Double-Uncertainty Assisted Spatial and Temporal Regularization Weighting for Learning-based Registration

In order to tackle the difficulty associated with the ill-posed nature of the image registration problem, researchers use regularization to constrain the solution space. For most learning-based registration approaches, the regularization usually has a fixed weight and only constrains the spatial transformation. Such convention has two limitations: (1) The regularization strength of a specific image pair should be associated with the content of the images, thus the ``one value fits all'' scheme is not ideal; (2) Only spatially regularizing the transformation (but overlooking the temporal consistency of different estimations) may not be the best strategy to cope with the ill-posedness. In this study, we propose a mean-teacher based registration framework. This framework incorporates an additional \textit{temporal regularization} term by encouraging the teacher model's temporal ensemble prediction to be consistent with that of the student model. At each training step, it also automatically adjusts the weights of the \textit{spatial regularization} and the \textit{temporal regularization} by taking account of the transformation uncertainty and appearance uncertainty derived from the perturbed teacher model. We perform experiments on multi- and uni-modal registration tasks, and the results show that our strategy outperforms the traditional and learning-based benchmark methods.