Correction to: AEAU-Net: An unsupervised end-to-end registration network by combining affine transformation and deformable medical image registration

Deformable medical image registration plays an essential role in clinical diagnosis and treatment. However, due to the large difference in image deformation, unsupervised convolutional neural network (CNN)-based methods cannot extract global features and local features simultaneously and cannot capture long-distance dependencies to solve the problem of excessive deformation. In this paper, an unsupervised end-to-end registration network is proposed for 3D MRI medical image registration, named AEAU-Net, which includes two-stage operations, i.e., an affine transformation and a deformable registration. These two operations are implemented by an affine transformation subnetwork and a deformable registration subnetwork, respectively. In the deformable registration subnetwork, termed as EAU-Net, we designed an efficient attention mechanism (EAM) module and a recursive residual path (RSP) module. The EAM module is embedded in the bottom layer of the EAU-Net to capture long-distance dependencies. The RSP model is used to obtain effective features by fusing deep and shallow features. Extensive experiments on two datasets, LPBA40 and Mindboggle101, were conducted to verify the effectiveness of the proposed method. Compared with baseline methods, this proposed method could obtain better registration performance. The ablation study further demonstrated the reasonability and validity of the designed architecture of the proposed method. Graphical abstract