Rotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for Cycle Graphs

TL;DR

This paper introduces a new primal-dual method for rotation averaging that converges globally and provides the first closed-form solution for cycle graphs, significantly improving accuracy and efficiency in geometric reconstruction.

Contribution

It presents a novel initialization-free primal-dual algorithm and derives the first optimal closed-form solution for rotation averaging in cycle graphs.

Findings

The primal-dual method empirically converges to the global optimum.

The closed-form solution outperforms existing methods in accuracy.

Methods achieve significant gains in precision and computational performance.

Abstract

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.