A reevaluation of area summation of contrast with compensation for retinal inhomogeneity

Increasing the area of a luminance-modulated sine wave grating decreases its contrast detection threshold. The process by which individual samples from discrete locations in the visual field are combined to achieve this is investigated here by analytic modeling. Several combinations and orders of transduction, template, and summation type were considered. Predictions from these models were compared to spatial summation results measured for two different stimulus types. The first was a set of circular sine-wave gratings (4 c deg -1) of various diameters, including a subset of “Swiss cheese” gratings that were modulated by a raised plaid to halve their total contrast over area (Meese and Summers, 2007 Proceedings of the Royal Society B 274 2891–2900). The second set of stimuli were rectangular grating patches presented both in the fovea and in the periphery replicating Robson and Graham (1981 Vision Research 21 409–18). In other conditions, these stimuli were multiplied by an attenuation surface that compensated for the confounding loss of contrast sensitivity with retinal eccentricity. Our analyses reveal that the full wealth of our results can be described by a single model. This involves spatial filtering, square-law transduction and linear summation of signal and internal noise within a template matched to stimulus extent.