The Bouma law of crowding, revised: Critical spacing is equal across parts, not objects
Bibliographic record
Abstract
Crowding is the inability to identify an object among flankers in the periphery. It is due to inappropriate incorporation of features from flanking objects in perception of the target. Crowding is characterized by measuring critical spacing, the minimum distance needed between a target and flankers to allow recognition. The existing Bouma law states that, at a given point and direction in the visual field, critical spacing, measured from the center of a target object to the center of a similar flanking object, is the same for all objects (Pelli & Tillman, 2008). Because flipping an object about its center preserves its center-to-center spacing to other objects, according to the Bouma law, crowding should be unaffected. However, because crowding is a result of feature combination, the location of features within an object might matter. In a series of experiments, we find that critical spacing is affected by the location of features within the flanker. For some flankers, a flip greatly reduces crowding even though it maintains target-flanker spacing and similarity. Our results suggest that the existing Bouma law applies to simple one-part objects, such as a single roman letter or a Gabor patch. Many objects consist of multiple parts; for example, a word is composed of multiple letters that crowd each other. To cope with such complex objects, we revise the Bouma law to say that critical spacing is equal across parts, rather than objects. This accounts for old and new findings.
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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 | 0.007 | 0.053 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.011 |
| Scholarly communication | 0.005 | 0.014 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.009 | 0.003 |
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".