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From Correspondences to Pose: Non-minimal Certifiably Optimal Relative Pose without Disambiguation
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Proposes C2P, a certifiably globally optimal non-minimal relative pose solver that encodes cheirality-like constraints in an SDP relaxation of a QCQP, so the pose is obtained without a post-hoc disambiguation step.
Problem
Relative pose from n>=5 calibrated correspondences normally yields four essential-matrix-consistent candidate poses that must be disambiguated afterward by a cheirality (positive-depth) check, adding overhead that scales with the number of points.
Approach
Replace the positive-depth check with necessary and sufficient geometric constraints (epipolar-based sign constraints plus a new characterization of the normalized essential manifold via the adjugate matrix) inside a QCQP, then relax to an SDP with redundant constraints so the dominant singular vector yields the geometrically valid pose; the slack variable also flags pure rotation.
Key results
- C2P delivers up to 4x faster runtime than the fastest alternative (Zhao + M) and up to 35x faster than the slowest at large n (>10^3 correspondences).
- In the small-n regime (12-30 correspondences), C2P matches Garcia-Salguero et al. in accuracy while being faster; for n in 10^2-10^4 all methods are equally accurate.
- The slack variable s_t^2 can detect near-pure-rotation motions via simple thresholding.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use C2P instead of Zhao's solver | Relative pose estimation · Synthetic data, 12–30 correspondences | rotation error | Helped |
| Use C2P instead of Zhao's solver | Relative pose estimation · Synthetic data, 12–30 correspondences | translation error | Helped |
| Use C2P instead of prior globally optimal solvers | Relative pose estimation · Synthetic data, 10²–10⁴ correspondences | runtime scaling | Helped |
| Add redundant constraints to C2P-fast (ablation) | C2P · Synthetic data, 12–30 correspondences | pose accuracy | Helped |
| Remove redundant constraints from C2P (ablation) | C2P · Synthetic data, 12–30 correspondences | pose accuracy | Hurt |
| Remove redundant constraints from C2P (ablation) | C2P · Synthetic data, 10²–10⁴ correspondences | pose accuracy | No clear effect |
Surprising findings
- The optimal SDP solution is consistently the dominant singular vector, and the relaxation is not generally rank-1, so rank-based recovery needs a different certificate.
Limitations
- Cannot handle outliers; requires robust wrapper such as RANSAC or GNC.
- Relies on an SDP solver (SDPA), which is slower than closed-form methods for small problems.
Experimental setup
Datasets: synthetic point correspondences Strecha et al. (six sequences, 97 wide-baseline pairs with SIFT)
Benchmarks: synthetic correspondence experiments Strecha et al. six-sequence dataset
Metrics: mean rotation error (deg) mean translation error (deg) runtime (s) pure-rotation detection via slack variable
Baselines: Zhao (2022) Garcia-Salguero et al. (2022) classic cheirality check (triangulation) Nister five-point
Builds on: Zhao non-minimal essential matrix estimation Garcia-Salguero tighter relaxation Briales et al. certifiable essential matrix Shor relaxation
Closest papers by meaning
- Practical Solutions to the Relative Pose of Three Calibrated Cameras (CVPR 2025 · similarity 0.92)
- Structure-Aware Correspondence Learning for Relative Pose Estimation (CVPR 2025 · similarity 0.89)
- FAR: Flexible Accurate and Robust 6DoF Relative Camera Pose Estimation (CVPR 2024 · similarity 0.89)
- Relative Pose Estimation through Affine Corrections of Monocular Depth Priors (CVPR 2025 · similarity 0.89)
- 3D-Aware Hypothesis & Verification for Generalizable Relative Object Pose Estimation (ICLR 2024 · similarity 0.88)
- EquiPose: Exploiting Permutation Equivariance for Relative Camera Pose Estimation (CVPR 2025 · similarity 0.87)
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