  In the past, optimization-based registration models have used
spatially-varying regularization to account for deformation variations in
different image regions. However, deep learning-based registration models have
mostly relied on spatially-invariant regularization. Here, we introduce an
end-to-end framework that uses neural networks to learn a spatially-varying
deformation regularizer directly from data. The hyperparameter of the proposed
regularizer is conditioned into the network, enabling easy tuning of the
regularization strength. The proposed method is built upon a Transformer-based
model, but it can be readily adapted to any network architecture. We thoroughly
evaluated the proposed approach using publicly available datasets and observed
a significant performance improvement while maintaining smooth deformation. The
source code of this work will be made available after publication.
