Code and data availability

For each observer, the proportion comparison chosen data for the 18 experimental blocks as well as the thresholds are provided as Supplementary Information (SI). The SI also provides the MATLAB scripts to generate Figures 2, 4, 5, 6, and 7 and the scripts to obtain thresholds of the linear receptive field formulation of the model (model described below). The computed retinal images used as input to the model are provided as .mat files in a zip folder. The SI is available at: https://github.com/vijaysoophie/EquivalentNoisePaper.

Psychometric functions for observer 2. We measured the proportion comparison chosen data at six values of the covariance scalar (σ²), separately in three blocks for each observer. The data for each block was fit with a cumulative normal to obtain the discrimination threshold (see Figure 2). Each panel plots the measured values and the cumulative fit to the proportion comparison data for each of the three blocks, for observer 2. The values in the legend provide the estimate of lightness discrimination threshold for each block obtained from the cumulative fit. See Supplementary Figure S3 for the psychometric functions of all observers.

Background variation increases lightness discrimination threshold. Mean (N = 4) log squared threshold versus log covariance scalar from the human psychophysics (red circles). The error bars represent +/− 1 SEM taken between observers. The fit of the STD formulation of the model (Equation 4) is shown as the red curve. The parameters corresponding to this fit are provided in the legend. The threshold of the fit linear receptive field (LINRF) formulation was estimated by simulation at 10 logarithmically spaced values of the covariance scalar (black squares). The black smooth curve is a smooth fit to these points of the functional form log10T2=a+b(x+c)d where x = log ₁₀σ² and a, b, c and d are parameters adjusted in the fit. This functional form was chosen simply to provide a smooth curve through the simulated thresholds and has no theoretical significance. The parameters of the LINRF fit are also provided in the legend.

Threshold of individual human observers. Mean (across sessions) squared threshold versus log covariance scalar for individual human observers. Same format as Figure 5; here, the error bars represent +/− 1 SEM taken across the three blocks for each observer. The parameters of the SDT and LINRF formulations were obtained separately for each observer and are provided in the legend, in order σi2,σe02.

Equivalent noise analysis. (a) The left panel shows the parameter estimates for the two model formulations for the mean data and each individual observer. From these, we can estimate the equivalent noise level (σ_enl) for background object reflectance variation corresponding to the full model of natural reflectance variation (covariance scalar σ² = 1). (b) The equivalent noise level is provided for the mean data and each individual observer in the right panel.