Bias introduced by mean orientation estimation methods

Many problems deal with two-dimensional random variables. One of them concerns the estimation of statistical parameters from a gradient vector field on a 2D-lattice. Special interest has been devoted to the extraction of orientation on textures. Unfortunately, the computation of directional statistics may introduce anomalies and distortions in the statistical distribution of orientation measures. This article gives a theoretical explanation to this phenomenon and provides a possible answer to such a problem, based on the sub-sampling of the gradient orientation field.