On the choice of band-pass quadrature filters

Band-pass quadrature filters are extensively used in computer vision to estimate information from images such as: phase, energy, frequency and orientation,(1) possibly at different scales and utilise this in further processing-tasks. The estimation is intrinsically noisy and depends critically on the choice of the quadrature filters. In this paper, we first study the mathematical properties of the quadrature filter pairs most commonly seen in the literature and then consider some new pairs derived from the classical feature detection literature. In the case of feature detection, we present the first attempt to design a quadrature pair based on filters derived for optimal edge/line detection. A comparison of the filters is presented in terms of feature detection performance, wherever possible, in the sense of Canny and in terms of phase stability. We conclude with remarks on how our analysis can aid in the choice of a filter pair for a given image processing task.