between 0.004 and 0.0004 that decreases linearly in exponential space after each batch i.e. $learnRate (t) = e^{-x_t} \rightarrow learnRate (t+1) = e^{-(x_t+\epsilon)}$.

![image](img/lowpass6new.pdf){width="0.99\linewidth"}

Multi-scale matching
--------------------

The *Flow Fields* approach [@bailer2015flow], which we use as basis for our optical flow pipeline compares patches at different scales using scale spaces [@lindeberg1994scale], i.e. all scales have the full image resolution. It creates feature maps for different scales by low-pass filtering the feature map of the highest scale (Figure  \[ffscales\] left). For SIFTFlow [@liu2008sift] features used in [@bailer2015flow], low-pass filtering features (i.e. feature $\rightarrow$ low-pass = feature $\rightarrow$ downsample $\rightarrow$ upsample) performs better than recalculating features for each scale on a different resolution (i.e. downsample $\rightarrow$ feature $\rightarrow$ upsample).

We observed the same effect for CNN based features – even if the CNN is also trained on the lower resolutions. However, with our modifications shown in Figure \[ffscales\] right (that are further motivated in Section \[eval\]), it is possible to obtain better results by recalculating features on different resolutions. We use a CNN trained and applied only on the highest image resolution for the highest and second highest scale. Furthermore, we use a CNN trained on 3 resolutions (100%, 50% and 25%) 