提出了一种基于δ函数的图象边缘检测算法.首先提出了正则化的 Shannonδ函数，它是低通滤波器，且其傅立叶变换是无限可微的，接着推导了正则化的 Shannonδ函数及其一阶导数的时域和频域公式，研究了正则化的 Shannonδ函数及其一阶导数与参数 s和 t的关系.然后根据正则化的 Shannonδ函数及其一阶导数，提出了两种边缘检测算法 :一种是用于精细地检测边缘的 D算法 ;另一种是用于从含噪图象中检测边缘的 C算法.D算法用正则化的 Shannonδ函数的一阶导数检测边缘.C算法用正则化的 Shannonδ函数平滑噪声，用正则化的 Shan-nonδ函数的一阶导数检测边缘.最后进行了仿真实验，仿真实验表明，D算法的性能由其参数决定，且该算法优于Sobel算法和 Prewitt算法 ;C算法优于 Sobel算法和 Prewitt算法，且与 Canny算法的性能相当.总之，该算法是一种能有效地从无噪声图象中检测细节边缘和从噪声图象中检测边缘的边缘检测算法

This paper discusses aδfunction based algorithm for image edge detection. This paper firstly proposed regularized Shannonδfunction, which is a low-pass filter and is infinitely differentiable in frequency domain, and overcomes the shortness of Shannonδfunction, that Shannonδfunction is an ideal low-pass IIR filter and its Fourier transform is not differentiable. This paper gives formulas of regularized Shannonδfunction and its first or- der derivative both in time domain and in frequency domain, and studies the relations between regularized Shannon δfunction and its first order derivative and the parameters ofsandt. Then this paper provides two kinds of edge detection algorithm based on regularized Shannonδfunction and its first order derivative. One is D algorithm for detecting image edge in detail, the other is C algorithm for detecting image edge from noised image. D algorithm uses the first order derivative of regularized Shannonδfunction for edge detection. C algorithm uses regularized Shannonδfunction for smoothing noise and uses the first order derivative of regularized Shannonδfunction for edge detection. Finally this paper does two simulation experiments. Simulation experiments of D algorithm show that, the property of this algorithm is related to its parameters and the edge detection ability of this algorithm is better than that of Sobel algorithm and Prewitt algorithm. Simulation experiments of C algorithm show that, this algorithm is better than Sobel algorithm and Prewitt algorithm and the edge detection ability of this algorithm is the same as that of Canny algorithm. In a word, the method of this paper is an efficient edge detecting algorithm for detecting details form clean image and detecting edges from noised image.