up computations, we use patch pruning (i.e., for brain imaging, e.g., patches outside the brain are not predicted as the momentum is expected to be zero there) and a large pixel stride (e.g., 14 for $15 \times 15 \times 15$ patches) for the sliding window of the predicted patches.

![image](image/CorrectionNetwork-rkwitt){width="\textwidth"}

Correction network
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We follow [@quicksilver] and use a two-step approach to improve overall prediction accuracy. An additional correction step, i.e., a [*correction network*]{}, corrects the prediction of the initial prediction network. Fig. \[fig:corr\] illustrates this two-step approach graphically. The correction network has the same structure as the prediction network. Only the inputs and outputs differ. For the prediction network, the inputs are the original moving image and the original target image; output is the predicted initial momentum. For the correction network, the inputs are the original moving image and the warped target image; the output is the momentum difference.

[ |c|c|c|c|c|c|c|c|c|]{}\
*Data Percentile* & 0.3% & 5% & 25% & 50% & 75% & 95% & 99.7%\
Longitudinal Training& **0.0156** & **0.0407** & **0.0761** & **0.1098** & **0.1559** & **0.2681** & **0.3238**\
Cross-sectional Training& 0.0544 & 0.1424 & 0.2641 & 0.3723 & 0.5067 & 0.7502 & 0.8425\
\
*Data 