Constraints on quadratic curves under perspective projection
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Bibliographic record
Abstract
The authors address the problem of three-dimensional (3-D) location estimation based on quadratic-curved features. They derive the mathematical relations or constraints on the 3-D position and orientation of quadratic-curved features using the standard rotation and the standard transformation concepts introduced by K.I. Kanatani, (1988), and assuming that the true size and shape of a given quadratic feature are known a priori, with its projection image given. In this context, an analytical method is introduced for estimation of the standard rotation and determination of the shape of a quadratic-curved feature at its canonical position. It is shown that, in general, knowledge of the true shape and size of a quadratic-curved feature does not yield a sufficient number of constraints to determine the 3-D position and orientation uniquely. As a result, extra constraints must be acquired from various sources of information and fused with these constraints to obtain unique 3-D position and orientation estimates.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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 it