Rotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for Cycle Graphs
This addresses a bottleneck in bundle adjustment and structure-from-motion for computer vision applications, though it appears incremental as it builds on existing maximum likelihood estimation approaches.
The paper tackles the non-convex optimization problem of rotation averaging in geometric reconstruction by proposing a primal-dual method that converges to the global optimum and deriving the first closed-form solution for cycle graphs, achieving significant gains in precision and performance.
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 spite of being an integral part of bundle adjustment and structure-from-motion, averaging rotations is both a non-convex and high-dimensional optimization problem. In this paper, we address it from a maximum likelihood estimation standpoint and make a twofold contribution. Firstly, we set forth a novel initialization-free primal-dual method which we show empirically to converge to the global optimum. Further, we derive what is to our knowledge, the first optimal closed-form solution for rotation averaging in cycle graphs and contextualize this result within spectral graph theory. Our proposed methods achieve a significant gain both in precision and performance.