from a distance between $p^+_2$ and $p^-_2$ of 9 pixels, CNN based features created on a 2x down-sampled image match more robustly than CNN based features created on the full image resolution. This is insufficient as the random search distance on scale 2 is only $2R = 4$ pixels. Thus, we use it for scale 3 (with random search distance $4R = 8 \approx 9$ pixels).

One can argue that by training the CNN with more close-by samples $N_{close}(p^+_2)$ more accuracy could be gained. But raising extremely the amount of close-by samples only reduces the accuracy threshold from 9 to 8 pixels. Using a CNN with smaller 32x32 patches instead of 56x56 patches does not raise the accuracy either– it even clearly decreases it. Figure \[scales\] (b) shows that downsampling decreases the matching robustness error significantly for larger distances. In fact, for a distance above 170 pixels, the relative error of *4x downsampling* is reduced by nearly 100% compared to *No downsampling* – which is remarkable.

[|C[1.95 cm]{}|C[1.1 cm]{}|C[1.2 cm]{}|C[1.1 cm]{}|C[1.1 cm]{}|C[1.2 cm]{}|C[1.2 cm]{}|C[1.2 cm]{}|C[1.2 cm]{}|]{} Approach/ Loss &EPE $>$3 px noc. & EPE $>$3 px all & EPE noc. & EPE all & robust- ness $r$\
$L_h$ & 7.26% 