Probabilistic estimation of optical flow in multiple band-pass directional channels

Abstract Band-pass directional filters are not normally used as pre-filters for optical flow estimation because their orientation selectivity tends to increase the aperture problem. Despite this fact, here we obtain multiple estimates of the velocity by applying the classic gradient constraint to the output of each filter of a bank of six directional second-order Gaussian derivatives at three spatial resolutions. We obtain estimates of the velocity and of its associate covariance matrix, which define a full probability density function for the Gaussian case. We use this probabilistic representation to combine the resulting multiple velocity estimates, by first segmenting them in coherent motion processes, and then combining the estimates inside each coherent group assuming independence. Segmentation maintains the ability to represent multiple motions and helps to reject outliers so that the final estimates are robust, while combination helps to reduce the initial aperture problem. Results for synthetic and real sequences are highly satisfactory. Mean angular errors in complex standard sequences are similar to those provided by most published methods.