In many digital images, edges do not have a step-like shape but appear as a ramp shape with a very low slope because of noise and blurring effects. In such cases, the white noise model does not hold and the edges are usually called diffuse edges. This paper describes a new second-order gradient based algorithm for the detection of diffuse edges. In the gradient-based edge detection algorithm, such as the LoG filter, there are three basic operations: smoothing as a preprocessing operation to reduce the noise effects, gradient generation - the main operation, and edge linking as a post-processing operation. We propose to use median filtering instead of Gaussian lowpass filtering to reduce the noise, and then introduce a complementary operator of 2D averaging as a second-order gradient generator, and a simple thresholding algorithm to detect zero-crossings. The edge image is finally constructed from edge thinning and linking operations. Simulation results obtained using the proposed edge detection algorithm in comparison with some other commonly used algorithms are included.