Epipolar Equation Weighting for Accurate Camera Motion from Two Consecutive Frames

This study addresses the problem of estimating camera motion from optical flows detected between successive frames. The problem is formulated as a geometric fitting problem with depth map values as nuisance parameters, and maximum likelihood estimation does not satisfy the Cramer-Rao lower bound. One of the authors has previously proposed an objective function for this problem. This objective function has degrees of freedom in weighting the epipolar equation at each pixel, and it was shown that by setting appropriate weights, an estimator with a smaller variance of the estimation error can be obtained than maximum likelihood estimation. However, to set theoretically optimal weights, the true values of the camera motion and depth maps are needed. In this paper, we first give a new discovery and interpretation of this objective function. We then show that weights equivalent to dividing the image into small regions and averaging the epipolar equations within each region to form a single constraint equation is effective. We further show that better camera motion estimation can be achieved by using the obtained estimates to approximate the optimal weights and then re-estimating them.