Dense Random Texture Detection using Beta Distribution Statistics

This note describes a method for detecting dense random texture using fully connected points sampled on image edges. An edge image is randomly sampled with points, the standard L2 distance is calculated between all connected points in a neighbourhood. For each point, a check is made if the point intersects with an image edge. If this is the case, a unity value is added to the distance, otherwise zero. From this an edge excess index is calculated for the fully connected edge graph in the range [1.0..2.0], where 1.0 indicate no edges. The ratio can be interpreted as a sampled Bernoulli process with unknown probability. The Bayesian posterior estimate of the probability can be associated with its conjugate prior which is a Beta($\alpha$, $\beta$) distribution, with hyper parameters $\alpha$ and $\beta$ related to the number of edge crossings. Low values of $\beta$ indicate a texture rich area, higher values less rich. The method has been applied to real-time SLAM-based moving object detection, where points are confined to tracked boxes (rois).