On the gray-level central and absolute central moments and the mass center of the gray-level variability in low-level image processing

The gray-level moments are usually used in image processing literature to describe how the gray-levels of a finite domain of the image are distributed with respect to the mean level. However, the gray-level central and absolute central moments can provide zero-crossings and ridges, respectively, at gray-level discontinuities as well as conventional operators like the Laplacian of Gaussian and the gradient of Gaussian. A mass center b of the gray-level variability can be also defined. When given a starting point p, vector b indicates the path which joins p to the nearest gray-level discontinuity. Moreover, when a moment of even order is used, vector b can indicate a point which is closer to the discontinuity than p regardless of the distance between p and the discontinuity. Therefore, given an approximate starting contour, a discontinuity can be located by iteratively computing the mass centers of the points of the starting contour.