Seeing double without confusion: Structure-from-motion in highly ambiguous scenes

3D reconstruction from an unordered set of images may fail due to incorrect epipolar geometries (EG) between image pairs arising from ambiguous feature correspondences. Previous methods often analyze the consistency between different EGs, and regard the largest subset of self-consistent EGs as correct. However, as demonstrated in [14], such a largest self-consistent set often corresponds to incorrect result, especially when there are duplicate structures in the scene. We propose a novel optimization criteria based on the idea of `missing correspondences´. The global minimum of our optimization objective function is associated with the correct solution. We then design an efficient algorithm for minimization, whose convergence to a local minimum is guaranteed. Experimental results show our method outperforms the state-of-the-art.