基于R-L分数阶微分梯度算子的边沿检测

Edge detection based on R-L fractional-order differential gradient operator

在处理数字图像中处理中,为了提取更加细微的边缘信息,克服经典梯度算法的不足,根据R-L分数阶微积分的定义和边缘检测的基本原理,推导出一维离散分数阶微分梯度算子,并且推广到二维,提出了一种基于R-L分数阶微分的新算子模板,并在实验中得以实现。实验结果表明,这种算子更能提取细节信息,使得边缘更加突出,与经典1阶和2阶的边缘检测算子相比,在处理以低频信号为主的图像时有一定的效果提升,而在处理以高频信号为主的图像时有较大的效果提升。

To extract more subtle edge information and overcome the defects of classical gradient algorithm, based on the principles of edge detection and the definition of R-L fractional-order differential and integral, an one-dimensional fractional-order differential gradient operator is derived and extended to two-dimensional in digital image processing. A new R-L fractional-order differential operator can be applied in the experiments, compared with classical operators of 1-order or 2-order, which shows that it extracts more detailed information in the edge detection, and enhances edges better. A new operator template based on the definition of R-L fractional-order differential is presented. On the one hand there are certain promoting effects to deal with low-frequency signal images, on the other hand there are outstanding promoting effects to deal with high-frequency signal image.