Exact Camera Location Recovery by Least Unsquared Deviations

We establish exact recovery for the Least Unsquared Deviations (LUD) algorithm of \"{O}zyesil and Singer. More precisely, we show that for sufficiently many cameras with given corrupted pairwise directions, where both camera locations and pairwise directions are generated by a special probabilistic model, the LUD algorithm exactly recovers the camera locations with high probability. A similar exact recovery guarantee was established for the ShapeFit algorithm by Hand, Lee and Voroninski. Comparing the two results, we conclude that in theory LUD can tolerate more corruption than ShapeFit.