Research map / 3D vision / Depth and stereo
PRaDA: Projective Radial Distortion Averaging
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Calibrates radial distortion of unordered image collections by solving pairwise projective two-view distortion problems, then averaging the per-pair division-model estimates into one consistent model per camera, without 3D points or full bundle adjustment.
Problem
Automatic calibration of radially distorted cameras from unordered image collections, especially challenging sparse or wide-angle fisheye images where full SfM or learning-based calibration is unreliable.
Approach
Decouple distortion calibration from 3D reconstruction by working in projective space: estimate pairwise one-parameter division-model distortion with a minimal F10 solver in LO-RANSAC, refine with Sampson error, fuse the inconsistent pairwise estimates via weighted functional least-squares averaging over the image plane, and finally refine globally with a robust Sampson loss.
Key results
- On ScanNet++, PRaDA achieves mean focal-adjusted reprojection error of 0.6 px versus 2.0 px for COLMAP and 1.8 px for GLOMAP (SIFT matches).
- On KITTI-360 camera 2, PRaDA mean error is 5.3 px versus 26.0 px for COLMAP and 18.4 px for GLOMAP.
- Initializing GLOMAP with PRaDA reduces sparse ScanNet++ mean rotation error from 28.99 deg to 4.51 deg.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PRaDA instead of DroidCalib | Radial distortion calibration · ScanNet++ | FA-RE mean (pixels): 1.2 -> 0.6 | Helped |
| Use PRaDA instead of GLOMAP | Radial distortion calibration · ETH3D (cam 4) | FA-RE mean (pixels): 18.4 -> 5.3 | Helped |
| Use PRaDA instead of DeepCalib | Radial distortion calibration · ETH3D (cam 5) | FA-RE mean (pixels): 18.2 -> 14.4 | Helped |
| Use PRaDA instead of DroidCalib | Radial distortion calibration · KITTI-360 (cam 2) | FA-RE mean (pixels): 102.2 -> 44.8 | Helped |
| Use PRaDA instead of COLMAP | Radial distortion calibration · KITTI-360 (cam 3) | FA-RE mean (pixels): 112.4 -> 50.2 | Helped |
| Use PRaDA instead of DeepCalib | Radial distortion calibration · WoodScape FV | FA-RE mean (pixels): 9.7 -> 51.2 | Hurt |
| Use PRaDA instead of DeepCalib | Radial distortion calibration · WoodScape RV | FA-RE mean (pixels): 14.5 -> 22.2 | Hurt |
| Use PRaDA instead of DeepCalib | Radial distortion calibration · WoodScape MVR | FA-RE mean (pixels): 14.5 -> 7.7 | Helped |
| Use PRaDA instead of DeepCalib | Radial distortion calibration · WoodScape MVL | FA-RE mean (pixels): 21.5 -> 9.4 | Helped |
| Initialize GLOMAP with PRaDA | GLOMAP · Sparse ScanNet++ test | Relative rotation error (mean, deg): 28.99 -> 4.51 | Helped |
| Initialize GLOMAP with PRaDA | GLOMAP · Sparse ScanNet++ test | Relative translation error (mean, deg): 27.39 -> 8.70 | Helped |
| Increase the number of frames used by PRaDA | PRaDA on WoodScape · WoodScape | FA-RE mean (pixels) | No clear effect |
Surprising findings
- Learning-based GeoCalib and DeepCalib yield much larger errors than SfM baselines on WoodScape forward/backward cameras, where PRaDA also degrades due to the degenerate case of distortion center near epipole.
Limitations
- Assumes radially symmetric distortion, so cannot reach subpixel error on non-radial ground-truth models such as ETH3D and KITTI-360.
- Depends on matcher quality and predefined RANSAC/inlier thresholds; Levenberg-Marquardt assumes Gaussian errors.
- Degenerate when the distortion center coincides with the epipole, e.g. cameras pointing forward or backward in WoodScape.
Experimental setup
Datasets: ETH3D KITTI-360 ScanNet++ WoodScape
Benchmarks: ETH3D KITTI-360 ScanNet++ WoodScape
Metrics: focal-adjusted reprojection error relative pose angular error
Baselines: COLMAP GLOMAP DroidCalib GeoCalib DeepCalib
Builds on: GLOMAP F10 minimal solver division camera model COLMAP LoFTR
Closest papers by meaning
- Camera Resection from Known Line Pencils and a Radially Distorted Scanline (CVPR 2025 · similarity 0.84)
- AnyMap: Learning a General Camera Model for Structure-from-Motion with Unknown Distortion in Dynamic Scenes (CVPR 2025 · similarity 0.84)
- Practical Solutions to the Relative Pose of Three Calibrated Cameras (CVPR 2025 · similarity 0.83)
- Minimal Perspective Autocalibration (CVPR 2024 · similarity 0.83)
- MaDCoW: Marginal Distortion Correction for Wide-Angle Photography with Arbitrary Objects (CVPR 2025 · similarity 0.82)
- Unbiased Estimator for Distorted Conics in Camera Calibration (CVPR 2024 · similarity 0.82)
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