# Efficient Relative Pose Estimation for Cameras and Generalized Cameras in Case of Known Relative Rotation Angle

arXiv: https://arxiv.org/abs/1901.11357 · HTML: https://mlsanity.com/paper/1901.11357/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2019.

## Built on by (most cited first, 6 of 6)

- [Affine Correspondences between Multi-Camera Systems for Relative Pose Estimation](https://mlsanity.com/paper/2306.12996/) (2023)
- [Optimizing Elimination Templates by Greedy Parameter Search](https://mlsanity.com/paper/2203.14901/) (2022)
- [Automatic Solver Generator for Systems of Laurent Polynomial Equations](https://mlsanity.com/paper/2307.00320/) (2023)
- [On Relative Pose Recovery for Multi-Camera Systems](https://mlsanity.com/paper/2102.11996/) (2021)
- [Shape-from-Template with Generalised Camera](https://mlsanity.com/paper/2508.13791/) (2025)
- [Efficient Minimal Solvers for Visual-Inertial Relative Pose Estimation in Multi-Camera Systems](https://mlsanity.com/paper/2606.09477/) (2026)

## Abstract (arXiv)

We propose two minimal solutions to the problem of relative pose estimation of (i) a calibrated camera from four points in two views and (ii) a calibrated generalized camera from five points in two views. In both cases, the relative rotation angle between the views is assumed to be known. In practice, such angle can be derived from the readings of a 3d gyroscope. We represent the rotation part of the motion in terms of unit quaternions in order to construct polynomial equations encoding the epipolar constraints. The Gr"obner basis technique is then used to efficiently derive the solutions. Our first solver for regular cameras significantly improves the existing state-of-the-art solution. The second solver for generalized cameras is novel. The presented minimal solvers can be used in a hypothesize-and-test architecture such as RANSAC for reliable pose estimation. Experiments on synthetic and real datasets confirm that our algorithms are numerically stable, fast and robust.