A statistical method is proposed which estimates an edge that is one of the basic features in image understanding. The conventional edge detection techniques are performed well for a deterministic singnal, but are not satisfactory for a statistical signal. In this paper, we use the likelihood function which takes account of the statistical property of a signal, and derive the decision function from it. We propose the maximum likelihood edge detection technique which estimates an edge point which maximizes the decision function mentioned above. We apply this technique to statistecal signals which are generated by using the random number generator. Simnulations show that the statistical edge detection technique gives satisfactory results. This technique is extended to the two-dimensional image and edges are found with a good accuracy.