Rotation Averaging: A Primal-Dual Method and Closed-Forms in Cycle Graphs

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.