The extended horopter: Quantifying retinal correspondence across changes of 3D eye position
Bibliographic record
Abstract
The theoretical horopter is an interesting qualitative tool for conceptualizing binocular correspondence, but its quantitative applications have been limited because they have ignored ocular kinematics and vertical binocular sensory fusion. Here we extend the mathematical definition of the horopter to a full surface over visual space, and we use this extended horopter to quantify binocular alignment and visualize its dependence on eye position. We reproduce the deformation of the theoretical horopter into a spiral shape in tertiary gaze as first described by Helmholtz (1867). We also describe a new effect of ocular torsion, where the Vieth-Müller circle rotates out of the visual plane for symmetric vergence conditions in elevated or depressed gaze. We demonstrate how these deformations are reduced or abolished when the eyes follow the modification of Listing's law during convergence called L2, which enlarges the extended horopter and keeps its location and shape constant across gaze directions.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".