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.