The common perceptual metric for human discrimination of number and density
Bibliographic record
Abstract
There is considerable interest in how humans estimate the number of objects in a scene, in the context of an extensive literature on how we estimate the density of objects (i.e. how closely spaced they are). If humans have a sense of “visual number” (as has been proposed) then it should operate independently of density perception. Here we show that it does not. We had subjects discriminate the density or numerosity of two patches that were mismatched in size and show that larger patches appear both denser and (somewhat) more numerous, and that size-mismatching elevates thresholds for discriminating number and (to a lesser degree) density. We propose that density and number are both initially encoded as the ratio of responses from a pair of filters tuned to low and high spatial frequencies, but that number-estimation requires that this measure be scaled by relative stimulus-size. This model explains the rather complex dependence of observers' accuracy and precision on patch-size variation, using a simple, biologically plausible common metric for number and density. Because this model does not have any explicit representation of “objects” it predicts that (for example) mismatching element size will drastically affect number and density discrimination, whereas contrast-mismatching will not (Tibber, Greenwood & Dakin, VSS 2011).
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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 | 0.001 | 0.013 |
| 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 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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".