# Numerically Computing Galois Groups of Minimal Problems

arXiv: https://arxiv.org/abs/2507.10407 · HTML: https://mlsanity.com/paper/2507.10407/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 65 references that are in the map.
- First posted on arXiv 14 Jul 2025.

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

- [PL1P -- Point-line Minimal Problems under Partial Visibility in Three Views](https://mlsanity.com/paper/2003.05015/) (2020)
- [Minimal Problems for the Calibrated Trifocal Variety](https://mlsanity.com/paper/1611.05947/) (2016)
- [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)
- [GPU-Based Homotopy Continuation for Minimal Problems in Computer Vision](https://mlsanity.com/paper/2112.03444/) (2021)
- [An Atlas for the Pinhole Camera](https://mlsanity.com/paper/2206.13468/) (2022)
- [Robust Self-calibration of Focal Lengths from the Fundamental Matrix](https://mlsanity.com/paper/2311.16304/) (2023)
- [Algebra and Geometry of Camera Resectioning](https://mlsanity.com/paper/2309.04028/) (2023)
- [Monodromy Solver: Sequential and Parallel](https://mlsanity.com/paper/1805.12212/) (2018)

## Abstract (arXiv)

I discuss a seemingly unlikely confluence of topics in algebra, numerical computation, and computer vision. The motivating problem is that of solving multiples instances of a parametric family of systems of algebraic (polynomial or rational function) equations. No doubt already of interest to ISSAC attendees, this problem arises in the context of robust model-fitting paradigms currently utilized by the computer vision community (namely "Random Sampling and Consensus", aka "RanSaC".) This talk will give an overview of work in the last 5+ years that aspires to measure the intrinsic difficulty of solving such parametric systems, and makes strides towards practical solutions.