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Practical Solutions to the Relative Pose of Three Calibrated Cameras
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Proposes practical approximate solvers for the four-points-in-three-calibrated-views (4p3v) relative pose problem by estimating approximate two-view geometry (affine or mean-point-augmented 5pt) and registering the third camera with P3P, with refinement, filtering, and early non-minimal refitting.
Problem
Relative pose estimation of three calibrated cameras from four point correspondences visible in all three views (the 4p3v problem), for which existing efficient solvers are approximate, hard to implement, or have high failure rates.
Approach
Use four correspondences to estimate an approximate two-view geometry, either affine (4pt affine fundamental matrix) or full essential matrix from a fifth approximate correspondence generated as the mean point of three input points, then register the third view with P3P; add ±δ shifted mean points, early non-minimal refitting, and 4th-point filtering/refinement.
Key results
- On PhotoTourism, 4p3v(M±δ)+R+F+ENM achieves AUC@10 of 77.14 vs 73.53 for 4p3v(HC) with PoseLib RANSAC (Table 2).
- 4p3v(M)+R+F solver outperforms 4p3v(HC) in both accuracy and runtime on PhotoTourism according to the paper.
- With ENM, 4p3v(A)+R+F+ENM reaches AUC@10 of 76.56 on PhotoTourism, comparable to the mean-point solvers.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use mean-point correspondences with δ variants instead of the affine approximation | 4p3v solver · PhotoTourism | AUC@10: 28.59 -> 77.14 | Helped |
| Use mean-point correspondences with δ variants instead of the affine approximation | 4p3v solver · Cambridge Landmarks | AUC@10: 35.19 -> 66.95 | Helped |
| Use mean-point correspondences with δ variants instead of the affine approximation | 4p3v solver · Aachen Day-Night v1.1 | AUC@10: 31.23 -> 57.42 | Helped |
| Add pose refinement (+R) (ablation) | 4p3v(M±δ) · PhotoTourism | AUC@10: 73.73 -> 77.00 | Helped |
| Add pose refinement (+R) (ablation) | 4p3v(M±δ) · Cambridge Landmarks | AUC@10: 65.25 -> 66.89 | Helped |
| Add pose refinement (+R) (ablation) | 4p3v(M±δ) · Aachen Day-Night v1.1 | AUC@10: 56.11 -> 57.26 | Helped |
| Add filtering (+F) after pose refinement (ablation) | 4p3v(M±δ)+R · PhotoTourism | AUC@10: 77.00 -> 76.87 | No clear effect |
| Add early non-minimal refitting (+ENM) (ablation) | 4p3v(M±δ)+R+F · PhotoTourism | AUC@10: 76.87 -> 77.14 | Helped |
| Add early non-minimal refitting (+ENM) (ablation) | 4p3v(M±δ)+R+F · Cambridge Landmarks | AUC@10: 66.75 -> 66.95 | Helped |
| Add early non-minimal refitting (+ENM) (ablation) | 4p3v(M±δ)+R+F · Aachen Day-Night v1.1 | AUC@10: 57.17 -> 57.42 | Helped |
| Add δ-offset mean-point hypotheses (ablation) | 4p3v(M) · PhotoTourism | AUC@10: 72.56 -> 73.73 | Mixed |
| Add pose refinement (+R) (ablation) | 4p3v(M) · PhotoTourism | AUC@10: 72.56 -> 74.88 | Helped |
Surprising findings
- Affine-based 4p3v(A) without early non-minimal refitting performs very poorly (median error about 25 degrees on PhotoTourism), but becomes competitive once ENM is applied.
- Simple 5pt+P3P with refinement, filtering, and ENM is competitive with the proposed mean-point solvers, although the proposed solvers are more accurate in the best configuration.
Limitations
- Approximate solvers' accuracy is scene-dependent without ENM refitting.
- Two-view variants do not outperform the 5pt solver; gains come from three-view refinement and filtering.
- ENM cannot be applied to the HC solver of [21] or easily to the epipole-sweep solver of [36].
Experimental setup
Datasets: PhotoTourism Cambridge Landmarks Aachen Day-Night v1.1
Benchmarks: PhotoTourism Cambridge Landmarks Aachen Day-Night v1.1
Metrics: AUC@5 AUC@10 AUC@20 mean pose error median pose error runtime
Baselines: 4p3v(HC) 5pt+P3P PoseLib RANSAC GC-RANSAC
Builds on: 5pt solver P3P solver 4pt affine fundamental matrix solver LO-RANSAC PoseLib
Closest papers by meaning
- From Correspondences to Pose: Non-minimal Certifiably Optimal Relative Pose without Disambiguation (CVPR 2024 · similarity 0.92)
- Efficient Solution of Point-Line Absolute Pose (CVPR 2024 · similarity 0.86)
- Relative Pose Estimation through Affine Corrections of Monocular Depth Priors (CVPR 2025 · similarity 0.86)
- Structure-Aware Correspondence Learning for Relative Pose Estimation (CVPR 2025 · similarity 0.86)
- FAR: Flexible Accurate and Robust 6DoF Relative Camera Pose Estimation (CVPR 2024 · similarity 0.86)
- 3D-Aware Hypothesis & Verification for Generalizable Relative Object Pose Estimation (ICLR 2024 · similarity 0.86)
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