detection, also it has a better anti-noise capability.