# Congruences and Concurrent Lines in Multi-View Geometry

arXiv: https://arxiv.org/abs/1608.05924 · HTML: https://mlsanity.com/paper/1608.05924/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Aug 2016.

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

- [Snapshot of Algebraic Vision](https://mlsanity.com/paper/2210.11443/) (2022)
- [Order-One Rolling Shutter Cameras](https://mlsanity.com/paper/2403.11295/) (2024)

## Abstract (arXiv)

We present a new framework for multi-view geometry in computer vision. A camera is a mapping between mathbbP3 and a line congruence. This model, which ignores image planes and measurements, is a natural abstraction of traditional pinhole cameras. It includes two-slit cameras, pushbroom cameras, catadioptric cameras, and many more. We study the concurrent lines variety, which consists of n-tuples of lines in mathbbP3 that intersect at a point. Combining its equations with those of various congruences, we derive constraints for corresponding images in multiple views. We also study photographic cameras which use image measurements and are modeled as rational maps from mathbbP3 to mathbbP2 or mathbbP1× mathbbP1.