# Snapshot of Algebraic Vision

arXiv: https://arxiv.org/abs/2210.11443 · HTML: https://mlsanity.com/paper/2210.11443/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 201 references that are in the map.
- First posted on arXiv 20 Oct 2022.

## Builds on (most cited first, 30 of 41)

- [A Survey of Structure from Motion](https://mlsanity.com/paper/1701.08493/) (2017)
- [SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group](https://mlsanity.com/paper/1612.07386/) (2016)
- [Rolling Shutter Camera Relative Pose: Generalized Epipolar Geometry](https://mlsanity.com/paper/1605.00475/) (2016)
- [Beyond Gr"obner Bases: Basis Selection for Minimal Solvers](https://mlsanity.com/paper/1803.04360/) (2018)
- [Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization](https://mlsanity.com/paper/2109.03349/) (2021)
- [Robust Group Synchronization via Cycle-Edge Message Passing](https://mlsanity.com/paper/1912.11347/) (2019)
- [Learning to Solve Hard Minimal Problems](https://mlsanity.com/paper/2112.03424/) (2021)
- [PLMP -- Point-Line Minimal Problems in Complete Multi-View Visibility](https://mlsanity.com/paper/1903.10008/) (2019)
- [A clever elimination strategy for efficient minimal solvers](https://mlsanity.com/paper/1703.05289/) (2017)
- [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)
- [A Minimal Solution for Two-view Focal-length Estimation using Two Affine Correspondences](https://mlsanity.com/paper/1706.01649/) (2017)
- [On the local stability of semidefinite relaxations](https://mlsanity.com/paper/1710.04287/) (2017)
- [Galois/monodromy groups for decomposing minimal problems in 3D reconstruction](https://mlsanity.com/paper/2105.04460/) (2021)
- [Five-point Fundamental Matrix Estimation for Uncalibrated Cameras](https://mlsanity.com/paper/1803.00260/) (2018)
- [A sparse resultant based method for efficient minimal solvers](https://mlsanity.com/paper/1912.10268/) (2019)
- [Estimation Contracts for Outlier-Robust Geometric Perception](https://mlsanity.com/paper/2208.10521/) (2022)
- [A Minimal Closed-Form Solution for Multi-Perspective Pose Estimation using Points and Lines](https://mlsanity.com/paper/1807.09970/) (2018)
- [On the Instability of Relative Pose Estimation and RANSAC's Role](https://mlsanity.com/paper/2112.14651/) (2021)
- [Distortion Varieties](https://mlsanity.com/paper/1610.01860/) (2016)
- [GPU-Based Homotopy Continuation for Minimal Problems in Computer Vision](https://mlsanity.com/paper/2112.03444/) (2021)
- [Optimizing Elimination Templates by Greedy Parameter Search](https://mlsanity.com/paper/2203.14901/) (2022)
- [GAPS: Generator for Automatic Polynomial Solvers](https://mlsanity.com/paper/2004.11765/) (2020)
- [On the Existence of Epipolar Matrices](https://mlsanity.com/paper/1510.01401/) (2015)
- [Critical configurations for two projective views, a new approach](https://mlsanity.com/paper/2112.05074/) (2021)
- [An Atlas for the Pinhole Camera](https://mlsanity.com/paper/2206.13468/) (2022)
- [The Quadrifocal Variety](https://mlsanity.com/paper/1501.01266/) (2015)
- [On Some Properties of Calibrated Trifocal Tensors](https://mlsanity.com/paper/1601.01467/) (2016)
- [The Chow Form of the Essential Variety in Computer Vision](https://mlsanity.com/paper/1604.04372/) (2016)

## Built on by (most cited first, 9 of 9)

- [Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal Tensor](https://mlsanity.com/paper/2409.09313/) (2024)
- [Algebra and Geometry of Camera Resectioning](https://mlsanity.com/paper/2309.04028/) (2023)
- [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)
- [An Algebraic Geometry Approach to Viewing Graph Solvability](https://mlsanity.com/paper/2504.03637/) (2025)
- [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)
- [QuadSync: Quadrifocal Tensor Synchronization via Tucker Decomposition](https://mlsanity.com/paper/2602.22639/) (2026)
- [Multiprojective Geometry of Compatible Triples of Fundamental and Essential Matrices](https://mlsanity.com/paper/2602.23450/) (2026)

## Abstract (arXiv)

In this survey article, we present interactions between algebraic geometry and computer vision, which have recently come under the header of algebraic vision. The subject has given new insights in multiple view geometry and its application to 3D scene reconstruction and carried a host of novel problems and ideas back into algebraic geometry.