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Minimal Perspective Autocalibration
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Introduces a depth-based formulation of two- and three-view minimal autocalibration with a complete taxonomy of minimal relaxations solved via homotopy continuation, yielding three solvers that beat Kruppa-based and branch-and-bound methods in accuracy on synthetic and real data.
Problem
Estimating camera intrinsics (calibration matrix K, constant across views) from point correspondences alone, where existing Kruppa-equation and stratified/modulus methods are sensitive to noise, degeneracies, or need projective reconstructions.
Approach
Jointly estimate K and unknown point depths using depth-consistency constraints (inter-point distances must agree across views), enumerate all minimal relaxations by removing subsets of these equations via 4-colorings of point pairs, and solve each offline-analyzed minimal problem with homotopy continuation.
Key results
- On Fountain-P11, fguvs achieves 0.035 relative focal length error versus 0.127 for the second-best method (Kruppa BnB), about 3.6x lower.
- In synthetic experiments, Kruppa-6 failure rates range from 4% to 13% due to indefinite DIAC, while the proposed solvers showed no failures.
- Integrating the fguv0 solver into COLMAP on KITTI-Depth reduces focal length error from 0.6510 (default guess) to 0.0720 without bundle adjustment.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the ffuv0 solver instead of Kruppa BnB | autocalibration · Fountain-P11 | ∆fg: 0.127 -> 0.017 | Helped |
| use the ffuv0 solver instead of Kruppa-6 | autocalibration · Herz-Jesu-P8 | Re: 1.112 -> 0.672 | Helped |
| assume square pixels and zero skew with ffuv0 rather than fully uncalibrated fguvs | autocalibration · Fountain-P11 | ∆fg: 0.035 -> 0.017 | Helped |
| initialize COLMAP with fguv0 rather than the default guess | COLMAP reconstruction · Fountain-P11 | ∆fg: 0.3350 -> 0.0058 | Helped |
| initialize COLMAP with fguv0 rather than the default guess | COLMAP reconstruction · Rathaus | Re: 0.624 -> 0.450 | Helped |
| initialize COLMAP with fguv0 rather than the default guess | COLMAP reconstruction · KITTI-Depth | ∆fg: 0.6510 -> 0.0720 | Helped |
| add bundle adjustment on K to COLMAPguess (ablation) | COLMAP reconstruction · Fountain-P11 | Re: 0.444 -> 0.212 | Helped |
| add bundle adjustment on K to COLMAPfguv0 (ablation) | COLMAP reconstruction · KITTI-Depth | Re: 0.409 -> 0.404 | No clear effect |
| add bundle adjustment on K to COLMAPfguv0 (ablation) | COLMAP reconstruction · KITTI-Depth | ∆uv: 0.0185 -> 0.1773 | Hurt |
Surprising findings
- The BnB methods are faster than the proposed solvers (by about 62%) yet provide inferior accuracy.
- On KITTI-Depth, bundle adjustment of K degraded principal point error by 9.58x relative to the fguv0 solver's estimate.
Limitations
- Solvers are slower than competing methods (BnB about 62% faster; Kruppa somewhat faster), and fguvs takes about 4 minutes to reach strict accuracy threshold.
- Solution count for some cases is only conjectural, and only roughly 20% of the 3313 fguvs cases were checked.
Experimental setup
Datasets: Fountain-P11 Herz-Jesu-P8 Rathaus KITTI-Depth
Benchmarks: Fountain-P11 Herz-Jesu-P8 Rathaus KITTI-Depth synthetic image sequences
Metrics: relative focal length error principal point error skew error reprojection error rotation and center angular error failure rate runtime
Baselines: Kruppa-6 Kruppa-7 Kruppa-8 Kruppa BnB Modulus BnB COLMAP default intrinsics guess
Builds on: Kruppa's equations modulus constraint minimal problems framework (Duff et al.) monodromy homotopy continuation
Closest papers by meaning
- Minimal Constraint Relaxation for Multiview Autocalibration (CVPR 2026 · similarity 0.91)
- A Clever Elimination Strategy for Efficient Minimal Solvers (CVPR 2017 · similarity 0.88)
- Practical Solutions to the Relative Pose of Three Calibrated Cameras (CVPR 2025 · similarity 0.86)
- From Correspondences to Pose: Non-minimal Certifiably Optimal Relative Pose without Disambiguation (CVPR 2024 · similarity 0.84)
- Camera Resection from Known Line Pencils and a Radially Distorted Scanline (CVPR 2025 · similarity 0.84)
- Sparse-view Pose Estimation and Reconstruction via Analysis by Generative Synthesis (NeurIPS 2024 · similarity 0.83)
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