# A sparse resultant based method for efficient minimal solvers

arXiv: https://arxiv.org/abs/1912.10268 · HTML: https://mlsanity.com/paper/1912.10268/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2019.

## Built on by (most cited first, 11 of 11)

- [Learning to Solve Hard Minimal Problems](https://mlsanity.com/paper/2112.03424/) (2021)
- [Snapshot of Algebraic Vision](https://mlsanity.com/paper/2210.11443/) (2022)
- [Optimizing Elimination Templates by Greedy Parameter Search](https://mlsanity.com/paper/2203.14901/) (2022)
- [Trust Your IMU: Consequences of Ignoring the IMU Drift](https://mlsanity.com/paper/2103.08286/) (2021)
- [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)
- [Simulator HC: Regression-based Online Simulation of Starting Problem-Solution Pairs for Homotopy Continuation in Geometric Vision](https://mlsanity.com/paper/2411.03745/) (2024)
- [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)
- [Solving Minimal Problems Without Matrix Inversion Using FFT-Based Interpolation](https://mlsanity.com/paper/2605.06572/) (2026)

## Abstract (arXiv)

Many computer vision applications require robust and efficient estimation of camera geometry. The robust estimation is usually based on solving camera geometry problems from a minimal number of input data measurements, i.e. solving minimal problems in a RANSAC framework. Minimal problems often result in complex systems of polynomial equations. Many state-of-the-art efficient polynomial solvers to these problems are based on Gr"obner bases and the action-matrix method that has been automatized and highly optimized in recent years. In this paper we study an alternative algebraic method for solving systems of polynomial equations, i.e., the sparse resultant-based method and propose a novel approach to convert the resultant constraint to an eigenvalue problem. This technique can significantly improve the efficiency and stability of existing resultant-based solvers. We applied our new resultant-based method to a large variety of computer vision problems and show that for most of the considered problems, the new method leads to solvers that are the same size as the the best available Gr"obner basis solvers and of similar accuracy. For some problems the new sparse-resultant based method leads to even smaller and more stable solvers than the state-of-the-art Gr"obner basis solvers. Our new method can be fully automatized and incorporated into existing tools for automatic generation of efficient polynomial solvers and as such it represents a competitive alternative to popular Gr"obner basis methods for minimal problems in computer vision.