# Universal Gr"obner Bases of (Universal) Multiview Ideals

arXiv: https://arxiv.org/abs/2509.12376 · HTML: https://mlsanity.com/paper/2509.12376/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 14 references that are in the map.
- First posted on arXiv 15 Sep 2025.

## Builds on (most cited first, 3 of 3)

- [Snapshot of Algebraic Vision](https://mlsanity.com/paper/2210.11443/) (2022)
- [An Atlas for the Pinhole Camera](https://mlsanity.com/paper/2206.13468/) (2022)
- [Algebra and Geometry of Camera Resectioning](https://mlsanity.com/paper/2309.04028/) (2023)

## Abstract (arXiv)

Multiview ideals arise from the geometry of image formation in pinhole cameras, and universal multiview ideals are their analogs for unknown cameras. We prove that a natural collection of polynomials form a universal Gr"obner basis for both types of ideals using a criterion introduced by Huang and Larson, and include a proof of their criterion in our setting. Symmetry reduction and induction enable the method to be deployed on an infinite family of ideals. We also give an explicit description of the matroids on which the methodology depends, in the context of multiview ideals.