Image registration is a fundamental step in medical image analysis. Ideally, the transformation that registers one image to another should be a diffeomorphism that is both invertible and smooth. Traditional methods like geodesic shooting approach the problem via differential geometry, with theoretical guarantees that the resulting transformation will be smooth and invertible. Most previous research using unsupervised deep neural networks for registration have used a local smoothness constraint (typically, a spatial variation loss) to address the smoothness issue. These networks usually produce non-invertible transformations with folding'' in multiple voxel locations, indicated by a negative determinant of the Jacobian matrix of the transformation. While using a loss function that specifically penalizes the folding is a straightforward solution, this usually requires carefully tuning the regularization strength, especially when there are also other losses. In this paper we address this problem from a different angle, by investigating possible training mechanisms that will help the network avoid negative Jacobians and produce smoother deformations. We contribute two independent ideas in this direction. Both ideas greatly reduce the number of folding locations in the predicted deformation, without making changes to the hyperparameters or the architecture used in the existing baseline registration network.
We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to ½ everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples. Deformable image registration is a fundamental task in medical image analysis, aiming to establish a dense and non-linear correspondence between a pair of images. Previous deep-learning studies usually employ supervised neural networks to directly learn the spatial transformation from one image to another, requiring task-specific ground-truth registration for model training. Due to the difficulty in collecting precise ground-truth registration, implementation of these supervised methods is practically challenging. Although several unsupervised networks have been recently developed, these methods usually ignore the inherent inverse-consistent property (essential for diffeomorphic mapping) of transformations between a pair of images. Also, existing approaches usually encourage the to-be-estimated transformation to be locally smooth via a smoothness constraint only, which could not completely avoid folding in the resulting transformation. To this end, we propose an Inverse-Consistent deep Network (ICNet) for unsupervised deformable image registration. Specifically, we develop an inverse-consistent constraint to encourage that a pair of images are symmetrically deformed toward one another, until both warped images are matched. Besides using the conventional smoothness constraint, we also propose an anti-folding constraint to further avoid folding in the transformation. The proposed method does not require any supervision information, while encouraging the diffeomoprhic property of the transformation via the proposed inverse-consistent and anti-folding constraints. We evaluate our method on T1-weighted brain magnetic resonance imaging (MRI) scans for tissue segmentation and anatomical landmark detection, with results demonstrating the superior performance of our ICNet over several state-of-the-art approaches for deformable image registration. Our code will be made publicly available.