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Image registration is a fundamental step in medical image analysis. Ideally,the transformation that registers one image to another should be adiffeomorphism that is both invertible and smooth. Traditional methods likegeodesic shooting approach the problem via differential geometry, withtheoretical guarantees that the resulting transformation will be smooth andinvertible. Most previous research using unsupervised deep neural networks forregistration have used a local smoothness constraint (typically, a spatialvariation loss) to address the smoothness issue. These networks usually producenon-invertible transformations with ``folding'' in multiple voxel locations,indicated by a negative determinant of the Jacobian matrix of thetransformation. While using a loss function that specifically penalizes thefolding is a straightforward solution, this usually requires carefully tuningthe regularization strength, especially when there are also other losses. Inthis paper we address this problem from a different angle, by investigatingpossible training mechanisms that will help the network avoid negativeJacobians and produce smoother deformations. We contribute two independentideas in this direction. Both ideas greatly reduce the number of foldinglocations in the predicted deformation, without making changes to thehyperparameters or the architecture used in the existing baseline registrationnetwork.

On Reducing Negative Jacobian Determinant of the Deformation Predicted by Deep Registration Networks