  Rotation averaging is a synchronization process on single or multiple
rotation groups, and is a fundamental problem in many computer vision tasks
such as multi-view structure from motion (SfM). Specifically, rotation
averaging involves the recovery of an underlying pose-graph consistency from
pairwise relative camera poses. Specifically, given pairwise motion in rotation
groups, especially 3-dimensional rotation groups (\eg, $\mathbb{SO}(3)$), one
is interested in recovering the original signal of multiple rotations with
respect to a fixed frame. In this paper, we propose a robust framework to solve
multiple rotation averaging problem, especially in the cases that a significant
amount of noisy measurements are present. By introducing the $\epsilon$-cycle
consistency term into the solver, we enable the robust initialization scheme to
be implemented into the IRLS solver. Instead of conducting the costly edge
removal, we implicitly constrain the negative effect of erroneous measurements
by weight reducing, such that IRLS failures caused by poor initialization can
be effectively avoided. Experiment results demonstrate that our proposed
approach outperforms state of the arts on various benchmarks.
