We introduce a new method for location recovery from pair-wise directions that leverages an efficient convex program that comes with exact recovery guarantees, even in the presence of adversarial outliers. When pairwise directions represent scaled relative positions between pairs of views (estimated for instance with epipolar geometry) our method can be used for location recovery, that is the determination of relative pose up to a single unknown scale. For this task, our method yields performance comparable to the state-of-the-art with an order of magnitude speed-up. Our proposed numerical framework is flexible in that it accommodates other approaches to location recovery and can be used to speed up other methods. These properties are demonstrated by extensively testing against state-of-the-art methods for location recovery on 13 large, irregular collections of images of real scenes in addition to simulated data with ground truth.
3D structure recovery from a collection of 2D images requires the estimation of the camera locations and orientations, i.e. the camera motion. For large, irregular collections of images, existing methods for the location estimation part, which can be formulated as the inverse problem of estimating n locations t 1 , t 2 , …, tn in ℝ 3 from noisy measurements of a subset of the pairwise directions t i −t j ∥t i −t j ∥, are sensitive to outliers in direction measurements. In this paper, we firstly provide a complete characterization of well-posed instances of the location estimation problem, by presenting its relation to the existing theory of parallel rigidity. For robust estimation of camera locations, we introduce a two-step approach, comprised of a pairwise direction estimation method robust to outliers in point correspondences between image pairs, and a convex program to maintain robustness to outlier directions. In the presence of partially corrupted measurements, we empirically demonstrate that our convex formulation can even recover the locations exactly. Lastly, we demonstrate the utility of our formulations through experiments on Internet photo collections.  We present a simple, effective method for solving structure from motion problems by averaging epipolar geometries. Based on recent successes in solving for global camera rotations using averaging schemes, we focus on the problem of solving for 3D camera translations given a network of noisy pairwise camera translation directions (or 3D point observations). To do this well, we have two main insights. First, we propose a method for removing outliers from problem instances by solving simpler low-dimensional subproblems, which we refer to as 1DSfM problems. Second, we present a simple, principled averaging scheme. We demonstrate this new method in the wild on Internet photo collections.