The First Absolute Central Moment in Low-Level Image Processing

The first absolute central moment is a statistical filter which measures the variability of the gray levels of the image with respect to the local mean. The analysis of the responses of the central and absolute central moments at noiseless isolated step discontinuities shows how the first absolute central moment can be usefully used to enhance these discontinuities. Moreover, experimental results show how a non-standard form of the absolute central moment should be used to enhance other image key points. At noiseless step discontinuities, the first absolute central moment provides a ridge map similar to the one provided by the GoG magnitude. However, unlike the GoG magnitude, a non-standard form of the first absolute central moment provides ridges at both edges and lines (pulse functions one pixel wide) and gives rise to local extrema of the ridges at line endings, corners, and intersections among different discontinuities. The analysis of the filter output in the presence of additive noise also shows that a generalized form of the first absolute central moment should be used to cope with noise properly. Both theoretical and experimental results show that, if right configurations of the generalized first absolute central moment are used, the filter retains most of its properties when real images are considered. Moreover, since the generalization of the original filter gives rise to a class of nonlinear filters, then the recovered edge information can be also usefully combined and two examples are illustrated in this paper. The first one shows how the zero-crossing map of an equivalent DoG filter can be obtained, whereas the second one shows how to obtain a local thresholding procedure.