# A Birotation Solution for Relative Pose Problems

arXiv: https://arxiv.org/abs/2505.02025 · HTML: https://mlsanity.com/paper/2505.02025/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 40 references that are in the map.
- First posted on arXiv 4 May 2025.

## Builds on (most cited first, 17 of 17)

- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [LoFTR: Detector-Free Local Feature Matching with Transformers](https://mlsanity.com/paper/2104.00680/) (2021)
- [MegaDepth: Learning Single-View Depth Prediction from Internet Photos](https://mlsanity.com/paper/1804.00607/) (2018)
- [LightGlue: Local Feature Matching at Light Speed](https://mlsanity.com/paper/2306.13643/) (2023)
- [Pyramid Stereo Matching Network](https://mlsanity.com/paper/1803.08669/) (2018)
- [RAFT-Stereo: Multilevel Recurrent Field Transforms for Stereo Matching](https://mlsanity.com/paper/2109.07547/) (2021)
- [MAGSAC: marginalizing sample consensus](https://mlsanity.com/paper/1803.07469/) (2018)
- [Unsupervised Scale-consistent Depth Learning from Video](https://mlsanity.com/paper/2105.11610/) (2021)
- [LEAP-VO: Long-term Effective Any Point Tracking for Visual Odometry](https://mlsanity.com/paper/2401.01887/) (2024)
- [Generalized Differentiable RANSAC](https://mlsanity.com/paper/2212.13185/) (2022)
- [Deep Keypoint-Based Camera Pose Estimation with Geometric Constraints](https://mlsanity.com/paper/2007.15122/) (2020)
- [An Efficient Solution to Non-Minimal Case Essential Matrix Estimation](https://mlsanity.com/paper/1903.09067/) (2019)
- [Equivalent Constraints for Two-View Geometry: Pose Solution/Pure Rotation Identification and 3D Reconstruction](https://mlsanity.com/paper/1810.05863/) (2018)
- [High-Precision Online Markerless Stereo Extrinsic Calibration](https://mlsanity.com/paper/1903.10705/) (2019)
- [SCIPaD: Incorporating Spatial Clues into Unsupervised Pose-Depth Joint Learning](https://mlsanity.com/paper/2407.05283/) (2024)
- [Dive Deeper into Rectifying Homography for Stereo Camera Online Self-Calibration](https://mlsanity.com/paper/2309.10314/) (2023)

## Abstract (arXiv)

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 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 hrefhttps://mias.group/birotation-solutionmias.group/birotation-solution upon publication.