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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，其效果都要比上述传统微分算子好
According to the left and right derivatives of image grayscale and its properties, several operators for extracting and detecting image edge and roof edge are constructed. Based on the theoretical and experimental results, several prewitt operators, Sobel operators, Canny operators and Laplacian operators are compared and analyzed. It is found that these operators include these important traditional differential operators, but also have the advantages of simple and flexible algorithm, high detection accuracy and strong anti-noise ability. The experimental results also show that the generalized left and right derivative operators described in this paper are better than the traditional differential operators in both the step edge detection and the roof edge detection without further refinement processing