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Michael Morgan, Isabelle Mareschal, Joshua Solomon; Sampling Efficiencies for Spatial Regularity. Journal of Vision 2010;10(7):1362. doi: https://doi.org/10.1167/10.7.1362.
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Observers performed a 2AFC (temporal) discrimination in which they had to decide which of two arrays of dots had the greater amount of spatial regularity in their spacing. The 11 dots in each array were arranged on a notional circle of radius R, centred on the fixation point. The actual eccentricity of each dot in the array was sampled independently from a uniform distribution over the interval [R-P-C(x), R+P+C(x)], where P was a pedestal common to both arrays, C(ref) was zero for the “reference” array, and C(test) was determined on each trial by a QUEST staircase designed to converge on the 84% correct discrimination point. Two-dimensional perturbations of dot positions on an a 11 x 11 rectangular grid were also investigated. As in a previously reported study of orientation variance [Morgan et al, 2008], data formed a ‘dipper’ function, having a minimum (best discrimination) at a non-zero pedestal value, and were well fit by a two-parameter model, in which one parameter represents the intrinsic (in this case, positional) noise, and the other parameter represents sampling efficiency. The latter varied between 4/11 and 6/11 in different observers and conditions. Sampling efficiencies of less than 4/11 could be ruled-out with high confidence. Sampling efficiencies were lower for the rectangular arrays ∼ (8/121), suggesting a limit on the absolute number of samples. Adding a second source of variance, by randomising the contrast polarity of the dots, which the observer was instructed to ignore, made performance worse by increasing intrinisic noise, with little if any effect on sampling efficiency. The same was true of adding irrelevant tangential perturbations in dot position. We conclude that there is some degree of obligatory confusion between different sources of variance, as in previous studies of colour camouflage [Morgan et al, 1992].
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