This research is devoted to the problems in the field of black and white image processing which are connected with the purpose to detect the maximum number of edges and to determine their exact coordinates as far as possible. It is made a critical analysis of the commonly accepted definition of the edge, modeled as a ramp. Consent to this definition there is only an edge which position is in the middle of the ramp connecting low and high level of intensity. Here the authors give a new edge definition, according to it there are two edges (contrary to the classical definition) - one on the low level and a second one - on the high level of intensity. As a result of this understanding the suggested here definition is mathematically formalized by the interrupted first derivative of the intensity function. Based on this definition authors work up an edge detector achieving sub-pixel accuracy when detects edge points' coordinates. There are synthesized appropriate test images and some of the well known edge detectors and the here suggested are applied to them. Results confirm authors' expectations for accuracy of localization and high informativity in the description of the objects in black and white images, which comes very close to their visual susceptibility