Reflection density in photographic color prints : Generalizations of the Williams-Clapper transform
Bibliographic record
Abstract
We present two generalizations of the Williams–Clapper transform for converting between transmission and reflection densities of a color print. The first generalization allows for arbitrary incident angle, viewing angle, and index of refraction. The second generalization is to the geometry of an integrating sphere with the specular reflection either included or excluded. Our derivation also clarifies a potential source of confusion: Williams and Clapper had noted that, because of the cancellation of two factors, a reflection print with a perfectly transmitting gelatin layer (and a base of perfect reflectance) has the same brightness as it would have in the absence of the gelatin layer. We find that this cancellation is in fact only approximate. The approximate nature of the cancellation was not readily apparent because of the fortuitous closeness of the cancellation for the particular geometry and indices of refraction considered by Williams and Clapper. We also discuss efficient numerical implementation of the transform and outline an example of an application.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.004 |
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".