Fundamental matrix from optical flow: optimal computation and reliability evaluation

The optical flow observed by a moving camera satisfies, in the absence of noise, a special equation analogous to the epipolar constraint arising in stereo vision. Computing the "flow fundamental matrix" of this equation is an essential prerequisite to undertaking three-dimensional analysis of the flow. This article presents an optimal formulation of the problem of estimating this matrix under an assumed noise model. This model admits independent Gaussian noise that is not necessarily isotropic or homogeneous. A theoretical bound is derived for the accuracy of the estimate. An algorithm is then devised that employs a technique called renormalization to deliver an estimate and then corrects the estimate so as to satisfy a particular decomposability condition. The algorithm also provides an evaluation of the reliability of the estimate. Epipoles and their associated reliabilities are computed in both simulated and real-image experiments. Experiments indicate that the algorithm delivers results in the vicinity of the theoretical accuracy bound. (C) 2000 SPIE and IS&T. [S1017-9909(00)01202-2].