由于数字图像中可能包含不同程度的噪声，使得边缘检测在图像处理中变得比较困难。传统的边缘检测算法对于信号中的噪声比较敏感，使得边缘信息不能完全准确地检测出来。本文提出了一种基于零交叉的噪声图像边缘检测方法。在文献［1］算子的基础上先平滑图像，计算图像的梯度，然后对梯度图像用新推导出的递归算子求二阶导数，并分别按行方向和列方向进行过零点检测，最后合并两个方向上检测到的过零点得到图像边缘。实验结果表明，该方法不仅对于含噪图像具有良好的边缘检测效果，而且由于所有滤波算子都是可递归执行的，大大减少了运算量和运算时间。

Detecting edges has become more difficult in image processing since images may contain areas with different degrees of noise.Many traditional methods for edge detection are sensitive to noise,so that the image edge can not be detected clearly. This article presents a noisy image edge detection method  based on zero crossing. This method first smoothes the image and calculates gradient on the basis of edge detection operator in reference［1］,then calculates the second derivative of the gradient image by the new recursive operator,and finds out the zero crossing points by rows and columns respectively,and finally merges all the zero crossing points and gets the image edge.The experimental results show that this method not only gives good edge detection effect,but also spends less computation and time by the recursive implementation of filtering operators.