Fundamental matrix from optical flow: optimal computation and reliability evaluation

The optical flow observed by a moving camera satisfies, in the absence of n oise, a special equation analogous to the epipolar constraint arising in st ereo vision. Computing the "flow fundamental matrix" of this equation is an essential prerequisite to undertaking three-dimensional analysis of the fl ow. This article presents an optimal formulation of the problem of estimati ng this matrix under an assumed noise model. This model admits independent Gaussian noise that is not necessarily isotropic or homogeneous. A theoreti cal bound is derived for the accuracy of the estimate. An algorithm is then devised that employs a technique called renormalization to deliver an esti mate and then corrects the estimate so as to satisfy a particular decomposa bility condition. The algorithm also provides an evaluation of the reliabil ity of the estimate. Epipoles and their associated reliabilities are comput ed 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].