Discovering and Exploiting 3D Symmetries in Structure from Motion

Many architectural scenes contain symmetric or repeated structures, which can generate erroneous image correspondences during structure from motion (Sfm) computation. Prior work has shown that the detection and removal of these incorrect matches is crucial for accurate and robust recovery of scene structure. In this paper, we point out that these incorrect matches, in fact, provide strong cues to the existence of symmetries and structural regularities in the unknown 3D structure. We make two key contributions. First, we propose a method to recover various symmetry relations in the structure using geometric and appearance cues. A set of structural constraints derived from the symmetries are imposed within a new constrained bundle adjustment formulation, where symmetry priors are also incorporated. Second, we show that the recovered symmetries enable us to choose a natural coordinate system for the 3D structure where gauge freedom in rotation is held fixed. Furthermore, based on the symmetries, 3D structure completion is also performed. Our approach significantly reduces drift through "structural" loop closures and improves the accuracy of reconstructions in urban scenes.