Bayesian Formulation of Gradient Orientation Matching

Gradient orientations are a common feature used in many computer vision algorithms. It is a good feature when the gradient magnitudes are high, but can be very noisy when the magnitudes are low. This means that some gradient orientations are matched with more confidence than others. By estimating this uncertainty, more weight can be put on the confident matches than those with higher uncertainty. To enable this, we derive the probability distribution of gradient orientations based on a signal to noise ratio defined as the gradient magnitude divided by the standard deviation of the Gaussian noise. The noise level is reasonably invariant over time, while the magnitude, has to be measured for every frame. Using this probability distribution we formulate the matching of gradient orientations as a Bayesian classification problem. A common application where this is useful is feature point matching. Another application is background/foreground segmentation. This paper will use the latter application as an example, but is focused on the general formulation. It is shown how the theory can be used to implement a very fast background/foreground segmentation algorithm that is capable of handling complex lighting variations