The number of sample warps used for training is increased, with the patch size used fixed at $9 \times 9$ pixels.

-   **Number of pixels used**: The patch size is increased, with the number of sample warps fixed at $m=5000$.

-   **Maximum parameter variation**: Using $m=5000$ sample warps and a $9\times 9$ patch, we increase the amount of variation in the translation parameters for training.

The results are shown in Fig. \[fig:synthetic\_lp\], where we show display RMSE with two plots as methods based on the re-formulation approach exhibit a much larger error compared to the other methods. From Fig. \[fig:synthetic\_lp\](a), we see that the learning time for our method increases very slowly as the number of sample warps increases. In contrast, the learning time for all other methods increases quickly with the number of sample warps. As the number of sample warps increases, the accuracy of all methods improves until around 5000 sample warps, and do not improve by much subsequently.

From Fig. \[fig:synthetic\_lp\](b), the learning time for our method is again much lower compared to other methods when larger patch sizes are used. In contrast to Fig. \[fig:synthetic\_lp\](a), learning time increases more quickly, and starts becoming expensive at a 