# Five-point Fundamental Matrix Estimation for Uncalibrated Cameras

arXiv: https://arxiv.org/abs/1803.00260 · HTML: https://mlsanity.com/paper/1803.00260/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2018.

## Built on by (most cited first, 11 of 11)

- [Learning to Solve Hard Minimal Problems](https://mlsanity.com/paper/2112.03424/) (2021)
- [Calibrated and Partially Calibrated Semi-Generalized Homographies](https://mlsanity.com/paper/2103.06535/) (2021)
- [Galois/monodromy groups for decomposing minimal problems in 3D reconstruction](https://mlsanity.com/paper/2105.04460/) (2021)
- [Snapshot of Algebraic Vision](https://mlsanity.com/paper/2210.11443/) (2022)
- [Relative Pose from SIFT Features](https://mlsanity.com/paper/2203.07930/) (2022)
- [Adaptive Reordering Sampler with Neurally Guided MAGSAC](https://mlsanity.com/paper/2111.14093/) (2021)
- [On Relative Pose Recovery for Multi-Camera Systems](https://mlsanity.com/paper/2102.11996/) (2021)
- [Multi-view Geometry: Correspondences Refinement Based on Algebraic Properties](https://mlsanity.com/paper/2205.01634/) (2022)
- [Consistent and Optimal Solution to Camera Motion Estimation](https://mlsanity.com/paper/2403.01174/) (2024)
- [From a few Accurate 2D Correspondences to 3D Point Clouds](https://mlsanity.com/paper/2206.08749/) (2022)
- [PLMP -- Point-Line Minimal Problems for Projective SfM](https://mlsanity.com/paper/2503.04351/) (2025)

## Abstract (arXiv)

We aim at estimating the fundamental matrix in two views from five correspondences of rotation invariant features obtained by e.g. the SIFT detector. The proposed minimal solver first estimates a homography from three correspondences assuming that they are co-planar and exploiting their rotational components. Then the fundamental matrix is obtained from the homography and two additional point pairs in general position. The proposed approach, combined with robust estimators like Graph-Cut RANSAC, is superior to other state-of-the-art algorithms both in terms of accuracy and number of iterations required. This is validated on synthesized data and 561 real image pairs. Moreover, the tests show that requiring three points on a plane is not too restrictive in urban environment and locally optimized robust estimators lead to accurate estimates even if the points are not entirely co-planar. As a potential application, we show that using the proposed method makes two-view multi-motion estimation more accurate.