A constant-false-alarm-rate (CFAR) edge detector based on the ratio between pixel values is described. The probability distribution of the image obtained by applying the edge detector is derived. Hence, the decision threshold can be theoretically determined for a given probability of false alarm as a function of the number of looks of the image under study and the size of the processing neighborhood. For a better and finer detection, the edge detector operates along the four usual directions over windows of increasing sizes. A test performed, for a given direction, on a radar image of an agricultural scene shows good agreement with the theoretical study. The operator is compared with the CFAR edge detectors suitable for radar images.