5 - Propagation de l'incertitude dimensionnelle dans le problème de l'ajustement d'ellipses. Application à la reconnaissance automatique de formes elliptiques dans les images
Bibliographic record
Abstract
The conic fitting from image points is a very old topic in estimation and pattern recognition. This problem gave rise to a lot of studies and arouses interests still today. Systematically, these works have been based on the algebraic representation of the conic to establish the optimization criteria. Less studied, the polar representation of the ellipse is costlier because it needs the optimization of the parametrization. Yet, we propose in this paper some new ideas about this question. First, we show that the estimation of the parameters and the parametrization separated permit to make the problem easier leading to a direct inversion and the search of the roots of a four degree polynomial respectively. We also show that the parametrization carries the dimensional characteristics of the ellipse and when it is correctly disrupted in the minimization process, we constraint the ellipse search space. This new result gives an estimate without dimensional bias in a noised and incomplete context. A confidence envelope is then estimated to direct the search for continuations of the ellipse. At last, we propose a hierarchical grouping and fitting stage following with a fuzzy decision step to detect automatically the elliptic shapes in the 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 | 0.004 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".