\section{Appendix}

\input{midl25_223_sections/midl25_223_atlas_estimation}
\begin{figure}[h]
    \centering
    \includegraphics[width=0.5\linewidth]{midl25_223_figures/coopnet_quality.png}
    \caption{Figure shows the outputs of CoopNet \cite{bhalodia2019cooperative} for a toy dataset of a torus with a bump and the Oasis-2D dataset. While registering the moving image to the fixed image, the predicted deformation fields provide large over, and the transformations are not diffeomorphic.}
    \label{fig:coopnet_eg}
\end{figure}

