Figure 6. Robustness of results and effects of symmetry transformations.

(A) The difference between the natural logarithms of the measured and predicted thresholds (red crosses and blue dots, respectively, in Figures 4C and 5) is approximately independent of the downsampling ratio ${\displaystyle N}$ and patch size ${\displaystyle R}$ used in preprocessing. The labels on the x-axis are in the format $N\times R$, with the violin plot and label in blue representing the analysis that we focused on in the rest of the paper. Each violin plot in the figure shows a kernel density estimate for the distribution of prediction errors for the 311 second-order single- and mixed-plane threshold measurements available in the psychophysics. The boxes show the 25th and 75th percentiles, and the lines indicate the medians. (B) Change in the natural logarithms of predicted (blue) or measured (red) thresholds following a symmetry transformation. Symmetry transformations that leave the natural image predictions unchanged also leave the psychophysical measurements unchanged. (See text for the special case of the exch(B,W) transformation.) The visualization style is the same as in panel A, except boxes and medians are not shown. The transformations starting with exch correspond to exchanges between gray levels; e.g., exch(B,W) exchanges black and white. lrFlip and udFlip are left-right and up-down geometric flips, respectively, while rot90 and rot180 are geometric rotations by the respective number of degrees (clockwise).