# Revisiting Sampson Approximations for Geometric Estimation Problems

arXiv: https://arxiv.org/abs/2401.07114 · HTML: https://mlsanity.com/paper/2401.07114/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 13 Jan 2024.

## Builds on (most cited first, 9 of 9)

- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [LoFTR: Detector-Free Local Feature Matching with Transformers](https://mlsanity.com/paper/2104.00680/) (2021)
- [LightGlue: Local Feature Matching at Light Speed](https://mlsanity.com/paper/2306.13643/) (2023)
- [From Coarse to Fine: Robust Hierarchical Localization at Large Scale](https://mlsanity.com/paper/1812.03506/) (2018)
- [Image Matching across Wide Baselines: From Paper to Practice](https://mlsanity.com/paper/2003.01587/) (2020)
- [DeepLSD: Line Segment Detection and Refinement with Deep Image Gradients](https://mlsanity.com/paper/2212.07766/) (2022)
- [Progressive-X: Efficient, Anytime, Multi-Model Fitting Algorithm](https://mlsanity.com/paper/1906.02290/) (2019)
- [CONSAC: Robust Multi-Model Fitting by Conditional Sample Consensus](https://mlsanity.com/paper/2001.02643/) (2020)
- [The Euclidean distance degree of an algebraic variety](https://mlsanity.com/paper/1309.0049/) (2013)

## Built on by (most cited first, 6 of 6)

- [Less Biased Noise Scale Estimation for Threshold-Robust RANSAC](https://mlsanity.com/paper/2503.13433/) (2025)
- [RANSAC Scoring Functions: Analysis and Reality Check](https://mlsanity.com/paper/2512.19850/) (2025)
- [PRaDA: Projective Radial Distortion Averaging](https://mlsanity.com/paper/2504.16499/) (2025)
- [Visual Sync: Multi-Camera Synchronization via Cross-View Object Motion](https://mlsanity.com/paper/2512.02017/) (2025)
- [A Framework for Reducing the Complexity of Geometric Vision Problems and its Application to Two-View Triangulation with Approximation Bounds](https://mlsanity.com/paper/2503.08142/) (2025)
- [Non-Minimal Sampling and Consensus for Prohibitively Large Datasets](https://mlsanity.com/paper/2604.22518/) (2026)

## Abstract (arXiv)

Many problems in computer vision can be formulated as geometric estimation problems, i.e. given a collection of measurements (e.g. point correspondences) we wish to fit a model (e.g. an essential matrix) that agrees with our observations. This necessitates some measure of how much an observation ``agrees" with a given model. A natural choice is to consider the smallest perturbation that makes the observation exactly satisfy the constraints. However, for many problems, this metric is expensive or otherwise intractable to compute. The so-called Sampson error approximates this geometric error through a linearization scheme. For epipolar geometry, the Sampson error is a popular choice and in practice known to yield very tight approximations of the corresponding geometric residual (the reprojection error). In this paper we revisit the Sampson approximation and provide new theoretical insights as to why and when this approximation works, as well as provide explicit bounds on the tightness under some mild assumptions. Our theoretical results are validated in several experiments on real data and in the context of different geometric estimation tasks.