Nonlinear processing and analysis of angular signals

Physical quantities referring to angles, like vector direction, color hue e.t.c. exhibit an inherently periodic nature. Due to this periodicity, digital lters and edge operators proposed for data on the line cannot be applied on such data. In this paper we introduce lters for angular signals (circular mean, circular median, circular a-trimmed mean, circular modiied trimmed mean). Particular emphasis is given to the circular median lter 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 quasi-range to circular data are proposed and expressions for their output pdf are derived. These \circular" quasi-ranges 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 1-D angular signals and hue images is used to illustrate the operation of the new lters and edge detectors.