Volterra filters for perceptual edge extraction

We investigate a class of quadratic Volterra filters, which can be used as computationally efficient edge detectors. Filters from this class are approximately equal to mean-weighted highpass filters, and therefore, they extract fewer edges from dark areas, which is a desirable property for many image enhancement applications. We study the one-dimensional case first and then generalize the results to two dimensions. Since the four-dimensional frequency response yields little insight in the properties of these filters, we also develop a technique for characterizing these filters in a more intuitive way. Using the observation that they map sinusoidal inputs to constant outputs, we employ two-dimensional oriented sinusoids to assess both the frequency characteristics and the degree to which a filter is isotropic, i.e., independent of the input orientation