# PL1P -- Point-line Minimal Problems under Partial Visibility in Three Views

arXiv: https://arxiv.org/abs/2003.05015 · HTML: https://mlsanity.com/paper/2003.05015/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2020.

## Built on by (most cited first, 16 of 16)

- [Learning to Solve Hard Minimal Problems](https://mlsanity.com/paper/2112.03424/) (2021)
- [Galois/monodromy groups for decomposing minimal problems in 3D reconstruction](https://mlsanity.com/paper/2105.04460/) (2021)
- [On the Instability of Relative Pose Estimation and RANSAC's Role](https://mlsanity.com/paper/2112.14651/) (2021)
- [Snapshot of Algebraic Vision](https://mlsanity.com/paper/2210.11443/) (2022)
- [GPU-Based Homotopy Continuation for Minimal Problems in Computer Vision](https://mlsanity.com/paper/2112.03444/) (2021)
- [Handbook on Leveraging Lines for Two-View Relative Pose Estimation](https://mlsanity.com/paper/2309.16040/) (2023)
- [An Atlas for the Pinhole Camera](https://mlsanity.com/paper/2206.13468/) (2022)
- [Minimal Perspective Autocalibration](https://mlsanity.com/paper/2405.05605/) (2024)
- [Automatic Solver Generator for Systems of Laurent Polynomial Equations](https://mlsanity.com/paper/2307.00320/) (2023)
- [Algebra and Geometry of Camera Resectioning](https://mlsanity.com/paper/2309.04028/) (2023)
- [Practical solutions to the relative pose of three calibrated cameras](https://mlsanity.com/paper/2303.16078/) (2023)
- [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)
- [Simulator HC: Regression-based Online Simulation of Starting Problem-Solution Pairs for Homotopy Continuation in Geometric Vision](https://mlsanity.com/paper/2411.03745/) (2024)
- [PLMP -- Point-Line Minimal Problems for Projective SfM](https://mlsanity.com/paper/2503.04351/) (2025)
- [Numerically Computing Galois Groups of Minimal Problems](https://mlsanity.com/paper/2507.10407/) (2025)

## Abstract (arXiv)

We present a complete classification of minimal problems for generic arrangements of points and lines in space observed partially by three calibrated perspective cameras when each line is incident to at most one point. This is a large class of interesting minimal problems that allows missing observations in images due to occlusions and missed detections. There is an infinite number of such minimal problems; however, we show that they can be reduced to 140616 equivalence classes by removing superfluous features and relabeling the cameras. We also introduce camera-minimal problems, which are practical for designing minimal solvers, and show how to pick a simplest camera-minimal problem for each minimal problem. This simplification results in 74575 equivalence classes. Only 76 of these were known; the rest are new. In order to identify problems that have potential for practical solving of image matching and 3D reconstruction, we present several smaller natural subfamilies of camera-minimal problems as well as compute solution counts for all camera-minimal problems which have less than 300 solutions for generic data.