深入地研究了数学形态学在边缘检测领域中的应用，系统地给出了形态差分算子的定义。同时，还研究了在受脉冲噪声污染的情况下，如何用形态差分算子准确地提取图象的边缘，并提出了几种具有抗噪能力的数学形态边缘检测算子。计算机模拟实验表明，正确使用数学形态的４种基本运算，将使数学形态边缘检测算子能较好地消除脉冲噪声对边缘的影响，效果优于其它边缘检测算子

This paper extensivey studies the application of mathematical morphology to the field of edge detecting. The definitions of morphological differentiating operators are systematically presented. In the mean time, several anti-noises morphological differentiating operators are developed to deal with the images corrupted by impulses. It is shown by computer simulations that, by appropriately using the four basic operators of mathematics morphology, the influence of impulsive noise on edge detecting will be eliminated by morphological differentiating operators. The morphological edge detectors will outperform other edge detectors.