# An Atlas for the Pinhole Camera

arXiv: https://arxiv.org/abs/2206.13468 · HTML: https://mlsanity.com/paper/2206.13468/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 69 references that are in the map.
- First posted on arXiv 27 Jun 2022.

## Builds on (most cited first, 5 of 5)

- [The Euclidean distance degree of an algebraic variety](https://mlsanity.com/paper/1309.0049/) (2013)
- [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)
- [On the Existence of Epipolar Matrices](https://mlsanity.com/paper/1510.01401/) (2015)
- [The Quadrifocal Variety](https://mlsanity.com/paper/1501.01266/) (2015)

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

- [Snapshot of Algebraic Vision](https://mlsanity.com/paper/2210.11443/) (2022)
- [Algebra and Geometry of Camera Resectioning](https://mlsanity.com/paper/2309.04028/) (2023)
- [Numerically Computing Galois Groups of Minimal Problems](https://mlsanity.com/paper/2507.10407/) (2025)
- [Universal Gr"obner Bases of (Universal) Multiview Ideals](https://mlsanity.com/paper/2509.12376/) (2025)
- [Learning Fast Monomial Orders for Gr"obner Basis Computations](https://mlsanity.com/paper/2602.02972/) (2026)

## Abstract (arXiv)

We introduce an atlas of algebro-geometric objects associated with image formation in pinhole cameras. The nodes of the atlas are algebraic varieties or their vanishing ideals related to each other by projection or elimination and restriction or specialization respectively. This atlas offers a unifying framework for the study of problems in 3D computer vision. We initiate the study of the atlas by completely characterizing a part of the atlas stemming from the triangulation problem. We conclude with several open problems and generalizations of the atlas.