# Trifocal Tensor and Relative Pose Estimation with Known Vertical Direction

arXiv: https://arxiv.org/abs/2512.19110 · HTML: https://mlsanity.com/paper/2512.19110/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 36 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Builds on (most cited first, 11 of 11)

- [ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual-Inertial and Multi-Map SLAM](https://mlsanity.com/paper/2007.11898/) (2020)
- [ORB-SLAM2: an Open-Source SLAM System for Monocular, Stereo and RGB-D Cameras](https://mlsanity.com/paper/1610.06475/) (2016)
- [Beyond Gr"obner Bases: Basis Selection for Minimal Solvers](https://mlsanity.com/paper/1803.04360/) (2018)
- [Learning to Solve Hard Minimal Problems](https://mlsanity.com/paper/2112.03424/) (2021)
- [A clever elimination strategy for efficient minimal solvers](https://mlsanity.com/paper/1703.05289/) (2017)
- [Globally Optimal Relative Pose Estimation with Gravity Prior](https://mlsanity.com/paper/2012.00458/) (2020)
- [A sparse resultant based method for efficient minimal solvers](https://mlsanity.com/paper/1912.10268/) (2019)
- [GPU-Based Homotopy Continuation for Minimal Problems in Computer Vision](https://mlsanity.com/paper/2112.03444/) (2021)
- [GAPS: Generator for Automatic Polynomial Solvers](https://mlsanity.com/paper/2004.11765/) (2020)
- [An Accurate and Real-time Relative Pose Estimation from Triple Point-line Images by Decoupling Rotation and Translation](https://mlsanity.com/paper/2403.11639/) (2024)
- [Automatic Solver Generator for Systems of Laurent Polynomial Equations](https://mlsanity.com/paper/2307.00320/) (2023)

## Built on by (most cited first, 2 of 2)

- [Efficient Minimal Solvers for Visual-Inertial Relative Pose Estimation in Multi-Camera Systems](https://mlsanity.com/paper/2606.09477/) (2026)
- [Efficient Minimal Solvers for Relative Pose Estimation in Autonomous Driving Applications](https://mlsanity.com/paper/2606.09569/) (2026)

## Abstract (arXiv)

This work presents two novel solvers for estimating the relative poses among views with known vertical directions. The vertical directions of camera views can be easily obtained using inertial measurement units (IMUs) which have been widely used in autonomous vehicles, mobile phones, and unmanned aerial vehicles (UAVs). Given the known vertical directions, our lgorithms only need to solve for two rotation angles and two translation vectors. In this paper, a linear closed-form solution has been described, requiring only four point correspondences in three views. We also propose a minimal solution with three point correspondences using the latest Gr"obner basis solver. Since the proposed methods require fewer point correspondences, they can be efficiently applied within the RANSAC framework for outliers removal and pose estimation in visual odometry. The proposed method has been tested on both synthetic data and real-world scenes from KITTI. The experimental results show that the accuracy of the estimated poses is superior to other alternative methods.