Certifiably Optimal Anisotropic Rotation Averaging

2025-03-10

AI Summary

This paper addresses the challenge of computing globally optimal solutions for rotation averaging under anisotropic noise modeling—a problem where conventional isotropic assumptions fail. Methodologically, we propose an enhanced compact semidefinite programming (SDP) relaxation over SE(3), grounded in Lie-algebraic formulation and covariance-weighted residuals, and introduce a perturbation-based deflation strategy to significantly improve relaxation tightness and convergence. Theoretically, our approach guarantees certifiably optimal solutions. Empirically, it recovers the global optimum on all standard benchmark datasets; moreover, reconstruction accuracy surpasses state-of-the-art methods in all but one scenario. To our knowledge, this is the first method to achieve verifiably globally optimal rotation averaging under general anisotropic noise.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Non-convex Optimization
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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 paper 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 show empirically that it is able to recover global optima in all tested datasets and leads to a more accurate reconstruction in all but one of the scenes.

Problem

• Addresses anisotropic rotation averaging in computer vision and robotics.
• Improves solution quality by incorporating intrinsic measurement uncertainties.
• Proposes a stronger relaxation for global optimization in anisotropic settings.

Innovation

• Incorporates anisotropic costs in rotation averaging
• Proposes stronger relaxation for global optimization
• Demonstrates improved accuracy in scene reconstruction