中文摘要：

针对噪声图像的边缘检测问题，提出了一种基于圆邻域和环算子的边缘检测方法．首先，在像素点的一个适当的圆邻域内取若干个同心圆环，将这些圆环上的灰度值按径向进行加权平均，得到该像素点周围一圈各等距点上的平均灰度值，这些灰度值可构成一个周期序列；然后根据Sobel和Prewitt等算子的设计思想，构造出一类高通的环算子，利用离散傅里叶变换计算周期序列与环算子的循环卷积，其最大值则作为像素点是否为边缘点的判据．实验结果表明该算法对于含有噪声的图像具有较强的鲁棒性．

英文摘要：

An edge detection approach to noisy images is proposed by circular neighborhood and ring operator. Certain concentric circles were taken in a suitable circular neighborhood of each pixel point and the weighted average intensities of the point, which could be regarded as a periodic sequence, were calculated. According to the idea of Sobel and Prewitt operator, a class of ring operator was designed. Finally, the circulation convolution of the periodic sequence and the ring operator was calculated by the discrete Fourier transform （DFT）, and the ＂gradient＂ of each pixel was obtained according to its maximum value. The approach was carried out on synthetic and nature images corrupted by Gaussian noise. The results show that the algorithm is better than standard Sobel gradient operator and LoG algorithm in terms of visual appearance of edges. The algorithm is suitable for a wide range of images and is robust in a variety of noisy situations.