Unconventional edge detector: preliminary theoretical investigation

We have previously described a range-based neighbourhood operator and an experimentally discovered unconventional edge detector based on it. The latter relies on data fitting in a pixel neighbourhood, and has a wide dynamic range. A preliminary theoretical investigation of its basis, and some of its properties, are presented in this paper. It is revealed that the edge sensitive feature is the range of pixel values in successive pixel annuli around a central pixel. It is also shown that the edge strength at any centre pixel may be approximated, in the first instance, by the sum of the logarithms of these annular range values. The derived approximation is illustrated with a synthetic image and a mammogram.