Each plot shows kernel-density estimates of the distribution of log prediction errors (defined as difference between log prediction and log measurement) after splitting the data into the subgroups indicated at the top right of each plot. Individual data points are shown on the abscissa. The median log prediction error is shown for each group in the corresponding color. (A) Predictions tend to underestimate thresholds in simple planes and overestimate thresholds in mixed planes (, Kolmogorov-Smirnov (K–S) test). As a reminder, the natural-image analysis predicts thresholds only up to a multiplicative factor, which is chosen in a way that makes the mean log prediction error over all second-order thresholds be zero. (B) Predictions tend to have greater error in planes defined by modular sums (such as the simple plane or the mixed plane ) than in planes defined by modular differences (such as the simple plane or the mixed plane ) (, K-S test). However, thresholds in neither subgroup are systematically over- or under-estimated. (C) There is no significant difference in predictions in on-axis directions (directions parallel to an axis in a simple or mixed coordinate plane), vs. all other (off-axis) directions (, K-S test). (D) Thresholds are more accurately predicted for ‘2-D’ correlations than ‘1-D’ correlations. A mixed plane like involves the same pair of checks in both directions, thus leading to correlations that are in a sense 1-D. In contrast, the mixed plane involves the three checks , , and , leading to 2-D correlations. While the medians of the errors in these two subgroups are similar (KS test ; Wilcoxon rank-sum test , medians 0.042 vs. 0.004, respectively), prediction error magnitude is lower for 2-D correlations (, KS-test on absolute log errors).