The Bouma law accounts for crowding in 50 observers

Jan W. Kurzawski, Augustin Burchell, Darshan Thapa, Jonathan Winawer, Najib J. Majaj, Denis G. Pelli

Research output: Contribution to journalArticlepeer-review


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 includes 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, where 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. Simulations, confirmed by data, show that peeking can skew estimates of crowding (e.g., greatly decreasing the mean or doubling the SD of log b). Using gaze tracking to prevent peeking, individual differences are robust, as evidenced by the much larger 0.08 SD of log b across observers than the mere 0.03 test–retest SD of log b measured in half an hour. The ease of measurement of crowding enhances its promise as a biomarker for dyslexia and visual health.

Original languageEnglish (US)
Article number6
JournalJournal of vision
Issue number8
StatePublished - 2023


  • asymmetries around the visual field
  • bouma’s law
  • critical spacing
  • crowding
  • crowding distance
  • object recognition
  • statistics of crowding

ASJC Scopus subject areas

  • Ophthalmology
  • Sensory Systems


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