  Previously, in (Hermundstad et al., 2014), we showed that when sampling is
limiting, the efficient coding principle leads to a "variance is salience"
hypothesis, and that this hypothesis accounts for visual sensitivity to binary
image statistics. Here, using extensive new psychophysical data and image
analysis, we show that this hypothesis accounts for visual sensitivity to a
large set of grayscale image statistics at a striking level of detail, and also
identify the limits of the prediction. We define a 66-dimensional space of
local grayscale light-intensity correlations, and measure the relevance of each
direction to natural scenes. The "variance is salience" hypothesis predicts
that two-point correlations are most salient, and predicts their relative
salience. We tested these predictions in a texture-segregation task using
un-natural, synthetic textures. As predicted, correlations beyond second order
are not salient, and predicted thresholds for over 300 second-order
correlations match psychophysical thresholds closely (median fractional error
<0.13).
