# Robust Self-calibration of Focal Lengths from the Fundamental Matrix

arXiv: https://arxiv.org/abs/2311.16304 · HTML: https://mlsanity.com/paper/2311.16304/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 57 references that are in the map.
- First posted on arXiv 27 Nov 2023.

## Builds on (most cited first, 10 of 10)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [LoFTR: Detector-Free Local Feature Matching with Transformers](https://mlsanity.com/paper/2104.00680/) (2021)
- [Image Matching across Wide Baselines: From Paper to Practice](https://mlsanity.com/paper/2003.01587/) (2020)
- [MAGSAC++, a fast, reliable and accurate robust estimator](https://mlsanity.com/paper/1912.05909/) (2019)
- [Graph-Cut RANSAC](https://mlsanity.com/paper/1706.00984/) (2017)
- [VSAC: Efficient and Accurate Estimator for H and F](https://mlsanity.com/paper/2106.10240/) (2021)
- [Comprehensive Data Set for Automatic Single Camera Visual Speed Measurement](https://mlsanity.com/paper/1702.06441/) (2017)
- [A linear method for camera pair self-calibration and multi-view reconstruction with geometrically verified correspondences](https://mlsanity.com/paper/1906.12075/) (2019)

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

- [RePoseD: Efficient Relative Pose Estimation With Known Depth Information](https://mlsanity.com/paper/2501.07742/) (2025)
- [FastMap: Revisiting Structure from Motion through First-Order Optimization](https://mlsanity.com/paper/2505.04612/) (2025)
- [Six-Point Method for Multi-Camera Systems with Reduced Solution Space](https://mlsanity.com/paper/2402.18066/) (2024)
- [Three-view Focal Length Recovery From Homographies](https://mlsanity.com/paper/2501.07499/) (2025)
- [Numerically Computing Galois Groups of Minimal Problems](https://mlsanity.com/paper/2507.10407/) (2025)

## Abstract (arXiv)

The problem of self-calibration of two cameras from a given fundamental matrix is one of the basic problems in geometric computer vision. Under the assumption of known principal points and square pixels, the well-known Bougnoux formula offers a means to compute the two unknown focal lengths. However, in many practical situations, the formula yields inaccurate results due to commonly occurring singularities. Moreover, the estimates are sensitive to noise in the computed fundamental matrix and to the assumed positions of the principal points. In this paper, we therefore propose an efficient and robust iterative method to estimate the focal lengths along with the principal points of the cameras given a fundamental matrix and priors for the estimated camera parameters. In addition, we study a computationally efficient check of models generated within RANSAC that improves the accuracy of the estimated models while reducing the total computational time. Extensive experiments on real and synthetic data show that our iterative method brings significant improvements in terms of the accuracy of the estimated focal lengths over the Bougnoux formula and other state-of-the-art methods, even when relying on inaccurate priors.