Theory and data for area summation of contrast with and without uncertainty:evidence for a noisy energy model

Abstract

Contrast sensitivity improves with the area of a sine-wave grating, but why? Here we assess this phenomenon against contemporary models involving spatial summation, probability summation, uncertainty, and stochastic noise. Using a two-interval forced-choice procedure we measured contrast sensitivity for circular patches of sine-wave gratings with various diameters that were blocked or interleaved across trials to produce low and high extrinsic uncertainty, respectively. Summation curves were steep initially, becoming shallower thereafter. For the smaller stimuli, sensitivity was slightly worse for the interleaved design than for the blocked design. Neither area nor blocking affected the slope of the psychometric function. We derived model predictions for noisy mechanisms and extrinsic uncertainty that was either low or high. The contrast transducer was either linear (c1.0) or nonlinear (c2.0), and pooling was either linear or a MAX operation. There was either no intrinsic uncertainty, or it was fixed or proportional to stimulus size. Of these 10 canonical models, only the nonlinear transducer with linear pooling (the noisy energy model) described the main forms of the data for both experimental designs. We also show how a cross-correlator can be modified to fit our results and provide a contemporary presentation of the relation between summation and the slope of the psychometric function.

Publication DOI: https://doi.org/10.1167/12.11.9
Divisions: College of Health & Life Sciences > School of Optometry > Optometry
College of Health & Life Sciences > Clinical and Systems Neuroscience
College of Health & Life Sciences
College of Health & Life Sciences > School of Psychology
College of Health & Life Sciences > School of Optometry > Centre for Vision and Hearing Research
Additional Information: Creative Commons Attribution Non-Commercial No Derivatives License
Uncontrolled Keywords: summation ,energy,contrast detection,integration,area,uncertainty,theory,Ophthalmology,Sensory Systems
Publication ISSN: 1534-7362
Full Text Link:
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
http://www.jour ... 2/11/9.abstract (Publisher URL)
PURE Output Type: Article
Published Date: 2012-10-17
Authors: Meese, Tim (ORCID Profile 0000-0003-3744-4679)
Summers, Robert (ORCID Profile 0000-0003-4857-7354)

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