# Critical configurations for two projective views, a new approach

arXiv: https://arxiv.org/abs/2112.05074 · HTML: https://mlsanity.com/paper/2112.05074/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 25 references that are in the map.
- First posted on arXiv 9 Dec 2021.

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

- [Snapshot of Algebraic Vision](https://mlsanity.com/paper/2210.11443/) (2022)
- [Critical configurations for three projective views](https://mlsanity.com/paper/2112.05478/) (2021)
- [A Taxonomy of Structure from Motion Methods](https://mlsanity.com/paper/2505.15814/) (2025)
- [Condition numbers in multiview geometry, instability in relative pose estimation, and RANSAC](https://mlsanity.com/paper/2310.02719/) (2023)
- [A Classification of Critical Configurations for any Number of Projective Views](https://mlsanity.com/paper/2401.03450/) (2024)

## Abstract (arXiv)

The problem of structure from motion is concerned with recovering 3-dimensional structure of an object from a set of 2-dimensional images. Generally, all information can be uniquely recovered if enough images and image points are provided, but there are certain cases where unique recovery is impossible; these are called critical configurations. In this paper we use an algebraic approach to study the critical configurations for two projective cameras. We show that all critical configurations lie on quadric surfaces, and classify exactly which quadrics constitute a critical configuration. The paper also describes the relation between the different reconstructions when unique reconstruction is impossible.