likely violated if $\mathrm{Var} (L_2(p_1,p^+_2))$ and $\mathrm{Var} (L_2(p_1,p^-_2))$ are large compared to the learned gap. Only with $L_t$ it is possible to force the network to keep the variance small compared to the gap. With $L_g$ it is only possible to control the gap but not the variance, while $l_h$ keeps the variance small but cannot limit the gap.

#### Matching Robustness plots

Some loss functions perform worse than others although they have a larger matching robustness $r$. This mostly can be explained by the fact that they perform poorly for large displacements (as shown in Figure \[losses\] (b)). Here, correct matches are usually more important as missing matches lead lo larger endpoint errors. An averaged $r$ over all pixels does not consider this.

Figure \[losses\] also shows the effect of parameter $t$ in $L_t$. Up to $ t\approx0.3$, all distances and flow displacements are improved, while small distances and displacements benefit more and up to a larger $t\approx0.4$. The improvement happens as unnecessary destructive training is avoided (see Section \[s31\]). Patches with small distances benefit more form larger $t$, likely as the *real gap* $ g_{real} = |L_2(p_1,p^-_2) - L_2(p_1,p^+_2)|$ is smaller here (as $p^-_2$ and $p^+_2$ are very 