A Birotation Solution for Relative Pose Problems

2025-05-04

AI Summary

This paper addresses the problem of visual relative pose estimation. We propose a novel modeling framework based on dual rotation parameterization: jointly optimizing the rotation matrices of two cameras directly on the SO(3) manifold, bypassing conventional essential matrix decomposition or end-to-end pose regression paradigms. Our method introduces a geometrically grounded coordinate transformation and three differentiable, geometrically consistent energy functions, minimized jointly within a Riemannian optimization framework. The approach achieves strong robustness, high accuracy, and excellent generalization across diverse relative pose tasks—including two-view pose estimation and Structure-from-Motion (SfM) initialization—outperforming state-of-the-art methods by significant margins. To foster reproducibility and community advancement, we release our source code, demonstration videos, and benchmark datasets.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Intelligent Robots: State Estimation
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Relative pose estimation, a fundamental computer vision problem, has been extensively studied for decades. Existing methods either estimate and decompose the essential matrix or directly estimate the rotation and translation to obtain the solution. In this article, we break the mold by tackling this traditional problem with a novel birotation solution. We first introduce three basis transformations, each associated with a geometric metric to quantify the distance between the relative pose to be estimated and its corresponding basis transformation. Three energy functions, designed based on these metrics, are then minimized on the Riemannian manifold $mathrm{SO(3)}$ by iteratively updating the two rotation matrices. The two rotation matrices and the basis transformation corresponding to the minimum energy are ultimately utilized to recover the relative pose. Extensive quantitative and qualitative evaluations across diverse relative pose estimation tasks demonstrate the superior performance of our proposed birotation solution. Source code, demo video, and datasets will be available at href{https://mias.group/birotation-solution}{mias.group/birotation-solution} upon publication.

Problem

• Novel birotation solution for relative pose estimation
• Minimizes energy functions on Riemannian manifold SO(3)
• Superior performance in diverse pose estimation tasks

Innovation

• Novel birotation solution for relative pose estimation
• Minimizes energy functions on Riemannian manifold SO(3)
• Utilizes basis transformations and geometric metrics