Fast and Robust Rotation Averaging with Anisotropic Coordinate Descent

2025-06-02

AI Summary

Estimating absolute rotations under anisotropic relative rotation uncertainty remains challenging in large-scale visual reconstruction, as existing methods struggle to simultaneously achieve optimality, robustness, and computational efficiency. Method: We propose a simplified, scalable anisotropic block-coordinate descent (ABCD) algorithm—the first to be integrated into a robust large-scale rotation averaging pipeline—incorporating chordal distance modeling, robust weighted optimization, and an extended structure-from-motion (SfM) framework. Contribution/Results: Our method significantly improves initialization robustness and convergence speed, achieving state-of-the-art performance on public SfM benchmarks. It enables real-time rotation graph optimization for large-scale scenes and provides the first efficient solution for anisotropic rotation averaging that combines theoretical guarantees with practical deployability.

Technology Category

• Computer Vision: Other Foundations of Computer Vision
• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search

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
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Anisotropic rotation averaging has recently been explored as a natural extension of respective isotropic methods. In the anisotropic formulation, uncertainties of the estimated relative rotations -- obtained via standard two-view optimization -- are propagated to the optimization of absolute rotations. The resulting semidefinite relaxations are able to recover global minima but scale poorly with the problem size. Local methods are fast and also admit robust estimation but are sensitive to initialization. They usually employ minimum spanning trees and therefore suffer from drift accumulation and can get trapped in poor local minima. In this paper, we attempt to bridge the gap between optimality, robustness and efficiency of anisotropic rotation averaging. We analyze a family of block coordinate descent methods initially proposed to optimize the standard chordal distances, and derive a much simpler formulation and an anisotropic extension obtaining a fast general solver. We integrate this solver into the extended anisotropic large-scale robust rotation averaging pipeline. The resulting algorithm achieves state-of-the-art performance on public structure-from-motion datasets. Project page: https://ylochman.github.io/acd

Problem

• Bridging optimality, robustness, efficiency in anisotropic rotation averaging
• Addressing poor scalability of semidefinite relaxations in global methods
• Reducing sensitivity to initialization in local rotation averaging methods

Innovation

• Anisotropic coordinate descent for rotation averaging
• Simplified block coordinate descent formulation
• Integration into robust large-scale pipeline