Fourth-root summation of contrast over area:no end in sight when spatially inhomogeneous sensitivity is compensated by a witch's hat

Baldwin, Alex S. and Meese, Tim S. (2015). Fourth-root summation of contrast over area:no end in sight when spatially inhomogeneous sensitivity is compensated by a witch's hat. Journal of Vision, 15 (15), pp. 1-12.

Abstract

Measurements of area summation for luminance-modulated stimuli are typically confounded by variations in sensitivity across the retina. Recently we conducted a detailed analysis of sensitivity across the visual field (Baldwin et al, 2012) and found it to be well-described by a bilinear “witch’s hat” function: sensitivity declines rapidly over the first 8 cycles or so, more gently thereafter. Here we multiplied luminance-modulated stimuli (4 c/deg gratings and “Swiss cheeses”) by the inverse of the witch’s hat function to compensate for the inhomogeneity. This revealed summation functions that were straight lines (on double log axes) with a slope of -1/4 extending to ≥33 cycles, demonstrating fourth-root summation of contrast over a wider area than has previously been reported for the central retina. Fourth-root summation is typically attributed to probability summation, but recent studies have rejected that interpretation in favour of a noisy energy model that performs local square-law transduction of the signal, adds noise at each location of the target and then sums over signal area. Modelling shows our results to be consistent with a wide field application of such a contrast integrator. We reject a probability summation model, a quadratic model and a matched template model of our results under the assumptions of signal detection theory. We also reject the high threshold theory of contrast detection under the assumption of probability summation over area.

Publication DOI: https://doi.org/10.1167/15.15.4
Dataset DOI: https://doi.org/10.17036/8733940b-83e9-4cbc-a4b6-9ba0f80e90d8
Divisions: Life & Health Sciences > Psychology
Life & Health Sciences > Optometry
Life & Health Sciences
Life & Health Sciences > Neurosciences research group
Related URLs:
Additional Information: Funding: EPSRC (EP/H000038/1). The raw data for the experiments reported here can be found at the following doi: http://dx.doi.org/10.17036/8733940b-83e9-4cbc-a4b6-9ba0f80e90d8
Uncontrolled Keywords: visual perception,retinal inhomogeneity,contrast detection,spatial vision,spatial summation,area summation,psychophysics,fourth-root summation,Ophthalmology,Sensory Systems
Published Date: 2015-11

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