Semidefinite Relaxations for Robust Multiview Triangulation

We propose the first convex relaxation for multiview triangulation that is robust to both noise and outliers. To this end, we extend existing semidefinite relaxation approaches to loss functions that include a truncated least squares cost to account for outliers. We propose two formulations, one based on epipolar constraints and one based on the fractional reprojection equations. The first is lower dimensional and remains tight under moderate noise and outlier levels, while the second is higher dimensional and therefore slower but remains tight even under extreme noise and outlier levels. We demonstrate through extensive experiments that the proposed approach allows us to compute provably optimal reconstructions and that empirically the relaxations remain tight even under significant noise and a large percentage of outliers.