Properties of energy edge detectors

The author introduces a framework for investigating the properties of energy edge detectors and uses it to derive some results of interest. He shows a necessary condition on the form of constituent linear filters in quadratic detectors, subject to some conditions, and demonstrates some limitations of such detectors. It is shown that no quadratic detector can detect an edge at 0 for both a sinewave and a cosine wave, which has implications for detecting narrowband edges with spatially local filters. It is also shown that the scale-space behavior of energy detectors is not well-behaved, in that it contains bifurcations as scale increases, i.e. new edges can be created as the image is smoothed