# PLMP -- Point-Line Minimal Problems in Complete Multi-View Visibility

arXiv: https://arxiv.org/abs/1903.10008 · HTML: https://mlsanity.com/paper/1903.10008/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2019.

## Built on by (most cited first, 18 of 18)

- [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)
- [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 Accurate and Real-time Relative Pose Estimation from Triple Point-line Images by Decoupling Rotation and Translation](https://mlsanity.com/paper/2403.11639/) (2024)
- [Minimal Perspective Autocalibration](https://mlsanity.com/paper/2405.05605/) (2024)
- [Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal Tensor](https://mlsanity.com/paper/2409.09313/) (2024)
- [Single-Scanline Relative Pose Estimation for Rolling Shutter Cameras](https://mlsanity.com/paper/2506.22069/) (2025)
- [Algebra and Geometry of Camera Resectioning](https://mlsanity.com/paper/2309.04028/) (2023)
- [Minimal Solvers for Full DoF Motion Estimation from Asynchronous Tracks](https://mlsanity.com/paper/2508.17537/) (2025)
- [Practical solutions to the relative pose of three calibrated cameras](https://mlsanity.com/paper/2303.16078/) (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)
- [An Algebraic Geometry Approach to Viewing Graph Solvability](https://mlsanity.com/paper/2504.03637/) (2025)
- [Detecting 3D Line Segments for 6DoF Pose Estimation with Limited Data](https://mlsanity.com/paper/2601.12090/) (2026)
- [Single-View Rolling-Shutter SfM](https://mlsanity.com/paper/2603.11888/) (2026)

## Abstract (arXiv)

We present a complete classification of all minimal problems for generic arrangements of points and lines completely observed by calibrated perspective cameras. We show that there are only 30 minimal problems in total, no problems exist for more than 6 cameras, for more than 5 points, and for more than 6 lines. We present a sequence of tests for detecting minimality starting with counting degrees of freedom and ending with full symbolic and numeric verification of representative examples. For all minimal problems discovered, we present their algebraic degrees, i.e. the number of solutions, which measure their intrinsic difficulty. It shows how exactly the difficulty of problems grows with the number of views. Importantly, several new minimal problems have small degrees that might be practical in image matching and 3D reconstruction.