New fundamental matrix estimation method using global optimization

The estimation of fundamental matrix is one of the most crucial steps in many computer vision applications such as 3D reconstruction, autocalibration and motion segmentation. In this paper, we give a new method for nonlinearly estimating the fundamental matrix from point correspondences using global optimization. We firstly parameterize the fundamental matrix in 7 unknowns in a way that the rank-two constraint is satisfied. Then, the fundamental matrix is estimated by globally minimize non-convex formulation in term of convex (linear matrix inequality) LMI relaxation and standard LMI techniques. In order to obtain robustness, we perform the computation in a RANSAC framework and consider nonlinear criteria minimizing meaningful geometric distances. The iterate process leads the estimation to a more accurate level. Experimental results show the effectiveness of the proposed method.