The Bouma law accounts for crowding in fifty observers

Abstract

Abstract Crowding is the failure to recognize an object due to surrounding clutter. Our visual crowding survey measured 13 crowding distances (or “critical spacings”) twice in each of 50 observers. The survey included three eccentricities (0, 5, and 10 deg), four cardinal meridians, two orientations (radial and tangential), and two fonts (Sloan and Pelli). The survey also tested foveal acuity, twice. Remarkably, fitting a two-parameter model, the well- known Bouma law — crowding distance grows linearly with eccentricity — explains 82% of the variance for all 13 × 50 measured log crowding distances, cross-validated. An enhanced Bouma law, with factors for meridian, crowding orientation, target kind, and observer, explains 94% of the variance, again cross-validated. These additional factors reveal several asymmetries, consistent with previous reports, which can be expressed as crowding- distance ratios: 0.62 horizontal:vertical, 0.79 lower:upper, 0.78 right:left, 0.55 tangential:radial, and 0.78 Sloan font:Pelli font. Across our observers, peripheral crowding is independent of foveal crowding and acuity. Evaluation of the Bouma factor b (the slope of the Bouma law) as a biomarker of visual health would be easier if there were a way to compare results across crowding studies that use different methods. We define a standardized Bouma factor b’ that corrects for differences from Bouma’s 25 choice alternatives, 75% threshold criterion, and linearly symmetric flanker placement. For radial crowding on the right meridian, the standardized Bouma factor b’ is 0.24 for this study, 0.35 for Bouma (1970), and 0.30 for the geometric mean across five representative modern studies, including this one, showing good agreement across labs, including Bouma’s. We found that guaranteeing fixation by gaze-contingent display halved the standard deviation across observers of the estimated log b . The reduction in standard deviation is explained by a “peeking” model in which the observer looked near an anticipated target location in 50% of unmonitored -fixation trials. Individual differences are robust, as evidenced by the much larger 0.08 SD of log b across observers than the 0.03 SD of test-retest within observers. Crowding’s ease of measurement enhances its promise as a biomarker for dyslexia and visual health.