# Three-view Focal Length Recovery From Homographies

arXiv: https://arxiv.org/abs/2501.07499 · HTML: https://mlsanity.com/paper/2501.07499/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 48 references that are in the map.
- First posted on arXiv 13 Jan 2025.

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

- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [LightGlue: Local Feature Matching at Light Speed](https://mlsanity.com/paper/2306.13643/) (2023)
- [Beyond Gr"obner Bases: Basis Selection for Minimal Solvers](https://mlsanity.com/paper/1803.04360/) (2018)
- [Learning to Solve Hard Minimal Problems](https://mlsanity.com/paper/2112.03424/) (2021)
- [A clever elimination strategy for efficient minimal solvers](https://mlsanity.com/paper/1703.05289/) (2017)
- [A sparse resultant based method for efficient minimal solvers](https://mlsanity.com/paper/1912.10268/) (2019)
- [GPU-Based Homotopy Continuation for Minimal Problems in Computer Vision](https://mlsanity.com/paper/2112.03444/) (2021)
- [Robust Self-calibration of Focal Lengths from the Fundamental Matrix](https://mlsanity.com/paper/2311.16304/) (2023)
- [Minimal Perspective Autocalibration](https://mlsanity.com/paper/2405.05605/) (2024)
- [Practical solutions to the relative pose of three calibrated cameras](https://mlsanity.com/paper/2303.16078/) (2023)

## Abstract (arXiv)

In this paper, we propose a novel approach for recovering focal lengths from three-view homographies. By examining the consistency of normal vectors between two homographies, we derive new explicit constraints between the focal lengths and homographies using an elimination technique. We demonstrate that three-view homographies provide two additional constraints, enabling the recovery of one or two focal lengths. We discuss four possible cases, including three cameras having an unknown equal focal length, three cameras having two different unknown focal lengths, three cameras where one focal length is known, and the other two cameras have equal or different unknown focal lengths. All the problems can be converted into solving polynomials in one or two unknowns, which can be efficiently solved using Sturm sequence or hidden variable technique. Evaluation using both synthetic and real data shows that the proposed solvers are both faster and more accurate than methods relying on existing two-view solvers. The code and data are available on https://github.com/kocurvik/hf