# A Minimal Solver for Relative Pose Estimation with Unknown Focal Length from Two Affine Correspondences

arXiv: https://arxiv.org/abs/2512.22833 · HTML: https://mlsanity.com/paper/2512.22833/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 28 Dec 2025.

## Builds on (most cited first, 14 of 14)

- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [A Large Dataset to Train Convolutional Networks for Disparity, Optical Flow, and Scene Flow Estimation](https://mlsanity.com/paper/1512.02134/) (2015)
- [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)
- [SfM-Net: Learning of Structure and Motion from Video](https://mlsanity.com/paper/1704.07804/) (2017)
- [Deep Two-View Structure-from-Motion Revisited](https://mlsanity.com/paper/2104.00556/) (2021)
- [DiffPoseNet: Direct Differentiable Camera Pose Estimation](https://mlsanity.com/paper/2203.11174/) (2022)
- [Beyond Gr"obner Bases: Basis Selection for Minimal Solvers](https://mlsanity.com/paper/1803.04360/) (2018)
- [A Minimal Solution for Two-view Focal-length Estimation using Two Affine Correspondences](https://mlsanity.com/paper/1706.01649/) (2017)
- [Minimal Solutions for Relative Pose with a Single Affine Correspondence](https://mlsanity.com/paper/1912.10776/) (2019)
- [Fusing the Old with the New: Learning Relative Camera Pose with Geometry-Guided Uncertainty](https://mlsanity.com/paper/2104.08278/) (2021)
- [Homography from two orientation- and scale-covariant features](https://mlsanity.com/paper/1906.11927/) (2019)
- [Relative planar motion for vehicle-mounted cameras from a single affine correspondence](https://mlsanity.com/paper/1912.06465/) (2019)
- [Learning Affine Correspondences by Integrating Geometric Constraints](https://mlsanity.com/paper/2504.04834/) (2025)

## Built on by (most cited first, 1 of 1)

- [Gravity-aware partially calibrated absolute pose estimation from affine- or rotation-covariant features](https://mlsanity.com/paper/2608.20056/) (2026)

## Abstract (arXiv)

In this paper, we aim to estimate the relative pose and focal length between two views with known intrinsic parameters except for an unknown focal length from two affine correspondences (ACs). Cameras are commonly used in combination with inertial measurement units (IMUs) in applications such as self-driving cars, smartphones, and unmanned aerial vehicles. The vertical direction of camera views can be obtained by IMU measurements. The relative pose between two cameras is reduced from 5DOF to 3DOF. We propose a new solver to estimate the 3DOF relative pose and focal length. First, we establish constraint equations from two affine correspondences when the vertical direction is known. Then, based on the properties of the equation system with nontrivial solutions, four equations can be derived. These four equations only involve two parameters: the focal length and the relative rotation angle. Finally, the polynomial eigenvalue method is utilized to solve the problem of focal length and relative rotation angle. The proposed solver is evaluated using synthetic and real-world datasets. The results show that our solver performs better than the existing state-of-the-art solvers.