Accurate liver segmentation from computed tomography (CT) scans is essential for liver cancer diagnosis and liver surgery planning. Convolutional neural network (CNN)-based models have limited segmentation performance due to their localized receptive fields. Hybrid models incorporating CNNs and transformers that can capture long-range dependencies have shown promising performance in liver segmentation with the cost of high model complexity. Therefore, a new network architecture named G-UNETR++ is proposed to improve accuracy in liver segmentation with moderate model complexity. Two gradient-based encoders that take the second-order partial derivatives (the first two elements from the last column of the Hessian matrix of a CT scan) as inputs are proposed to learn the 3D geometric features such as the boundaries between different organs and tissues. In addition, a hybrid loss function that combines dice loss, cross-entropy loss, and Hausdorff distance loss is designed to address class imbalance and improve segmentation performance in challenging cases. The proposed method was evaluated on three public datasets, the Liver Tumor Segmentation (LiTS) dataset, the 3D Image Reconstruction for Comparison of Algorithms Database (3D-IRCADb), and the Segmentation of the Liver Competition 2007 (Sliver07) dataset, and achieved 97.38%, 97.50%, and 97.32% in terms of the dice similarity coefficient for liver segmentation on the three datasets, respectively. The proposed method outperformed the other state-of-the-art models on the three datasets, which demonstrated the strong effectiveness, robustness, and generalizability of the proposed method in liver segmentation.

Background/Objectives: This study aimed to develop a fully automatic method for liver tumor segmentation based on our previously developed gradient-enhanced network G-UNETR++. Methods: The proposed method consists of segmentation of the full liver region from computed tomography (CT) images using G-UNETR++, masking the CT images with the extracted liver region to exclude non-liver regions, and liver tumor segmentation from the masked CT images, also using G-UNETR++. To train and evaluate the model, a total of 131 CT scans (97 for training, 20 for validation, and 20 for testing) from the publicly available LiTS dataset were used. Furthermore, another public dataset, the 3DIRCADb dataset consisting of 20 CT scans was used for cross-validation of the effectiveness and generalizability of our method. Results: Experimental results showed that our method outperformed state-of-the-art models over both the LiTS dataset and the 3DIRCADb dataset, with an average dice score of 0.844 and 0.832 over the two datasets, respectively. Conclusions: The proposed method is effective in clinical application to help physicians with liver tumor diagnosis and treatment.