Nonlinear processing and analysis of angular signals

Physical quantities referring to angles, like vector direction, color hue, etc., exhibit an inherently periodic nature. Due to this periodicity, digital filters and edge operators proposed for data on the line cannot be applied on such data. We introduce filters for angular signals (circular mean, circular median, circular a-trimmed mean, circular modified trimmed mean). Particular emphasis is given to the circular median filter, for which some interesting properties are derived. We also use estimators of circular dispersion to introduce edge detectors for angular signals. Three variations for the extension of quasirange to circular data are proposed, and expressions for their output PDF are derived. These "circular" quasiranges have good and user-controlled properties as edge detectors in noisy angular signals. The performance of the proposed edge operators is evaluated on angular edges, using certain quantitative criteria. Finally, a series of experiments featuring one-dimensional (1-D) angular signals and hue images is used to illustrate the operation of the new filters and edge detectors.