IConDiffNet: an unsupervised inverse-consistent diffeomorphic network for medical image registration

This paper introduces a novel unsupervised inverse-consistent diffeomorphic registration network termed IConDiffNet, which incorporates an energy constraint that minimizes the total energy expended during the deformation process. The IConDiffNet architecture consists of two symmetric paths, each employing multiple recursive cascaded updating blocks (neural networks) to handle different virtual time steps parameterizing the path from the initial undeformed image to the final deformation. These blocks estimate velocities corresponding to specific time steps, generating a series of smooth time-dependent velocity vector fields. Simultaneously, the inverse transformations are estimated by corresponding blocks in the inverse path. By integrating these series of time-dependent velocity fields from both paths, optimal forward and inverse transformations are obtained, aligning the image pair in both directions. 
We evaluate our proposed method on a 3D image registration task with a large-scale brain MRI image dataset containing 375 subjects. The proposed IConDiffNet achieves fast and accurate DIR with better Dice scores, lower Hausdorff distance metric, and lower total energy spent during the deformation in the test dataset compared to competing state-of-the-art DL-based diffeomorphic DIR methods. Visualization shows that IConDiffNet produces more complicated transformations that better align structures than the VoxelMoprh-Diff, SYMNet, and ANTs-SyN methods.
The proposed IConDiffNet represents an advancement in unsupervised deep-learning-based DIR approaches. By ensuring inverse consistency and diffeomorphic properties in the outcome transformations, IConDiffNet offers a pathway for improved registration accuracy, particularly in clinical settings where diffeomorphic properties are crucial. Furthermore, the generality of IConDiffNet's network structure supports direct extension to diverse 3D image registration challenges. This adaptability is facilitated by the flexibility of the objective function used in optimizing the network, which can be tailored to suit different registration tasks.