Abstract: The present fractional differential operators for edge detection are constructed based on 0~1-order fractional differential. There are rare papers which discuss the edge detection based on 1~2-order fractional differential. This paper analyses the effect of 1~2-order fractional differential to signal, and then constructs a novel mask operator for edge detection based on 1~2-order fractional differential. Experimental results demonstrate that the novel fractional operator is better than the normal integer order differential operators, and has better edge detection results than some present 0~1-order fractional differential operators.

Key words: edge detection, fractional differentiation, mask operator, 1~2-order differential

摘要： 现有的分数阶微分边缘检测算子大都是基于0~1阶分数阶微分而构造，鲜有文献讨论基于1~2阶分数阶微分的边缘检测算子。为此，分析了1~2阶分数阶微分对信号的作用，基于1~2阶分数阶微分构造了一种新的边缘检测掩模算子。实验结果表明，该算子不仅优于常用整数阶微分算子，而且比现有的一些0~1阶分数阶微分算子具有更好的边缘检测效果。

关键词: 边缘检测, 分数阶微分, 掩模算子, 1~2阶微分