A cornerstone of geometric reconstruction, rotation averaging seeks the set
of absolute rotations that optimally explains a set of measured relative
orientations between them. In addition to being an integral part of bundle
adjustment and structure-from-motion, the problem of synchronizing rotations
also finds applications in visual simultaneous localization and mapping, where
it is used as an initialization for iterative solvers, and camera network
calibration. Nevertheless, this optimization problem is both non-convex and
high-dimensional. In this paper, we address it from a maximum likelihood
estimation standpoint and make a twofold contribution. Firstly, we set forth a
novel primal-dual method, motivated by the widely accepted spectral
initialization. Further, we characterize stationary points of rotation
averaging in cycle graphs topologies and contextualize this result within
spectral graph theory. We benchmark the proposed method in multiple settings
and certify our solution via duality theory, achieving a significant gain in
precision and performance.

通过最大似然估计的方法，本文针对旋转平均问题提出了一种新的原始 - 对偶方法，以解决在计算机视觉和摄像机网络标定中使用的非凸高维优化问题，并在多个情境中对该方法进行了基准测试，通过对偶理论验证了解决方案的有效性和性能提升。