LieMorph: Transformer-based Image Registration Using Flows on Lie Groups

We propose a data-driven approach for deformable image registration that extends the TransMorph architecture with a module based on the flow equation formulated on matrix fields. Choosing a suitable Lie group allows us to precisely control components of the deformation that should be ignored by the regularization and provides a powerful plug-in replacement for the deformation field generator in learning-based methods. Combined with the TransMorph architecture, our method performs favorably on the IXI and OASIS datasets. Our implementation is available at https://github.com/sennhoj321/Liemorph.