Robust Camera Translation Estimation via Rank Enforcement

Camera translation averaging, aiming to recover the global camera locations from a given set of camera translation directions, is a challenging problem for Structure from Motion (SfM) in the field of computer vision, largely due to the fact that the given relative translation directions from a set of noisy essential matrices are generally of low accuracy. To tackle this problem, we first reveal a novel but a simple property of the camera translation matrix consisting of all the pairwise camera translations among an arbitrary set of cameras that the rank of this translation matrix is always smaller or equal to 4. Then, by explicitly enforcing this rank property, a novel translation estimation method for computing global camera locations is proposed, called TERE. Moreover, to further improve the performances of the explored TERE in the two aspects of accuracy and speed, an iterative batch-based translation estimation method is proposed, called B-TERE, where a small-scale batch of cameras is selected without replacement from the given set of cameras according to a simple camera selection strategy at each iterative step, and the locations of the selected cameras are estimated by the proposed TERE accordingly. Extensive experimental results on various datasets demonstrate that our proposed methods could achieve better performances in comparison to several state-of-the-art methods.