A step edge detector algorithm based on symbolic analysis

This paper analyzes the noise error, in both the module and the argument in the calculation of the gradient vector of the images illumination function. The results show that the behavior of the argument is more robust than that of the module. A proposal is made for a symbolic analysis of the argument of the gradient vector to detect the contour of the objects in the image. This shows that it is possible to use smaller windows to calculate the gradient vector without infringing the contradiction proposed by Marr and Hildreth (1980) and Canny (1983). Finally, a description is given of an edge detection algorithm where their most important characteristics are: a) it introduces a symbolic analysis of the argument of the gradient vector to detect edges; and b) It uses smaller window to approximate the value of the gradient vector allowing to locate the edge with precision.