Spectral Synchronization of Multiple Views in SE(3)

This paper addresses the problem of rigid-motion synchronization (a.k.a. motion averaging) in the Special Euclidean Group SE(3), which finds application in structure-from-motion and registration of multiple three-dimensional (3D) point-sets. After relaxing the geometric constraints of rigid motions, we derive a simple closed-form solution based on a spectral decomposition, which is then projected onto SE(3). Our formulation is extremely efficient, as rigid-motion synchronization is cast to an eigenvalue decomposition problem. Robustness to outliers is gained through Iteratively Reweighted Least Squares. Besides providing a theoretically appealing solution, since our method recovers at the same time both rotations and translations, we demonstrate through experimental results that our approach is significantly faster than the state of the art, while providing accurate estimates of rigid motions.