# A Classification of Critical Configurations for any Number of Projective Views

arXiv: https://arxiv.org/abs/2401.03450 · HTML: https://mlsanity.com/paper/2401.03450/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 44 references that are in the map.
- First posted on arXiv 7 Jan 2024.

## Builds on (most cited first, 4 of 4)

- [PLMP -- Point-Line Minimal Problems in Complete Multi-View Visibility](https://mlsanity.com/paper/1903.10008/) (2019)
- [PL1P -- Point-line Minimal Problems under Partial Visibility in Three Views](https://mlsanity.com/paper/2003.05015/) (2020)
- [Critical configurations for two projective views, a new approach](https://mlsanity.com/paper/2112.05074/) (2021)
- [Critical configurations for three projective views](https://mlsanity.com/paper/2112.05478/) (2021)

## Built on by (most cited first, 1 of 1)

- [Do Latent Tokens Think? A Causal and Adversarial Analysis of Chain-of-Continuous-Thought](https://mlsanity.com/paper/2512.21711/) (2025)

## Abstract (arXiv)

Structure from motion is the process of recovering information about cameras and 3D scene from a set of images. Generally, in a noise-free setting, all information can be uniquely recovered if enough images and image points are provided. There are, however, certain cases where unique recovery is impossible, even in theory; these are called critical configurations. We use a recently developed algebraic approach to classify all critical configurations for any number of projective cameras. We show that they form well-known algebraic varieties, such as quadric surfaces and curves of degree at most 4. This paper also improves upon earlier results both by finding previously unknown critical configurations and by showing that some configurations previously believed to be critical are in fact not.