# PLMP -- Point-Line Minimal Problems for Projective SfM

arXiv: https://arxiv.org/abs/2503.04351 · HTML: https://mlsanity.com/paper/2503.04351/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 51 references that are in the map.
- First posted on arXiv 6 Mar 2025.

## Builds on (most cited first, 12 of 12)

- [Beyond Gr"obner Bases: Basis Selection for Minimal Solvers](https://mlsanity.com/paper/1803.04360/) (2018)
- [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)
- [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)
- [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)
- [A Minimal Closed-Form Solution for Multi-Perspective Pose Estimation using Points and Lines](https://mlsanity.com/paper/1807.09970/) (2018)
- [On the Existence of Epipolar Matrices](https://mlsanity.com/paper/1510.01401/) (2015)
- [Order-One Rolling Shutter Cameras](https://mlsanity.com/paper/2403.11295/) (2024)

## Abstract (arXiv)

We completely classify all minimal problems for Structure-from-Motion (SfM) where arrangements of points and lines are fully observed by multiple uncalibrated pinhole cameras. We find 291 minimal problems, 73 of which have unique solutions and can thus be solved linearly. Two of the linear problems allow an arbitrary number of views, while all other minimal problems have at most 9 cameras. All minimal problems have at most 7 points and at most 12 lines. We compute the number of solutions of each minimal problem, as this gives a measurement of the problem's intrinsic difficulty, and find that these number are relatively low (e.g., when comparing with minimal problems for calibrated cameras). Finally, by exploring stabilizer subgroups of subarrangements, we develop a geometric and systematic way to 1) factorize minimal problems into smaller problems, 2) identify minimal problems in underconstrained problems, and 3) formally prove non-minimality.