Kalman filter for improving optical flow accuracy along moving boundaries

In this paper, we propose a Kalman filtering for improving accuracy in determining optical flow along moving boundaries. Firstly, a quantitative analysis on the error decreasing rate in iteratively determining optical flow using the correlation-based technique is given. It concludes that this error decreasing rate is varied for different regions in an image plane: it is larger for the regions where intensity varies more drastically, it is smaller for those where intensity varies more smoothly. Secondly, we propose a Kalman filter to realize the task of applying different number of necessary iterations in determining optical flow to deblur boundary and enhance accuracy. The idea is whenever the standard deviation of optical flow at a pixel is less than certain criterion, i.e., good accuracy has been achieved, the Kalman filter will not further update optical flow at this pixel, thus conserving accuracy along moving boundaries. Assuming that estimated optical flow field is contaminated by a Gaussian white noise, we give appropriate considerations to the system and measurement noise covariance matrices, Q and R, respectively. In this way, the Kalman filter is used to eliminate noise, raise accuracy and refine accuracy along discontinuities. Finally, an experiment is presented to demonstrate the efficiency of our Kalman filter. Two objects are considered. One is stationary, while another is in translation. Unified optical flow field (UOFF) quantities are determined by using the proposed technique. The 3D position and speeds are then estimated by using UOFF approach. Both results obtained with and without the Kalman filter are given. A more than 10% improvement is achieved in this experiment. It is expected that the more moving boundaries in the scene, the more effectively the scheme works.