  Many existing learning-based deformable image registration methods impose
constraints on deformation fields to ensure they are globally smooth and
continuous. However, this assumption does not hold in cardiac image
registration, where different anatomical regions exhibit asymmetric motions
during respiration and movements due to sliding organs within the chest.
Consequently, such global constraints fail to accommodate local discontinuities
across organ boundaries, potentially resulting in erroneous and unrealistic
displacement fields. In this paper, we address this issue with MemWarp, a
learning framework that leverages a memory network to store prototypical
information tailored to different anatomical regions. MemWarp is different from
earlier approaches in two main aspects: firstly, by decoupling feature
extraction from similarity matching in moving and fixed images, it facilitates
more effective utilization of feature maps; secondly, despite its capability to
preserve discontinuities, it eliminates the need for segmentation masks during
model inference. In experiments on a publicly available cardiac dataset, our
method achieves considerable improvements in registration accuracy and
producing realistic deformations, outperforming state-of-the-art methods with a
remarkable 7.1\% Dice score improvement over the runner-up semi-supervised
method. Source code will be available at https://github.com/tinymilky/Mem-Warp.
