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Ipek Oruc, Michael S. Landy, Denis G. Pelli; Noise masking reveals channels for second-order letters. Journal of Vision 2005;5(8):183. doi: https://doi.org/10.1167/5.8.183.
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We used critical-band masking to characterize channels mediating 2nd-order letter identification.
METHODS: Stimuli were noisy 2nd-order letters (Sloan font: D, N, R, S or Z). Stimulus contrast was (Mv)0.5Sv+(Mh)0.5Sh, where Sv and Sh are carrier patterns (4 c/deg horizontal and vertical sine wave gratings, random phase). Modulator Mv=0.5+kL+N, where L is a letter, k is 2nd-order contrast, and N is a low- or high-pass noise mask. Mv is clipped at 0 and 1. Mh = 1-Mv. Thus, letters are regions with increased vertical energy on a plaid background. The 2nd-order noise adds patches of increased horizontal or vertical energy that mask the letter. The square root in the definition of stimulus contrast ensures that expected contrast energy is constant across the stimulus. Interleaved staircases controlled 2nd-order contrast k. This results in a plot of identification threshold elevation (relative to no noise) as a function of noise cut-off frequency. The derivative of this curve provides an estimate of channel tuning.
RESULTS: Observers used an approx. 1–1.5-octave-wide channel for this task. The preferred spatial frequency of this channel (in cycles/letter) was fixed across noise conditions (indicating the inability of observers to switch channels to improve signal-to-noise ratio) and across different letter sizes (indicating scale invariance), for a fixed carrier frequency (again in cycles/letter). The channel's preferred spatial frequency was proportional to stimulus carrier frequency (when both are given as cycles/letter). We define a stroke frequency for 2nd-order letters (identical to the carrier frequency in c/deg) and use a previous definition of stroke frequency for 1st-order letters (Majaj et al., Vis. Res., 42, 1165–1184, 2002). With these definitions, the preferred spatial frequency of the letter identification channel is proportional to stroke frequency for 2nd-order letters, and is lower in frequency than the channels used for 1st-order letter identification.
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