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N. Toyofuku, S. A. Klein, T. Carney; First plus third harmonic summation in noise: Classification templates. Journal of Vision 2001;1(3):445. doi: 10.1167/1.3.445.
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© 2016 Association for Research in Vision and Ophthalmology.
Background. Graham & Nachmias (1971) found minimal subthreshold summation of 1st plus 3rd harmonic sine wave gratings, strongly supporting a multiple channel model against an ideal observer template (single channel) model. However, there is mounting evidence that in the suprathreshold regime the template model does a better job. We performed the Graham & Nachmias experiment in the presence of noise to discriminate between the two models and reconstruct possible templates used by observers. Methods. The noise was the sum of 1st through 8th harmonic gratings. The contrast of each harmonic had a 5% Gaussian standard deviation in both sine and cosine phases. Four cosine test patterns were used with harmonics of: 2nd, 6th, 2nd plus 6th and 2nd minus 6th. Both brief (0.2 and 0.75 sec) and long (1.5 and 2.0 sec) presentation durations were used to manipulate scrutiny. We used the method of constant stimuli with 4 test contrasts and 4 responses. A classification template was obtained by linear regressing the responses on the saved cosine noise amplitudes. Thresholds were also compared trial by trial to an ideal observer. Results. With short duration presentations observers had close to zero summation. With long duration and the 2nd plus 6th pattern, both observers had substantial summation, compatible with ideal observer energy summation. For the 2nd minus 6th pattern neither observer was able to construct an efficient template and minimal summation was found. The classification images indicated approximately one-octave bandwidths. One observer had a strong negative 4th harmonic for the 2nd plus 6th harmonic template. Discussion. With long durations that allow for scrutiny some templates can be formed efficiently (peaks add but not peaks subtract) improving results beyond that of multiple channel prediction. The classification images can reveal the templates being used. Template construction may be a common strategy in repetitive focused tasks that allow for scrutiny.
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