Nonlinear Estimation of the Fundamental Matrix with Only Five Unknowns

Two images captured by an uncalibrated binocular vision system are related by the epipolar geometry. This geometry is completely characterized by a 3 x 3 matrix, called the fundamental matrix, which can be obtained from a set of point correspondences. This paper presents a new nonlinear method to calculate the fundamental matrix. To impose the rank two restriction, the method uses a quite simple parametrization. It has the advantage of having a reduced search space, with only five unknowns. Experimental tests demonstrated that the new method obtain accurate results for a large set of point correspondences. In this case, the quality of the estimated matrix is as good as the obtained with other nonlinear methods. However, the results are obtained at a low computational cost and with rapid convergence.