A Comparison between the First Absolute Central Moment and the Gradient of Gaussian when Detecting Edges in Presence of Gaussian Noise

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, graylevel 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.