# A clever elimination strategy for efficient minimal solvers

arXiv: https://arxiv.org/abs/1703.05289 · HTML: https://mlsanity.com/paper/1703.05289/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2017.

## Built on by (most cited first, 17 of 17)

- [Calibrated and Partially Calibrated Semi-Generalized Homographies](https://mlsanity.com/paper/2103.06535/) (2021)
- [RePoseD: Efficient Relative Pose Estimation With Known Depth Information](https://mlsanity.com/paper/2501.07742/) (2025)
- [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)
- [Optimizing Elimination Templates by Greedy Parameter Search](https://mlsanity.com/paper/2203.14901/) (2022)
- [Relative Pose from SIFT Features](https://mlsanity.com/paper/2203.07930/) (2022)
- [AffineGlue: Joint Matching and Robust Estimation](https://mlsanity.com/paper/2307.15381/) (2023)
- [Trust Your IMU: Consequences of Ignoring the IMU Drift](https://mlsanity.com/paper/2103.08286/) (2021)
- [Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal Tensor](https://mlsanity.com/paper/2409.09313/) (2024)
- [Partially calibrated semi-generalized pose from hybrid point correspondences](https://mlsanity.com/paper/2209.15072/) (2022)
- [Sparse resultant based minimal solvers in computer vision and their connection with the action matrix](https://mlsanity.com/paper/2301.06443/) (2023)
- [Automatic Solver Generator for Systems of Laurent Polynomial Equations](https://mlsanity.com/paper/2307.00320/) (2023)
- [Trifocal Tensor and Relative Pose Estimation with Known Vertical Direction](https://mlsanity.com/paper/2512.19110/) (2025)
- [On Relative Pose Recovery for Multi-Camera Systems](https://mlsanity.com/paper/2102.11996/) (2021)
- [Three-view Focal Length Recovery From Homographies](https://mlsanity.com/paper/2501.07499/) (2025)
- [PLMP -- Point-Line Minimal Problems for Projective SfM](https://mlsanity.com/paper/2503.04351/) (2025)
- [QuadSync: Quadrifocal Tensor Synchronization via Tucker Decomposition](https://mlsanity.com/paper/2602.22639/) (2026)

## Abstract (arXiv)

We present a new insight into the systematic generation of minimal solvers in computer vision, which leads to smaller and faster solvers. Many minimal problem formulations are coupled sets of linear and polynomial equations where image measurements enter the linear equations only. We show that it is useful to solve such systems by first eliminating all the unknowns that do not appear in the linear equations and then extending solutions to the rest of unknowns. This can be generalized to fully non-linear systems by linearization via lifting. We demonstrate that this approach leads to more efficient solvers in three problems of partially calibrated relative camera pose computation with unknown focal length and/or radial distortion. Our approach also generates new interesting constraints on the fundamental matrices of partially calibrated cameras, which were not known before.