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Chien-Chung Chen, Yu-Hsin Cynthia Yeh, Christopher W. Tyler; Length summation in noise. Journal of Vision 2019;19(9):11. doi: 10.1167/19.9.11.
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To investigate the effect of background noise on visual summation, we measured the contrast detection thresholds for targets with or without a white noise mask in luminance contrast. The targets were Gabor patterns placed at 3° eccentricity to either the left or right of the fixation and elongated along an arc of the same radius to ensure equidistance from fixation for every point along the long axis. The task was a spatial two-alternative forced-choice (2AFC) paradigm in which the observer had to indicate whether the target was on the left or the right of the fixation. The threshold was measured at 75% accuracy with a staircase procedure. The detection threshold decreased with target length with slope −1/2 on log-log coordinates for target lengths between 30′ and 300′ half-height full-width (HHFW), defining a range of ideal matched-filter summation extending up to about 200′ (or about 16× the center width of the Gabor targets). The summation curves for different noise contrasts were shifted copies of each other. For the threshold versus mask contrast (TvN) functions, the target threshold was constant for noise levels up to about −22 dB, then increased with noise contrast to a linear asymptote on log-log coordinates. Since the “elbow” of the target threshold versus noise function is an index of the level of the equivalent noise experienced by the visual system during target detection, our results suggest that the signal-to-noise ratio was invariant with target length. We further show that a linear-nonlinear-linear gain-control model can fully account for these results with far fewer parameters than a matched-filter model.
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