Shonan Rotation Averaging: Global Optimality by Surfing $SO(p)^n$

TL;DR

Shonan Rotation Averaging introduces a fast, scalable algorithm that guarantees globally optimal solutions for rotation averaging problems by leveraging semidefinite relaxation and manifold optimization, improving accuracy without sacrificing efficiency.

Contribution

It presents a novel approach combining semidefinite relaxation with manifold minimization to solve large-scale rotation averaging problems globally optimally.

Findings

Achieves global optimality in rotation averaging

Maintains scalability and speed of existing structure-from-motion pipelines

Effective on large-scale instances with mild noise assumptions

Abstract

Shonan Rotation Averaging is a fast, simple, and elegant rotation averaging algorithm that is guaranteed to recover globally optimal solutions under mild assumptions on the measurement noise. Our method employs semidefinite relaxation in order to recover provably globally optimal solutions of the rotation averaging problem. In contrast to prior work, we show how to solve large-scale instances of these relaxations using manifold minimization on (only slightly) higher-dimensional rotation manifolds, re-using existing high-performance (but local) structure-from-motion pipelines. Our method thus preserves the speed and scalability of current SFM methods, while recovering globally optimal solutions.