We present a non-incremental approach to structure from motion. Our solution is based on robustly computing global rotations from relative geometries and feeding these into the known-rotation framework to create an initial solution for bundle adjustment. To increase robustness we present a new method for constructing reliable point tracks from pairwise matches. We show that our method can be seen as maximizing the reliability of a point track if the quality of the weakest link in the track is used to evaluate reliability. To estimate the final geometry we alternate between bundle adjustment and a robust version of the known-rotation formulation. The ability to compute both structure and camera translations independent of initialization makes our algorithm insensitive to degenerate epipolar geometries. We demonstrate the performance of our system on a number of image collections.1