Dense Random Texture Detection using Beta Distribution Statistics
Soeren Molander
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).