# Globally Optimal Relative Pose Estimation with Gravity Prior

arXiv: https://arxiv.org/abs/2012.00458 · HTML: https://mlsanity.com/paper/2012.00458/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2020.

## Built on by (most cited first, 13 of 13)

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Vanishing Point Estimation in Uncalibrated Images with Prior Gravity Direction](https://mlsanity.com/paper/2308.10694/) (2023)
- [A survey of top-down approaches for human pose estimation](https://mlsanity.com/paper/2202.02656/) (2022)
- [Robust Frame-to-Frame Camera Rotation Estimation in Crowded Scenes](https://mlsanity.com/paper/2309.08588/) (2023)
- [Transformation Decoupling Strategy based on Screw Theory for Deterministic Point Cloud Registration with Gravity Prior](https://mlsanity.com/paper/2311.01432/) (2023)
- [Bottom-up approaches for multi-person pose estimation and it's applications: A brief review](https://mlsanity.com/paper/2112.11834/) (2021)
- [Trifocal Tensor and Relative Pose Estimation with Known Vertical Direction](https://mlsanity.com/paper/2512.19110/) (2025)
- [Consistent and Optimal Solution to Camera Motion Estimation](https://mlsanity.com/paper/2403.01174/) (2024)
- [Globally Optimal Solution to the Generalized Relative Pose Estimation Problem using Affine Correspondences](https://mlsanity.com/paper/2512.17188/) (2025)
- [Building Information Models to Robot-Ready Site Digital Twins (BIM2RDT): An Agentic AI Safety-First Framework](https://mlsanity.com/paper/2509.20705/) (2025)
- [PiLoT v2: Pixel-to-Orthogonal Map Alignment for Free-view UAV Geo-localization](https://mlsanity.com/paper/2606.31098/) (2026)
- [Gravity-aware partially calibrated absolute pose estimation from affine- or rotation-covariant features](https://mlsanity.com/paper/2608.20056/) (2026)
- [Efficient and Robust Absolute Pose Estimation via Gravity-Prior-Driven Transformation Decoupling and Pose Refinement](https://mlsanity.com/paper/2609.00713/) (2026)

## Abstract (arXiv)

Smartphones, tablets and camera systems used, e.g., in cars and UAVs, are typically equipped with IMUs (inertial measurement units) that can measure the gravity vector accurately. Using this additional information, the y-axes of the cameras can be aligned, reducing their relative orientation to a single degree-of-freedom. With this assumption, we propose a novel globally optimal solver, minimizing the algebraic error in the least-squares sense, to estimate the relative pose in the over-determined case. Based on the epipolar constraint, we convert the optimization problem into solving two polynomials with only two unknowns. Also, a fast solver is proposed using the first-order approximation of the rotation. The proposed solvers are compared with the state-of-the-art ones on four real-world datasets with approx. 50000 image pairs in total. Moreover, we collected a dataset, by a smartphone, consisting of 10933 image pairs, gravity directions, and ground truth 3D reconstructions.