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中文摘要：
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。
英文摘要：
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.
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Stability analysis for the generalized Hopfield neural networks with multi-level activation function
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