数学形态学是几何形态分析和描述的有力工具,已经构成了一种新的数字图像分析理论。文中从频域的角度出发,给出了形态尺度空间中腐蚀和膨胀的频率响应,并且证明了形态腐蚀和膨胀操作算子是一种低通滤波器,而信号经微分再经腐蚀和膨胀的综合作用相当于带通滤波器。 Mathematical morphology is a powerful tool for geometric analysis and description, and has formed a new theory of digital image analysis. In this paper, the frequency response of corrosion and expansion in the form-scale space is given from the perspective of the frequency domain. It is also proved that the operator of morphological erosion and expansion is a low-pass filter, and the signal is differentiated and then corroded and expanded The combined effect of the equivalent of band-pass filter.