# Globally Optimal Solution to the Generalized Relative Pose Estimation Problem using Affine Correspondences

arXiv: https://arxiv.org/abs/2512.17188 · HTML: https://mlsanity.com/paper/2512.17188/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 51 references that are in the map.
- First posted on arXiv 19 Dec 2025.

## Builds on (most cited first, 18 of 18)

- [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-SLAM2: an Open-Source SLAM System for Monocular, Stereo and RGB-D Cameras](https://mlsanity.com/paper/1610.06475/) (2016)
- [KITTI-360: A Novel Dataset and Benchmarks for Urban Scene Understanding in 2D and 3D](https://mlsanity.com/paper/2109.13410/) (2021)
- [Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age](https://mlsanity.com/paper/1606.05830/) (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)
- [Project AutoVision: Localization and 3D Scene Perception for an Autonomous Vehicle with a Multi-Camera System](https://mlsanity.com/paper/1809.05477/) (2018)
- [DiffPoseNet: Direct Differentiable Camera Pose Estimation](https://mlsanity.com/paper/2203.11174/) (2022)
- [Globally Optimal Relative Pose Estimation with Gravity Prior](https://mlsanity.com/paper/2012.00458/) (2020)
- [Affine Correspondences between Multi-Camera Systems for Relative Pose Estimation](https://mlsanity.com/paper/2306.12996/) (2023)
- [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)
- [Minimal Cases for Computing the Generalized Relative Pose using Affine Correspondences](https://mlsanity.com/paper/2007.10700/) (2020)
- [POSEAMM: A Unified Framework for Solving Pose Problems using an Alternating Minimization Method](https://mlsanity.com/paper/1904.04858/) (2019)
- [DeepMLE: A Robust Deep Maximum Likelihood Estimator for Two-view Structure from Motion](https://mlsanity.com/paper/2210.05517/) (2022)
- [On Relative Pose Recovery for Multi-Camera Systems](https://mlsanity.com/paper/2102.11996/) (2021)

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

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)

## Abstract (arXiv)

Mobile devices equipped with a multi-camera system and an inertial measurement unit (IMU) are widely used nowadays, such as self-driving cars. The task of relative pose estimation using visual and inertial information has important applications in various fields. To improve the accuracy of relative pose estimation of multi-camera systems, we propose a globally optimal solver using affine correspondences to estimate the generalized relative pose with a known vertical direction. First, a cost function about the relative rotation angle is established after decoupling the rotation matrix and translation vector, which minimizes the algebraic error of geometric constraints from affine correspondences. Then, the global optimization problem is converted into two polynomials with two unknowns based on the characteristic equation and its first derivative is zero. Finally, the relative rotation angle can be solved using the polynomial eigenvalue solver, and the translation vector can be obtained from the eigenvector. Besides, a new linear solution is proposed when the relative rotation is small. The proposed solver is evaluated on synthetic data and real-world datasets. The experiment results demonstrate that our method outperforms comparable state-of-the-art methods in accuracy.