Calibration of Cameras with Radially Symmetric Distortion
Bibliographic record
Abstract
We present algorithms for plane-based calibration of general radially distorted cameras. By this, we understand cameras that have a distortion center and an optical axis such that the projection rays of pixels lying on a circle centered on the distortion center form a right viewing cone centered on the optical axis. The camera is said to have a single viewpoint (SVP) if all such viewing cones have the same apex (the optical center); otherwise, we speak of NSVP cases. This model encompasses the classical radial distortion model [5], fisheyes, and most central or noncentral catadioptric cameras. Calibration consists in the estimation of the distortion center, the opening angles of all viewing cones, and their optical centers. We present two approaches of computing a full calibration from dense correspondences of a single or multiple planes with known euclidean structure. The first one is based on a geometric constraint linking viewing cones and their intersections with the calibration plane (conic sections). The second approach is a homography-based method. Experiments using simulated and a broad variety of real cameras show great stability. Furthermore, we provide a comparison with Hartley-Kang's algorithm [12], which, however, cannot handle such a broad variety of camera configurations, showing similar performance.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".