Stable Structure from Motion using Rotational Consistency

A challenging problem in multi-view structure from motion is the existence of repetitive structures, short baselines, or even moving objects. These can give rise to incorrect geometries that may completely ruin the quality of the reconstruction. Methods solving for all views at once will fail due to the inconsistencies and incremental methods that add one view at a time risk getting stuck in a poor local minimum. This paper presents new theory and methods to handle these problems. Essential to the approach is the fact that structure from motion with known rotations can be solved optimally using convex optimization. The main contribution is thus a robust way to estimate these orientations with theoretical approximation guarantees. Like many standard methods, we begin by estimating two-view geometries. Using the number of point correspondences as a measure of certainty, we seek a maximum-weight set of consistent pairwise rotations. Next, these are used to provide a robust estimate of the camera orientations which can be fed into the convex optimization scheme. The algorithm has been evaluated on a large collection of real world data sets comparing favorably to the state-of-the-art.