# Algebra and Geometry of Camera Resectioning

arXiv: https://arxiv.org/abs/2309.04028 · HTML: https://mlsanity.com/paper/2309.04028/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 41 references that are in the map.
- First posted on arXiv 7 Sep 2023.

## Builds on (most cited first, 8 of 8)

- [Beyond Gr"obner Bases: Basis Selection for Minimal Solvers](https://mlsanity.com/paper/1803.04360/) (2018)
- [PLMP -- Point-Line Minimal Problems in Complete Multi-View Visibility](https://mlsanity.com/paper/1903.10008/) (2019)
- [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)
- [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)
- [A convex relaxation to compute the nearest structured rank deficient matrix](https://mlsanity.com/paper/1904.09661/) (2019)
- [An Atlas for the Pinhole Camera](https://mlsanity.com/paper/2206.13468/) (2022)

## Built on by (most cited first, 2 of 2)

- [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)

## Abstract (arXiv)

We study algebraic varieties associated with the camera resectioning problem. We characterize these resectioning varieties' multigraded vanishing ideals using Gr"obner basis techniques. As an application, we derive and re-interpret celebrated results in geometric computer vision related to camera-point duality. We also clarify some relationships between the classical problems of optimal resectioning and triangulation, state a conjectural formula for the Euclidean distance degree of the resectioning variety, and discuss how this conjecture relates to the recently-resolved multiview conjecture.