# Fast and Robust Certifiable Estimation of the Relative Pose Between Two Calibrated Cameras

arXiv: https://arxiv.org/abs/2101.08524 · HTML: https://mlsanity.com/paper/2101.08524/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 63 references that are in the map.
- First posted on arXiv 21 Jan 2021.

## Builds on (most cited first, 12 of 12)

- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection](https://mlsanity.com/paper/1909.08605/) (2019)
- [SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group](https://mlsanity.com/paper/1612.07386/) (2016)
- [PL-SLAM: a Stereo SLAM System through the Combination of Points and Line Segments](https://mlsanity.com/paper/1705.09479/) (2017)
- [A Quaternion-based Certifiably Optimal Solution to the Wahba Problem with Outliers](https://mlsanity.com/paper/1905.12536/) (2019)
- [Lagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutions](https://mlsanity.com/paper/1506.00746/) (2015)
- [An Efficient Solution to Non-Minimal Case Essential Matrix Estimation](https://mlsanity.com/paper/1903.09067/) (2019)
- [Certifiable Relative Pose Estimation](https://mlsanity.com/paper/2003.13732/) (2020)
- [A note on Probably Certifiably Correct algorithms](https://mlsanity.com/paper/1509.00824/) (2015)
- [Certifiably Globally Optimal Extrinsic Calibration from Per-Sensor Egomotion](https://mlsanity.com/paper/1809.03554/) (2018)
- [Geometric Interpretations of the Normalized Epipolar Error](https://mlsanity.com/paper/2008.01254/) (2020)

## Built on by (most cited first, 5 of 5)

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [From Correspondences to Pose: Non-minimal Certifiably Optimal Relative Pose without Disambiguation](https://mlsanity.com/paper/2312.05995/) (2023)
- [Robust Frame-to-Frame Camera Rotation Estimation in Crowded Scenes](https://mlsanity.com/paper/2309.08588/) (2023)
- [Towards Understanding The Semidefinite Relaxations of Truncated Least-Squares in Robust Rotation Search](https://mlsanity.com/paper/2207.08350/) (2022)
- [Non-Minimal Sampling and Consensus for Prohibitively Large Datasets](https://mlsanity.com/paper/2604.22518/) (2026)

## Abstract (arXiv)

This work contributes an efficient algorithm to compute the Relative Pose problem (RPp) between calibrated cameras and certify the optimality of the solution, given a set of pair-wise feature correspondences affected by noise and probably corrupted by wrong matches. We propose a family of certifiers that is shown to increase the ratio of detected optimal solutions. This set of certifiers is incorporated into a fast essential matrix estimation pipeline that, given any initial guess for the RPp, refines it iteratively on the product space of 3D rotations and 2-sphere. In addition, this fast certifiable pipeline is integrated into a robust framework that combines Graduated Non-convexity and the Black-Rangarajan duality between robust functions and line processes. We proved through extensive experiments on synthetic and real data that the proposed framework provides a fast and robust relative pose estimation. We make the code publicly available urlhttps://github.com/mergarsal/FastCertRelPose.git.