An effective resolution definition or how to choose an edge detector, its scale parameter and the threshold?

In this paper, we propose a new quantitative method to choose parameters values of edge detectors based on linear first derivative filters. First, the resolution is explicitly defined as the smallest distance d between edges that the user wants to detect. A new criterion C_d of signal to noise ratio improvement is defined as a function of d. Maximizing this criterion for a given filter defines its best scale parameter value. Then, we analyze quantitatively the effect of the third Canny criterion C₃ (mean distance between noise maxima), and the effect of C_d on the number of false detections. Finally, we discuss quantitatively the choice of the scale parameter and threshold as a function of the desired resolution, output quality, and of the input signal to noise ratio