一种基于分数阶次微积分模板的新型边缘检测方法

利用分数阶次微分和分数阶次积分组成复合导数, 在复合导数基础上提出了一种边缘检测新算子. 为实现分数阶次微分, 推导出一种新的复数模板. 通过检测一维曲线, 验证了复合导数可以近似模拟一阶导数并具有抑制噪声的能力. 二维图像的检测结果表明, 新算子在无噪声干扰情况下可以精确、有效地完成边缘检测任务; 在有噪声情况下可以有效地抑制噪声干扰. 最后, 对新算子进行了定量分析并与 Canny 算子进行比较. 结果表明新算子具有低定位错误率的优势.

A Novel Edge Detection Method Based on Fractional-order Calculus Mask

In this paper, a new edge detection operator based on a composite derivative is proposed, which is realized by the combination of fractional differentiation and integration. The new complex edge-detection mask is also deduced for the implementation of fractional differentiation. The abilities of the compound derivative in terms of approximate simulation of first-order derivative and suppression of noise are demonstrated through one-dimensional examples. The experimental results of two-dimensional examples indicate that without the contamination of noise, the new operator can accurately detect the edge, while with the noise contamination, the new operator can effectively suppress the noise. Finally, quantitative analysis of the new operator is given. The results of the comparison between the new operator and Canny operator show that the new operator has the advantage of a low mispositioning rate.