# On the Instability of Relative Pose Estimation and RANSAC's Role

arXiv: https://arxiv.org/abs/2112.14651 · HTML: https://mlsanity.com/paper/2112.14651/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 29 Dec 2021.

## Builds on (most cited first, 7 of 7)

- [MAGSAC++, a fast, reliable and accurate robust estimator](https://mlsanity.com/paper/1912.05909/) (2019)
- [A Survey of Structure from Motion](https://mlsanity.com/paper/1701.08493/) (2017)
- [Neural-Guided RANSAC: Learning Where to Sample Model Hypotheses](https://mlsanity.com/paper/1905.04132/) (2019)
- [Algebraic Characterization of Essential Matrices and Their Averaging in Multiview Settings](https://mlsanity.com/paper/1904.02663/) (2019)
- [PL1P -- Point-line Minimal Problems under Partial Visibility in Three Views](https://mlsanity.com/paper/2003.05015/) (2020)
- [Machine learning the real discriminant locus](https://mlsanity.com/paper/2006.14078/) (2020)
- [The Chow Form of the Essential Variety in Computer Vision](https://mlsanity.com/paper/1604.04372/) (2016)

## Built on by (most cited first, 10 of 10)

- [DKM: Dense Kernelized Feature Matching for Geometry Estimation](https://mlsanity.com/paper/2202.00667/) (2022)
- [Two-View Geometry Scoring Without Correspondences](https://mlsanity.com/paper/2306.01596/) (2023)
- [IMP: Iterative Matching and Pose Estimation with Adaptive Pooling](https://mlsanity.com/paper/2304.14837/) (2023)
- [Snapshot of Algebraic Vision](https://mlsanity.com/paper/2210.11443/) (2022)
- [BANSAC: A dynamic BAyesian Network for adaptive SAmple Consensus](https://mlsanity.com/paper/2309.08690/) (2023)
- [Reprojection Errors as Prompts for Efficient Scene Coordinate Regression](https://mlsanity.com/paper/2409.04178/) (2024)
- [Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal Tensor](https://mlsanity.com/paper/2409.09313/) (2024)
- [Condition numbers in multiview geometry, instability in relative pose estimation, and RANSAC](https://mlsanity.com/paper/2310.02719/) (2023)
- [Higher-Order Group Synchronization](https://mlsanity.com/paper/2505.21932/) (2025)
- [EAR-Net: Pursuing End-to-End Absolute Rotations from Multi-View Images](https://mlsanity.com/paper/2310.10051/) (2023)

## Abstract (arXiv)

In this paper we study the numerical instabilities of the 5- and 7-point problems for essential and fundamental matrix estimation in multiview geometry. In both cases we characterize the ill-posed world scenes where the condition number for epipolar estimation is infinite. We also characterize the ill-posed instances in terms of the given image data. To arrive at these results, we present a general framework for analyzing the conditioning of minimal problems in multiview geometry, based on Riemannian manifolds. Experiments with synthetic and real-world data then reveal a striking conclusion: that Random Sample Consensus (RANSAC) in Structure-from-Motion (SfM) does not only serve to filter out outliers, but RANSAC also selects for well-conditioned image data, sufficiently separated from the ill-posed locus that our theory predicts. Our findings suggest that, in future work, one could try to accelerate and increase the success of RANSAC by testing only well-conditioned image data.