基于左右导数算子类的边缘提取

Edges detection operators based on right and left derivatives

根据图像灰度的左右导数及其性质构造了几个提取和检测图像阶跃型边缘和屋顶型边缘的算子，并从理论和实验结果上同Ｐｒｅｗｉｔｔ 算子、Ｓｏｂｅｌ 算子、Ｃａｎｎｙ 算子及Ｌａｐｌａｃｉａｎ 算子等进行了比较和分析，发现此类算子包含了这些重要的传统微分算子，而且还具有算法简单灵活，检测精度高和抗噪声干扰能力较强等优点。实验结果还表明在没有进行进一步细化加工的情况下，文中所述的广义左右导数算子无论是检测阶跃型边缘还是屋顶型边缘。

Using the right derivative and left derivative of the image′s gray function, a class of operators to detect the step edges and roof edges are constructed. By comparing and analyzing it with Prewitt, Sobel, Canny and Laplacian operator in the theory and experimental demonstrations, we find that the operators are not only with advantages of simplicity, convenience, higher accuracy of detection and better ability of reducing noise, but also more general than some important classical differential operators. The experimental demonstrations also show whether detecting step edges or detecting roof edges, the effect of the general right and left derivative operators is better than those of all above typical differential operators in the case of no any thinning process.