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Christopher P. Taylor, Patrick J. Bennett, Allison B. Sekuler; Narrow-band channels optimally sum a broad band of spatial frequency information. Journal of Vision 2006;6(6):115. doi: https://doi.org/10.1167/6.6.115.
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© ARVO (1962-2015); The Authors (2016-present)
Previous work (Kersten, 1987) suggests that spatial frequency summation in one-dimensional noise patterns is well described by an ideal observer for stimulus bandwidths up to 6 octaves. However, classification image studies have shown that a two-octave wide channel is used to detect such patterns (Levi & Klein, 2005; Taylor et al., 2003). This leads to the puzzle - how does a narrow-band channel produce optimal summation over a broad bandwidth? Here we show that this puzzle can be resolved by assuming: i) stimuli are filtered by a channel whose frequency response approaches, but does not equal, zero; and ii) the dominant noise occurs prior to filtering. With these assumptions, a quantitative model predicts nearly ideal spatial frequency summation across a broad bandwidth. The model also predicts that components in comb-filtered broadband noise - i.e., noise in which every fourth frequency component carries information - should not be summed optimally. We tested this prediction by measuring detection thresholds for regular noise and comb-filtered noise using a 2-IFC task. Stimuli had a center-frequency of 5 cpd and a frequency bandwidth of 0.5–6 octaves. As before, detection thresholds for noise, expressed as r.m.s. contrast, increased with the quarter-root of the number of frequency components, but thresholds for comb-filtered noise increased with the square-root of the number of components. Hence, as predicted, optimal summation breaks down with comb-filtered noise. The results suggest that narrow-band channels may produce optimal summation of broadband noise patterns.
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