A STABLE AND ACCURATE ALGORITHM FOR COMPUTING EPIPOLAR GEOMETRY

This paper addresses the problem of computing the fundamental matrix w hich describes a geometric relationship between a pair of stereo image s: the epipolar geometry. In the uncalibrated case, epipolar geometry captures all the 3D information available from the scene. It is of cen tral importance for problems such as 3D reconstruction, self-calibrati on and feature tracking. Hence, the computation of the fundamental mat rix is of great interest. The existing classical methods(14) use two s teps: a linear step followed by a nonlinear one. However, in some case s, the linear step does not yield a close form solution for the fundam ental matrix, resulting in more iterations for the nonlinear step whic h is not guaranteed to converge to the correct solution. In this paper , a novel method based on virtual parallax is proposed. The problem is formulated differently; instead of computing directly the 3 x 3 funda mental matrix, we compute a homography with one epipole position, and show that this is equivalent to computing the fundamental matrix. Simp le equations are derived by reducing the number of parameters to estim ate. As a consequence, we obtain an accurate fundamental matrix with a stable linear computation. Experiments with simulated and real images validate our method and clearly show the improvement over the classic al 8-point method.