Deformation decomposition serves as a good solution for deformable image registration when the deformation is large. Current deformation decomposition methods can be categorized into cascade-based methods and pyramid-based methods. However, cascade-based methods suffer from heavy computational burdens and long inference time due to their structures of repeated subnetworks, while the effectiveness of pyramid-based methods is constrained by their limited numbers of resolution levels. In this paper, to address both the insufficient and inefficient decomposition problems in current deformation decomposition methods, we propose a recursive decomposition network (RDN) to offer a novel solution for deformable image registration. Stage-wise recursion can efficiently decompose a large deformation into different pyramid estimation stages without using repeated subnetworks like in cascade-based methods. Level-wise recursion can sufficiently decompose the deformation inside each resolution level instead of only one-time estimation like in pyramid-based methods. Extensive experiments and ablation studies on two representative datasets validate the effectiveness and efficiency of our proposed RDN.

Unsupervised deformable image registration benefits from progressive network structures such as Pyramid and Cascade. However, existing progressive networks only consider the single-scale deformation field in each level or stage and ignore the long-term connection across non-adjacent levels or stages. In this paper, we present a novel unsupervised learning approach named Self-Distilled Hierarchical Network (SDHNet). By decomposing the registration procedure into several iterations, SDHNet generates hierarchical deformation fields (HDFs) simultaneously in each iteration and connects different iterations utilizing the learned hidden state. Specifically, hierarchical features are extracted to generate HDFs through several parallel gated recurrent units, and HDFs are then fused adaptively conditioned on themselves as well as contextual features from the input image. Furthermore, different from common unsupervised methods that only apply similarity loss and regularization loss, SDHNet introduces a novel self-deformation distillation scheme. This scheme distills the final deformation field as the teacher guidance, which adds constraints for intermediate deformation fields on deformation-value and deformation-gradient spaces respectively. Experiments on five benchmark datasets, including brain MRI and liver CT, demonstrate the superior performance of SDHNet over state-of-the-art methods with a faster inference speed and a smaller GPU memory. Code is available at https://github.com/Blcony/SDHNet.

Images captured in clinic such as MRI scans are usually in 3D formats with high spatial resolutions. Existing learning-based models for medical image registration consume large GPU memories and long inference time, which is difficult to be deployed in resource-limited diagnosis scenarios. To address this problem, instead of shrinking the model size as in previous works, we turn to reducing the input resolution of existing registration models and boosting their performance through knowledge distillation. Specifically, we propose a cross-resolution distillation (CRD) scheme, which is designed to train low-resolution models under the guidance of corresponding high-resolution models. Nevertheless, due to the resolution gap between features in high/low-resolution models, straightforward distillation is difficult to apply. To overcome this challenge, we first introduce a feature-shifted teacher (FST) to shift and fuse features of high/low-resolution models. Then, we exploit this teacher model to guide the learning of the low-resolution student model with distillation losses on both features and deformation fields. Finally, we only need to use the distilled student model during inference. Experimental results on four 3D medical image datasets demonstrate that the low-resolution models trained through our CRD scheme use fewer than 20% GPU memories and less than 20% inference time while achieving competitive performance compared with corresponding high-resolution models.