Research map / 3D vision / Depth and stereo
Camera Resection from Known Line Pencils and a Radially Distorted Scanline
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Proposes minimal and closed-form solvers (6-, 7-, and 8+-point) for absolute camera pose from a single radially distorted pixel scanline observing a planar marker of known line pencils.
Problem
Estimating the absolute 6-DOF pose of a single camera from the 1D observations of one radially distorted image scanline, where the observed marker points are collinear in the pinhole model and the pose is therefore underdetermined.
Approach
Uses a planar marker of two co-planar line pencils plus known radial distortion to undistort scanline points into a non-collinear 2D curve; recovers the pattern intersection via conic pencils and cross ratios (minimal 6-point, 7-point closed form) or via a homography (linear 8+-point solver).
Key results
- The 8+-point linear solver is robust to near-collinear configurations, while the 6-point and 7-point solvers fail when the point po lies within about 2 pixels of the degenerate conic.
- On real data, the 8+-point solver using a block of 400 rows gives 2.25 degrees orientation error and 1.30% translation error.
- Compared with the binocular solvers of [5], the proposed solvers are less numerically stable; the 7-point solver is about 31 us and the 6-point about 411 us in MATLAB.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use all observations from two scanlines instead of interleaved observations | 8+-point solver · Real data, two scanlines 400 rows apart | orientation error: 5.60 degrees -> 3.49 degrees | Helped |
| Use all observations from two scanlines instead of interleaved observations | 8+-point solver · Real data, two scanlines 400 rows apart | translation error: 3.46% -> 2.06% | Helped |
| Use observations from a 400-row block instead of the two scanlines | 8+-point solver · Real data, 400-row block | orientation error: 3.49 degrees -> 2.25 degrees | Helped |
| Use observations from a 400-row block instead of the two scanlines | 8+-point solver · Real data, 400-row block | translation error: 2.06% -> 1.30% | Helped |
| Add Gaussian noise with σ = 0.5 pixels to scanline observations | 6-point, 7-point, and 8+-point solvers · Synthetic data, dx = 128 pixels | pose estimation error | Hurt |
| Reduce the magnitude of radial distortion coefficients toward zero | 6-point, 7-point, and 8+-point solvers · Synthetic data | orientation error | Hurt |
| Use scanlines close to the center of distortion | 6-point, 7-point, and 8+-point solvers · Synthetic data, varying image row y | pose estimation error | Hurt |
| Use observations closer to the degenerate conic configuration | 6-point and 7-point solvers · Synthetic data, dc < 2 | pose estimation error | Hurt |
| Decrease the minimum separation between 1D observations | 6-point and 7-point solvers · Synthetic data | pose estimation error | Hurt |
| Increase marker viewing distance or viewing angle | 6-point and 7-point solvers · Synthetic data | pose estimation error | Hurt |
| Use 8+-point solver instead of the solvers of [5] | Camera resection from known line pencils · Synthetic data, numerical stability comparison | pose estimation error | Hurt |
| Use the 8+-point solver rather than the 6-point and 7-point solvers near collinear configurations | Camera resection from known line pencils · Synthetic data, near the center of distortion | pose estimation error | Helped |
Surprising findings
- Single-scanline solvers are less stable than the binocular scanline-pair solvers of prior work, which the authors attribute to the broader spatial context there.
- Real-data errors remain several degrees, so single-scanline solvers need scanline blocks to mitigate noise sensitivity.
Limitations
- Sensitive to pixel noise; sigma 0.5 px noticeably increases error.
- Degrades near the distortion center where observations become nearly collinear.
- Does not handle occlusions; all pattern lines must be visible in the scanline.
Experimental setup
Datasets: synthetic scanline observations generated with LI-IMX274 intrinsics real scanline captures with a LI-IMX274 camera
Benchmarks: synthetic scanline pose experiments real multi-scanline stability test
Metrics: orientation error (degrees) translation error (%) median execution time (us) number of solutions
Baselines: 10-pt solver [5] 6-pt solver [5]
Builds on: Brown distortion model Chasles theorem Dibene and Dunn binocular scanline pose [5] E3Q3 polynomial solver
Closest papers by meaning
- Efficient Solution of Point-Line Absolute Pose (CVPR 2024 · similarity 0.88)
- Practical Solutions to the Relative Pose of Three Calibrated Cameras (CVPR 2025 · similarity 0.85)
- PRaDA: Projective Radial Distortion Averaging (CVPR 2025 · similarity 0.84)
- Three-view Focal Length Recovery From Homographies (CVPR 2025 · similarity 0.84)
- Minimal Perspective Autocalibration (CVPR 2024 · similarity 0.84)
- Revisiting Sampson Approximations for Geometric Estimation Problems (CVPR 2024 · similarity 0.84)
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