mlsanityData to 7 Oct 2026

Beyond Gr"obner Bases: Basis Selection for Minimal Solvers

arXiv 1803.04360 ↗First posted 12 Mar 2018cs.CVcited by 25

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Abstract (arXiv)

Many computer vision applications require robust estimation of the underlying geometry, in terms of camera motion and 3D structure of the scene. These robust methods often rely on running minimal solvers in a RANSAC framework. In this paper we show how we can make polynomial solvers based on the action matrix method faster, by careful selection of the monomial bases. These monomial bases have traditionally been based on a Gr"obner basis for the polynomial ideal. Here we describe how we can enumerate all such bases in an efficient way. We also show that going beyond Gr"obner bases leads to more efficient solvers in many cases. We present a novel basis sampling scheme that we evaluate on a number of problems.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Mar 2018.

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Citing papers per year: 2021: 4; 2022: 6; 2023: 3; 2024: 5; 2025: 5; 2026: 2.

25 papers.

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  1. 2022The 8-Point Algorithm as an Inductive Bias for Relative Pose Prediction by ViTscited by 38
  2. 2021Learning to Solve Hard Minimal Problemscited by 18
  3. 2022ARCS: Accurate Rotation and Correspondence Searchcited by 15
  4. 2024FAR: Flexible, Accurate and Robust 6DoF Relative Camera Pose Estimationcited by 12
  5. 2022Estimation Contracts for Outlier-Robust Geometric Perceptioncited by 11
  6. 2022Snapshot of Algebraic Visioncited by 9
  7. 2021GPU-Based Homotopy Continuation for Minimal Problems in Computer Visioncited by 8
  8. 2022Optimizing Elimination Templates by Greedy Parameter Searchcited by 8
  9. 2024Order-One Rolling Shutter Camerascited by 5
  10. 2021Trust Your IMU: Consequences of Ignoring the IMU Driftcited by 3
  11. 2022Partially calibrated semi-generalized pose from hybrid point correspondencescited by 2
  12. 2023Sparse resultant based minimal solvers in computer vision and their connection with the action matrixcited by 2
13 more
  1. 2023Automatic Solver Generator for Systems of Laurent Polynomial Equationscited by 2
  2. 2023Algebra and Geometry of Camera Resectioningcited by 2
  3. 2025Trifocal Tensor and Relative Pose Estimation with Known Vertical Directioncited by 2
  4. 2021On Relative Pose Recovery for Multi-Camera Systemscited by 1
  5. 2024MinBackProp -- Backpropagating through Minimal Solverscited by 1
  6. 2024Simulator HC: Regression-based Online Simulation of Starting Problem-Solution Pairs for Homotopy Continuation in Geometric Visioncited by 1
  7. 2025A Minimal Solver for Relative Pose Estimation with Unknown Focal Length from Two Affine Correspondencescited by 1
  8. 2024Online Stability Improvement of Groebner Basis Solvers using Deep Learningcited by 0
  9. 2025Three-view Focal Length Recovery From Homographiescited by 0
  10. 2025PLMP -- Point-Line Minimal Problems for Projective SfMcited by 0
  11. 2025Radially Distorted Homographies, Revisitedcited by 0
  12. 2026Learning Fast Monomial Orders for Gr"obner Basis Computationscited by 0
  13. 2026Solving Minimal Problems Without Matrix Inversion Using FFT-Based Interpolationcited by 0