The Bouma law accounts for crowding in fifty observers

Abstract

Crowding is the failure to recognize an object due to surrounding clutter. Its strength varies across the visual field and individuals. To characterize the statistics of crowding—ultimately to relate psychophysics of crowding to physiology—we measured radial crowding distance and acuity of 105 observers along the four cardinal meridians of the visual field. Fitting the well-known Bouma law — crowding distance depends linearly on radial eccentricity — explains 52% of the variance in log crowding distance, cross-validated. Our enhanced Bourma model, with factors for observer, meridian, and target kind, explains 72% of the variance, again cross-validated. The meridional factors confirm previously reported asymmetries. We find a 0.62 horizontal:vertical advantage, a 0.92 lower:upper advantage, and a 0.82 right:left advantage. Crowding distance and acuity have a correlation of 0.41 at the fovea, which drops to 0.23 at ±5 deg along the horizontal midline. Acuity and crowding represent the size and spacing limits of perception. Since they are dissociated in clinical populations (Song et al., 2014; Strappini et al., 2017) and shown here to be only moderately correlated in our sample of mostly university students, clinical testing to predict real-world performance should consider measuring both. In sum, enhancing the Bouma law with terms for meridian, observer, and target kind provides an excellent fit to our 105-person survey of crowding.

Emergence of crowding: The role of contrast and orientation salience

“…However, as we did not quantify the increase in perceived contrast, it was not possible to know the extent to which conspicuity/salience increased due to the addition of color for different observers. There was also a considerable degree of individual variation in both crowded and uncrowded performance, similar to what has been previously reported ( Greenwood, Szinte, Sayim, & Cavanagh, 2017 ; Kurzawski, Burchell, Thapa, Majaj, Winawer, & Pelli, 2021 ; Petrov & Meleshkevich, 2011a ). However, although those studies report individual variability for high-contrast, suprathreshold stimuli, we observe variability at a range of contrasts that is much closer to feature-discrimination threshold.…”

“…Almost all crowding studies use suprathreshold stimuli and hence crowding should be reliably observed in all participants (e.g. Kurzawski et al 2021 ). Even with low-contrast stimuli, if the contrast is tailored to exceed each individual participant's discrimination threshold (say by setting it at a specific multiple of unflanked discrimination contrast threshold), crowding should be observed.…”

Linking individual differences in human primary visual cortex to contrast sensitivity around the visual field

“…The present group level data, and an extended dataset (n=54), showed a small bias towards more V1 surface area dedicated to the right than left horizontal meridian. It might be that a left-right horizontal meridian asymmetry relates to visual tasks in which an advantage along the right horizontal meridian exists, such as crowding [47][48][49] and letter recognition 50,51 . A larger left than right hemisphere V1 has been previously reported 4 (but see 2,28 ).…”

Characterizing the in-out asymmetry in visual crowding

“…However, IOA is stronger while crowding is weaker along the horizontal meridian than along the vertical (HVA). Further, the strongest asymmetry observed in crowding is the HVA ( Kurzawski et al, 2021 ), which is the one that shows the reversal in asymmetry for IOA. This suggests that asymmetries in IOA are not simply inherited from crowding asymmetries.…”

“…Crowding is known to be worse in the upper than in the lower visual field (VA; Intriligator & Cavanagh, 2001 ) and worse along the vertical meridian than along the horizontal meridian (HVA; Greenwood et al, 2017 ). Crowding is also worse in the left visual field than in the right visual field (HA; Greenwood et al, 2017 ; Kurzawski, Burchall, Thapa, Majaj, Winawer, & Pelli, 2021 ). At first glance, it might appear that the asymmetries in IOA are simply inherited from already prevalent asymmetries in crowding.…”