Investigation of the Cross-Ratios Method for Point-of-Gaze Estimation
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The cross-ratios method for point-of-gaze (PoG) estimation uses the invariance property of cross-ratios in projective transformations. The inherent causes of the subject-dependent PoG estimation bias exhibited by this method have not been well characterized in the literature. Using a model of the eye and the components of a system (camera, light sources) that estimates PoG, a theoretical framework for the cross-ratios method is developed. The analysis of the cross-ratios method within this framework shows that the subject-dependent estimation bias is caused mainly by: 1) the angular deviation of the visual axis from the optic axis and 2) the fact that the virtual image of the pupil center is not coplanar with the virtual images of the light sources that illuminate the eye (corneal reflections). The theoretical framework provides a closed-form analytical expression that predicts the estimation bias as a function of subject-specific eye parameters. The theoretical framework also provides a clear physical interpretation for an existing empirically derived two-step procedure that compensates for the estimation bias and shows that the first step of this procedure is equivalent to moving the corneal reflections to a new plane that minimizes the distance from this plane to the virtual image of the pupil center.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.000 | 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