# Minimal Solutions for Relative Pose with a Single Affine Correspondence

arXiv: https://arxiv.org/abs/1912.10776 · HTML: https://mlsanity.com/paper/1912.10776/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2019.

## Built on by (most cited first, 12 of 12)

- [DKM: Dense Kernelized Feature Matching for Geometry Estimation](https://mlsanity.com/paper/2202.00667/) (2022)
- [STAA-SNN: Spatial-Temporal Attention Aggregator for Spiking Neural Networks](https://mlsanity.com/paper/2503.02689/) (2025)
- [Fusing the Old with the New: Learning Relative Camera Pose with Geometry-Guided Uncertainty](https://mlsanity.com/paper/2104.08278/) (2021)
- [TS-SNN: Temporal Shift Module for Spiking Neural Networks](https://mlsanity.com/paper/2505.04165/) (2025)
- [E-Graph: Minimal Solution for Rigid Rotation with Extensibility Graphs](https://mlsanity.com/paper/2207.10008/) (2022)
- [Trust Your IMU: Consequences of Ignoring the IMU Drift](https://mlsanity.com/paper/2103.08286/) (2021)
- [On Relative Pose Recovery for Multi-Camera Systems](https://mlsanity.com/paper/2102.11996/) (2021)
- [Globally Optimal Solution to the Generalized Relative Pose Estimation Problem using Affine Correspondences](https://mlsanity.com/paper/2512.17188/) (2025)
- [A Minimal Solver for Relative Pose Estimation with Unknown Focal Length from Two Affine Correspondences](https://mlsanity.com/paper/2512.22833/) (2025)
- [Affine Correspondences in Stereo Vision: Theory, Practice, and Limitations](https://mlsanity.com/paper/2603.01836/) (2026)
- [Efficient Minimal Solvers for Visual-Inertial Relative Pose Estimation in Multi-Camera Systems](https://mlsanity.com/paper/2606.09477/) (2026)
- [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 present four cases of minimal solutions for two-view relative pose estimation by exploiting the affine transformation between feature points and we demonstrate efficient solvers for these cases. It is shown, that under the planar motion assumption or with knowledge of a vertical direction, a single affine correspondence is sufficient to recover the relative camera pose. The four cases considered are two-view planar relative motion for calibrated cameras as a closed-form and a least-squares solution, a closed-form solution for unknown focal length and the case of a known vertical direction. These algorithms can be used efficiently for outlier detection within a RANSAC loop and for initial motion estimation. All the methods are evaluated on both synthetic data and real-world datasets from the KITTI benchmark. The experimental results demonstrate that our methods outperform comparable state-of-the-art methods in accuracy with the benefit of a reduced number of needed RANSAC iterations.