  We present a new unsupervised learning algorithm, "FAIM", for 3D medical
image registration. With a different architecture than the popular "U-net", the
network takes a pair of full image volumes and predicts the displacement fields
needed to register source to target. Compared with "U-net" based registration
networks such as VoxelMorph, FAIM has fewer trainable parameters but can
achieve higher registration accuracy as judged by Dice score on region labels
in the Mindboggle-101 dataset. Moreover, with the proposed penalty loss on
negative Jacobian determinants, FAIM produces deformations with many fewer
"foldings", i.e. regions of non-invertibility where the surface folds over
itself. In our experiment, we varied the strength of this penalty and
investigated changes in registration accuracy and non-invertibility in terms of
number of "folding" locations. We found that FAIM is able to maintain both the
advantages of higher accuracy and fewer "folding" locations over VoxelMorph,
over a range of hyper-parameters (with the same values used for both networks).
Further, when trading off registration accuracy for better invertibility, FAIM
required less sacrifice of registration accuracy. Codes for this paper will be
released upon publication.
