Lens distortion calibration by explicit straight-line to distorted-line geometric mapping
Bibliographic record
Abstract
Medium and wide-angle off-shelf cameras are often used in computer-vision applications despite their large lens distortion. Algorithms to correct for radial and tangential distortion are available; however, they often use non-linear optimization search methods that rely on carefully chosen starting points. This paper presents a method to correct for both radial symmetric lens distortion and decentering lens distortion using an iterative geometric approach to find the distortion center, and a closed-form solution for all other distortion parameters. The method is based on deriving an equivalent radial symmetric distortion model that accounts for both radial and tangential distortion. The technique uses the simple geometric relationship between a straight line and its distorted counterpart under this distortion model. The distortion calibration involves firstly determining the axis of symmetry of several distorted lines. The intersection of these axes is then computed and considered as the point of best radial symmetry (PBRS). The inclinations of the axes of symmetry of the distorted lines are then used in a closed-form solution to determine the distortion coefficients. One advantage of this approach is that higher-order coefficients can be included as needed, with their computation still achieved in closed form. The simplicity of the lens distortion calibration technique has been demonstrated in a simulation using synthetic images.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".