Abstract: On the basis of the order Wilcoxon rank sum statistics in relative half-neighborhood of image pixels, concepts called order Wilcoxon rank sum statistics, statistic gap of order Wilcoxon rank sum, and membership degree of an image edge are proposed. Based on the gap statistic of order Wilcoxon rank sum, a multi-scale images edge detection model is established. Because the proposed model has the property of multi-scale, the excellent anti-noise in the interior of the region, and the noise weakening faintish edge, the corresponding algorithm has good performance in image edge detection. The difference of edge detection between the model and Prewitt operator is analyzed. Lots of experimental examples verify the capacity of the model. Finally, an investigation is taken to compare the difference of edge detection under the circumstance of different scales.