  This work proposes NePhi, a generalizable neural deformation model which
results in approximately diffeomorphic transformations. In contrast to the
predominant voxel-based transformation fields used in learning-based
registration approaches, NePhi represents deformations functionally, leading to
great flexibility within the design space of memory consumption during training
and inference, inference time, registration accuracy, as well as transformation
regularity. Specifically, NePhi 1) requires less memory compared to voxel-based
learning approaches, 2) improves inference speed by predicting latent codes,
compared to current existing neural deformation based registration approaches
that \emph{only} rely on optimization, 3) improves accuracy via instance
optimization, and 4) shows excellent deformation regularity which is highly
desirable for medical image registration. We demonstrate the performance of
NePhi on a 2D synthetic dataset as well as for real 3D lung registration. Our
results show that NePhi can match the accuracy of voxel-based representations
in a single-resolution registration setting. For multi-resolution registration,
our method matches the accuracy of current SOTA learning-based registration
approaches with instance optimization while reducing memory requirements by a
factor of five.
