<title>Kalman filter for improving optical flow accuracy along moving boundaries</title>

Abstract

Optical flow is an important source of information of motion and structure of objects in 3D world. Once the optical flow field is computed accurately, the measurement of image velocity can be used widely in many tasks in computer vision area. Current computer vision techniques require that the relative errors in the optical flow be less than 10%. However, to reduce error in optical flow determination is still a difficult problem. 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. This indicates that the iterations needed in optical flow determination should not be uniform for different image regions. That is, for the moving boundaries, where intensity usually changes bigger, less iterations are needed than for other regions. This is reasonable. In fact, the confidence measure is usually high along moving boundaries since richer information exists there. Therefore, an optical flow algorithm needs to have less iterations along moving boundaries than in other areas so that the better estimation of optical flow along boundaries can be propagated into other areas instead of being blurred by those in other areas. 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. Loosely speaking, 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.