Epipole and Fundamental Matrix Estimation Using the Virtual Parallax Property

This paper addresses the problem of computing the fundamental matrix which describes a geometric relationship between a pair of stereo images : the epipolar geometry. In the uncalibrated case, epipolar geometry captures all the 3D information available from the scene. It is of a central importance for problems such as 3D reconstruction, self-calibration and feature tracking. Hence, the computation of the fundamental matrix is of great interest. The existing methods 10] uses two steps : a linear step followed by a non linear one. But the linear step gives rarely a close form solution for the fundamental matrix resulting in more iterations for the non linear step which 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 diierently, instead of computing directely the 3 3 fundamental matrix, we compute a homography with one epipole position, and show that this is equivalent to compute the fundamental matrix. Simple equations are derived by reducing the number of parameters to estimate. As a consequence, we obtain an accurate fundamental matrix of rank 2 with a stable linear computation. Experiments with simulated and real images validate our method and clearly show the improvement over the existing methods.