IConDiffNet: an unsupervised inverse-consistent diffeomorphic network for medical image registration
Authors: Liao Rui , F Williamson Jeffrey , Xia Tianyu , Ge Tao , A O’Sullivan Joseph 
Published: January 2025

Objective. Deformable image registration (DIR) is critical in many medical imaging applications. Diffeomorphic transformations, which are smooth invertible mappings with smooth inverses preserve topological properties and are an anatomically plausible means of constraining the solution space in many settings. Traditional iterative optimization-based diffeomorphic DIR algorithms are computationally costly and are not able to consistently resolve large and complicated deformations in medical image registration. Convolutional neural network implementations can rapidly estimate the transformation in through a pre-trained model. However, the structure design of most neural networks for DIR fails to systematically enforce diffeomorphism and inverse consistency. In this paper, a novel unsupervised neural network structure is proposed to perform a fast, accurate, and inverse-consistent diffeomorphic DIR. Approach. 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. Main result. Our proposed method was evaluated on a three-dimensional inter-patient image registration task with a large-scale brain MRI image dataset containing 375 subjects. The proposed IConDiffNet achieves fast and accurate DIR with better DSC, lower Hausdorff distance metric, and lower total energy spent during the deformation in the test dataset compared to competing state-of-the-art deep-learning diffeomorphic DIR approaches. Visualization shows that IConDiffNet produces more complicated transformations that better align structures than the VoxelMorph-Diff, SYMNet, and ANTs-SyN methods. Significance. 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.