A convex optimization approach to robust fundamental matrix estimation

This paper considers the problem of estimating the fundamental matrix from corrupted point correspondences. A general nonconvex framework is proposed that explicitly takes into account the rank-2 constraint on the fundamental matrix and the presence of noise and outliers. The main result of the paper shows that this non-convex problem can be solved by solving a sequence of convex semi-definite programs, obtained by exploiting a combination of polynomial optimization tools and rank minimization techniques. Further, the algorithm can be easily extended to handle the case where only some of the correspondences are labeled, and, to exploit co-ocurrence information, if available. Consistent experiments show that the proposed method works well, even in scenarios characterized by a very high percentage of outliers.