Research map / 3D vision / Human pose estimation
Efficient Solution of Point-Line Absolute Pose
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Gives algebraically optimal minimal solvers for absolute pose from mixed point-line correspondences (P2P1L reduced to a quadratic, P1P2L to a quartic), faster and more stable than prior E3Q3-based and Ramalingam solvers.
Problem
Minimal absolute camera pose estimation from mixed 3D-2D correspondences: two points plus one line (P2P1L) and one point plus two lines (P1P2L), where prior practical solvers needed degree 4 (P2P1L) or degree 8 (P1P2L) polynomial root finding.
Approach
Uses a special reference frame in world and camera coordinates plus Galois-group insights to decompose the problems, reducing P2P1L to a univariate quadratic and P1P2L to a univariate quartic, with closed-form recovery of the remaining pose entries.
Key results
- P2P1L solver runs in 313.8 ns on average, about 6x faster than 3Q3 (1860.6 ns).
- P1P2L solver runs in 504.0 ns on average, about 4x faster than 3Q3 (1967.1 ns).
- In RANSAC on Oxford Multi-view data, P1P2L solver averages 0.59x the runtime of 3Q3 (speed-up up to ~3.5x on some scenes).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace 3Q3 with the proposed P2P1L solver | P2P1L · Synthetic solver runtime | runtime: 1860.6 -> 313.8 ns | Helped |
| replace 3Q3 with the proposed P1P2L solver | P1P2L · Synthetic solver runtime | runtime: 1967.1 -> 504.0 ns | Helped |
| replace 3Q3 with the proposed solver | P2P1L RANSAC · Oxford Multi-view | average speed-up vs. 3Q3: 1x -> 0.94x | Hurt |
| replace 3Q3 with the proposed solver | P1P2L RANSAC · Oxford Multi-view | average speed-up vs. 3Q3: 1x -> 0.59x | Hurt |
| rotate the world frame to stabilize P1P2L (ablation) | P1P2L solver · Generic synthetic | mean rotation error: 0.00050 -> 9.0e-09 | Helped |
| rotate the world frame to stabilize P1P2L (ablation) | P1P2L solver · Coplanar synthetic | mean rotation error: 0.00022 -> 1.1 | Hurt |
| use the P2P1L coplanar-case fix (ablation) | P2P1L solver · Coplanar synthetic | mean rotation error: 2.4 -> 1.2e-12 | Helped |
| use the P2P1L coplanar-case fix (ablation) | P2P1L solver · Generic synthetic | mean rotation error: 7.1e-11 -> 3.2e-09 | Hurt |
Surprising findings
- The stabilized P1P2L solver fails in the coplanar case, while the unstabilized one handles it; the two P2P1L variants show the reverse pattern, so each needs a different variant per configuration.
Limitations
- Solver numerical stability depends on the configuration: P1P2L needs a rotation fix for Z1-Z2 near zero, and the P2P1L/P1P2L variants differ for coplanar inputs.
- RANSAC speedup for P2P1L is marginal (about 0.94x average) because scoring and local optimization dominate runtime.
Experimental setup
Datasets: Oxford Multi-view Data (for RANSAC experiments) synthetic data
Benchmarks: Oxford Multi-view Data
Metrics: rotation error translation error runtime (ns) RANSAC runtime (ms)
Baselines: 3Q3 (E3Q3 solver in PoseLib) Ramalingam et al. solver (SVD) Ramalingam et al. solver (LU)
Builds on: Ramalingam et al. special reference frame solver E3Q3 solver Nister et al. algebraic optimality framework Barreto/Galois group decomposition (Bertsch et al.) LO-RANSAC
Closest papers by meaning
- A Robust and Efficient Algorithm for the PnL Problem Using Algebraic Distance to Approximate the Reprojection Distance (AAAI 2019 · similarity 0.88)
- Camera Resection from Known Line Pencils and a Radially Distorted Scanline (CVPR 2025 · similarity 0.88)
- From Correspondences to Pose: Non-minimal Certifiably Optimal Relative Pose without Disambiguation (CVPR 2024 · similarity 0.87)
- Practical Solutions to the Relative Pose of Three Calibrated Cameras (CVPR 2025 · similarity 0.86)
- Absolute Pose from One or Two Scaled and Oriented Features (CVPR 2024 · similarity 0.84)
- Learning Affine Correspondences by Integrating Geometric Constraints (CVPR 2025 · similarity 0.84)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.