Efficient Algorithms for Rotation Averaging Problems

TL;DR

This paper introduces two novel algorithms for rotation averaging in computer vision, offering guaranteed convergence to stationary points and superior performance, especially for large-scale problems, with potential to reach globally optimal solutions.

Contribution

The paper proposes two new algorithms based on block coordinate descent and successive upper-bound minimization, with convergence guarantees and suitability for large-scale problems.

Findings

Algorithms outperform existing methods in convergence speed

Proposed methods can achieve globally optimal solutions

Parallel implementation enhances scalability

Abstract

The rotation averaging problem is a fundamental task in computer vision applications. It is generally very difficult to solve due to the nonconvex rotation constraints. While a sufficient optimality condition is available in the literature, there is a lack of \yhedit{a} fast convergent algorithm to achieve stationary points. In this paper, by exploring the problem structure, we first propose a block coordinate descent (BCD)-based rotation averaging algorithm with guaranteed convergence to stationary points. Afterwards, we further propose an alternative rotation averaging algorithm by applying successive upper-bound minimization (SUM) method. The SUM-based rotation averaging algorithm can be implemented in parallel and thus is more suitable for addressing large-scale rotation averaging problems. Numerical examples verify that the proposed rotation averaging algorithms have superior convergence performance as compared to the state-of-the-art algorithm. Moreover, by checking the sufficient optimality condition, we find from extensive numerical experiments that the proposed two algorithms can achieve globally optimal solutions.