similar for small distances). For large displacements patches get more chaotic (due to more motion blur, occlusions etc.), which forces larger variances of the $L_2$ distances and thus a larger gap is required to counter the larger variance.

$L_g$ performs worse than $L_t$ mainly at small distances and large displacements. Likely, the larger variance is more destructive for small distances, as the *real gap* $g_{real}$ is smaller (more sensitive) here. Figure \[losses\] also shows that low-pass filtering the feature map increases the matching robustness for all distances and displacements. In our tests, a $2.25 \times$ low-pass performed the best (tested with $\pm 0.25$). Engineered SIFTFlow features can benefit from much larger low-pass filters which makes the original pipeline (Figure \[ffscales\] left) extremely efficient for them. However, using them with our pipeline (which recalculates features on different resolutions) shows that their low matching robustness is justified (see Table \[trainkitti\]). SIFTFlow also performs better in outlier filtering. Due to such effects that can so far not directly be trained, it is still challenging to beat well designed purely heuristic approaches with learning. In fact, existing CNN based approaches often still underperform purely heuristic approaches – even direct predecessors (see Section \[s43\]).

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