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


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.

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Divisions: College of Health & Life Sciences > School of Optometry
College of Health & Life Sciences > Clinical and Systems Neuroscience
College of Health & Life Sciences
College of Health & Life Sciences > Vision, Hearing and Language
College of Health & Life Sciences > Centre for Vision and Hearing Research
Additional Information: © 2015 ARVO Funding: EPSRC (EP/H000038/1). The raw data for the experiments reported here can be found at the following doi:
Uncontrolled Keywords: visual perception,retinal inhomogeneity,contrast detection,spatial vision,spatial summation,area summation,psychophysics,fourth-root summation,Ophthalmology,Sensory Systems
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2015-11-01
Accepted Date: 2015-01-01
Authors: Baldwin, Alex S.
Meese, Tim S. (ORCID Profile 0000-0003-3744-4679)



Version: Published Version

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