A Convex Optimization Approach to Robust Fundamental Matrix Estimation

This paper considers the problem of recovering a subspace arrangement from noisy samples, potentially corrupted with outliers. Our main result shows that this problem can be formulated as a constrained polynomial optimization, for which a monotonically convergent sequence of tractable convex relaxations can be obtained by exploiting recent developments in sparse polynomial optimization. Further, these results allow for deriving conditions certifying that a finite order relaxation has converged to a solution. A salient feature of the proposed approach is its ability to incorporate existing a-priori information about the noise, co-ocurrences, and percentage of outliers. These results are illustrated with several examples where the proposed algorithm is shown to outperform existing approaches.