Registration by Regression (RbR): a framework for interpretable and flexible atlas registration

In human neuroimaging studies, atlas registration enables mapping MRI scans to a common coordinate frame, which is necessary to aggregate data from multiple subjects. Machine learning registration methods have achieved excellent speed and accuracy but lack interpretability and flexibility at test time (since their deformation model is fixed). More recently, keypoint-based methods have been proposed to tackle these issues, but their accuracy is still subpar, particularly when fitting nonlinear transforms. Here we propose Registration by Regression (RbR), a novel atlas registration framework that: is highly robust and flexible; can be trained with cheaply obtained data; and operates on a single channel, such that it can also be used as pretraining for other tasks. RbR predicts the (x, y, z) atlas coordinates for every voxel of the input scan (i.e., every voxel is a keypoint), and then uses closed-form expressions to quickly fit transforms using a wide array of possible deformation models, including affine and nonlinear (e.g., Bspline, Demons, invertible diffeomorphic models, etc.). Robustness is provided by the large number of voxels informing the registration and can be further increased by robust estimators like RANSAC. Experiments on independent public datasets show that RbR yields more accurate registration than competing keypoint approaches, over a wide range of deformation models.