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Beyond Grobner Bases: Basis Selection for Minimal Solvers
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Select a heuristic sampled monomial basis instead of the GRevLex basis | Polynomial minimal solvers · Relative pose F+λ 8pt | elimination template size: 11 × 20 -> 7 × 16 | Helped |
| Select a heuristic sampled monomial basis instead of the GRevLex basis | Polynomial minimal solvers · Relative pose E+f 6pt | elimination template size: 21 × 30 -> 11 × 20 | Helped |
| Select a heuristic sampled monomial basis instead of the GRevLex basis | Polynomial minimal solvers · Stitching fλ+R+fλ 3pt | elimination template size: 48 × 66 -> 18 × 36 | Helped |
| Select a heuristic sampled monomial basis instead of the GRevLex basis | Polynomial minimal solvers · Relative pose E+fλ 7pt | elimination template size: 181 × 200 -> 69 × 90 | Helped |
| Select a heuristic sampled monomial basis instead of the Gröbner-fan basis | Polynomial minimal solvers · Relative pose E+fλ 7pt (elim. λ) | elimination template size: 37 × 56 -> 24 × 43 | Helped |
| Use the proposed sampled-basis solver instead of Larsson et al. [29] | Three-point image stitching · Three-point image stitching | runtime: 0.38 -> 0.16 | Helped |
| Use the proposed sampled-basis solver instead of Byröd et al. [8] | Three-point image stitching · Three-point image stitching | runtime: 0.89 -> 0.16 | Helped |
| Choose a sampled basis for the proposed relative-pose formulation | Relative pose E+fλ 7pt with λ eliminated · Synthetic instances | runtime: 10 ms -> 1.2 ms | Helped |
| Use the proposed relative-pose solver instead of Kukelova et al. [27] | Relative pose E+fλ 7pt with λ eliminated · 1,000 random synthetic instances | numerical stability | Hurt |
| Replace the heuristic sampler with uniform sampling over M | P4Pfr solver basis selection · P4Pfr | elimination template size | Hurt |
| Replace the heuristic sampler with uniform sampling over all monomials of the same degree | P4Pfr solver basis selection · P4Pfr | elimination template size | Hurt |
| Use the heuristic sampled basis instead of the Gröbner-fan basis | P4Pfr solver · P4Pfr | elimination template size: 54 × 70 -> 54 × 70 | No clear effect |
Closest papers by meaning
- A Sparse Resultant Based Method for Efficient Minimal Solvers (CVPR 2020 · similarity 0.93)
- A Clever Elimination Strategy for Efficient Minimal Solvers (CVPR 2017 · similarity 0.87)
- Efficient Solution of Point-Line Absolute Pose (CVPR 2024 · similarity 0.83)
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- An N-Point Linear Solver for Line and Motion Estimation with Event Cameras (CVPR 2024 · similarity 0.82)
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