Certifiably Optimal Anisotropic Rotation Averaging
This work addresses a key subproblem in computer vision and robotics by improving solution quality in anisotropic settings, though it is incremental as it builds on existing rotation averaging methods.
The paper tackles the challenge of global optimization for anisotropic rotation averaging, where measurement uncertainties are explicitly included, by proposing a stronger relaxation that recovers global optima in all tested datasets and leads to more accurate reconstructions in most scenes.
Rotation averaging is a key subproblem in applications of computer vision and robotics. Many methods for solving this problem exist, and there are also several theoretical results analyzing difficulty and optimality. However, one aspect that most of these have in common is a focus on the isotropic setting, where the intrinsic uncertainties in the measurements are not fully incorporated into the resulting optimization task. Recent empirical results suggest that moving to an anisotropic framework, where these uncertainties are explicitly included, can result in an improvement of solution quality. However, global optimization for rotation averaging has remained a challenge in this scenario. In this work we show how anisotropic costs can be incorporated in certifiably optimal rotation averaging. We also demonstrate how existing solvers, designed for isotropic situations, fail in the anisotropic setting. Finally, we propose a stronger relaxation and empirically show that it recovers global optima in all tested datasets and leads to more accurate reconstructions in almost all scenes.