A comparison between the first absolute central moment and the gradient of Gaussian when detecting edges in presence of Gaussian noise

Abstract

The gray-level absolute central moment of the first order provides ridges at gray-level discontinuities as well as a conventional gradient of Gaussian (GoG). A mass center b of the gray-level variability can also be associated to the first absolute central moment. When given a starting point p, vector b indicates the path which joins p to the nearest gray-level discontinuity as well as the gradient of the GoG magnitude. However, when the right configuration of the operator is chosen, vector b indicates a point which is closer to the discontinuity than p, regardless of the distance between p and the discontinuity. Therefore, when using vector b, gray-level discontinuities can be located with an iterative approach. In this paper, the edge detection properties of the first absolute central moment are compared with those of the GoG.