Summation of contrast across the visual field: a common “fourth root” rule holds from the fovea to the periphery

Increasing the area of a grating stimulus tends to reduce the contrast at which it can be detected. We can use the relationship between stimulus area and this “threshold” contrast to study the detection process. Contrast signals combine linearly over short distances, as if summed within the receptive fields that define the inputs to early visual neurons. Beyond this range, the effects of area summation decrease. We set out to find whether the relationship between stimulus area and threshold is the same across the visual field. We measured thresholds for detecting “tiger tail” strips of grating (that grow orthogonal to the major axis of those presumed early receptive fields) in the fovea, parafovea (3 deg), and periphery (10.5 deg). The interpretation of previous studies taking similar approaches has been complicated by the variation in local contrast sensitivity across the visual field. In our study, we have mapped a detailed “Witch Hat” attenuation surface of this inhomogeneity for our three participants. We used this both in our model to account for the results, as well as to generate “compensated” stimuli that are equally detectable at each location within the stimulus extent. Our results follow a common fourth root summation rule in the fovea, parafovea, and periphery. Our “noisy energy” model predicts this behaviour through a combination of: i) the Witch Hat surface, ii) linear filtering by receptive fields that mimic those of V1 simple cells, iii) square-law contrast transduction, and iv) the application of an internal template that devotes the participant’s attention to the extent of the stimulus. Fitting this model with one global sensitivity parameter (per participant) accounts for the foveal and parafoveal data (56 thresholds), with one further parameter allowing us to also model the periphery (84 thresholds).