Abstract
Threshold contrasts were determined for complex gratings made from pairs of sine-wave gratings with various spatial frequencies and contrast ratios. It was found that the plots representing the relationship between the contrast of two-component gratings with frequencies f 1=2.0 deg−1 and f 2=kf 1, (1.03 ⩽ k ⩽ 3.0), when the compound was at threshold (the so-called contrast threshold curves), tend to have either an elliptical (for k ⩽ 1.5) or a rectangular (for k=3) form. Nevertheless, the elliptical fits as the matched-channel model predicted, and the roundedly rectangular fits, as the probability-summation models predicted, were very poor. Furthermore, statistical analysis shows that two of the six contrast threshold curves exhibiting a significant local disturbance fail to be convex.Theoretical treatment in terms of convex analysis shows that such a convexity violation of the contrast threshold curves rules out the possibility of detection being produced by a single linear channel as well as a parallel array of linear channels, either with or without probability summation, provided that the detection principle of the most sensitive channel is adopted. The adaptive matched-channel model originally proposed by Hauske cannot also account for the results obtained; however, it can be modified to be in line with them. We hypothesise that the detection in our experiment is likely to occur by means of several (no more than seven or eight) adaptive partially matched channels.
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Logvinenko, A.D. Lack of convexity of threshold curves for compound grating: implications for modelling visual pattern detection. Biol. Cybern. 70, 55–64 (1993). https://doi.org/10.1007/BF00202566
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DOI: https://doi.org/10.1007/BF00202566