Deformable image registration (DIR) of lung four-dimensional computed tomography (4DCT) plays a vital role in a wide range of clinical applications. Most of the existing deep learning-based lung 4DCT DIR methods focus on pairwise registration which aims to register two images with large deformation. However, the temporal continuities of deformation fields between phases are ignored. This paper proposes a fast and accurate deep learning-based lung 4DCT DIR approach that leverages the temporal component of 4DCT images. Methods: We present Lung-CRNet, an end-to-end convolutional recurrent registration neural network for lung 4DCT images and reformulate 4DCT DIR as a spatiotemporal sequence predicting problem in which the input is a sequence of three-dimensional computed tomography images from the inspiratory phase to the expiratory phase in a respiratory cycle. The first phase in the sequence is selected as the only reference image and the rest as moving images. Multiple convolutional gated recurrent units (ConvGRUs) are stacked to capture the temporal clues between images. The proposed network is trained in an unsupervised way using a spatial transformer layer. During inference, Lung-CRNet is able to yield the respective displacement field for each reference-moving image pair in the input sequence. Results: We have trained the proposed network using a publicly available lung 4DCT dataset and evaluated performance on the widely used the DIR-Lab dataset. The mean and standard deviation of target registration error are 1.56 ± 1.05 mm on the DIR-Lab dataset. The computation time for each forward prediction is less than 1 s on average. Conclusions: The proposed Lung-CRNet is comparable to the existing stateof -the-art deep learning-based 4DCT DIR methods in both accuracy and speed. Additionally, the architecture of Lung-CRNet can be generalized to suit other groupwise registration tasks which align multiple images simultaneously.

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Purpose:Automatic liver segmentation from computed tomography (CT) images is an essential preprocessing step for computer-aided diagnosis of liver diseases. However, due to the large differences in liver shapes, low-contrast to adjacent tissues, and existence of tumors or other abnormalities, liver segmentation has been very challenging. This study presents an accurate and fast liver segmentation method based on a novel probabilistic active contour (PAC) model and its fast global minimization scheme (3D-FGMPAC), which is explainable as compared with deep learning methods. Methods:The proposed method first constructs a slice-indexed-histogram to localize the volume of interest (VOI) and estimate the probability that a voxel belongs to the liver according its intensity. The probabilistic image would be used to initialize the 3D PAC model. Secondly, a new contour indicator function, which is a component of the model, is produced by combining the gradientbased edge detection and Hessian-matrix-based surface detection. Then, a fast numerical scheme derived for the 3D PAC model is performed to evolve the initial probabilistic image into the global minimizer of the model, which is a smoothed probabilistic image showing a distinctly highlighted liver. Next, a simple regiongrowing strategy is applied to extract the whole liver mask from the smoothed probabilistic image. Finally, a B-spline surface is constructed to fit the patch of the rib cage to prevent possible leakage into adjacent intercostal tissues. Results:The proposed method is evaluated on two public datasets.The average Dice score, volume overlap error, volume difference, symmetric surface distance and volume processing time are 0.96, 7.35%, 0.02%, 1.17 mm and 19.8 s for the Sliver07 dataset, and 0.95, 8.89%, −0.02%, 1.45 mm and 23.08 s for the 3Dircadb dataset, respectively. Conclusions:The proposed fully-automatic approach can effectively segment the liver from low-contrast and complex backgrounds. The quantitative and qualitative results demonstrate that the proposed segmentation method outperforms state-of -the-art traditional automatic liver segmentation algorithms and achieves very competitive performance compared with recent deep leaning-based methods.