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.