###### Abstract  
The segmentation of hepatic vessels is crucial for liver surgical planning. It is also a challenging task because of its small diameter. Hepatic vessels are often captured in images of low contrast and resolution. Our research uses filter enhancement to improve their contrast, which helps with their detection and final segmentation. We have designed a specific fusion of the Ranking Orientation Responses of Path Operators (RORPO) enhancement filter with a raw image, and we have compared it with the fusion of different enhancement filters based on Hessian eigenvectors. Additionally, we have evaluated the 3D U-Net and 3D V-Net neural networks as segmentation architectures, and have selected 3D V-Net as a better segmentation architecture in combination with the vessel enhancement technique. Furthermore, to tackle the pixel imbalance between the liver (background) and vessels (foreground), we have examined several variants of the Dice Loss functions, and have selected the Weighted Dice Loss for its performance. We have used public 3D Image Reconstruction for Comparison of Algorithm Database (3D-IRCADb) dataset, in which we have manually improved upon the annotations of vessels, since the dataset has poor-quality annotations for certain patients. The experiments demonstrate that our method achieves a mean dice score of 76.2%, which outperforms other state-of-the-art techniques.  
liver vessel segmentation; hepatic vessel segmentation; 3D U-Net; 3D V-Net; Hessian; Frangi; Sato; RORPO; improved annotations; Weighted Dice Loss function +
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of the raw image with the RORPO (The Ranking Orientations Responses of Path Operators) [1] enhanced image. This is then utilized by the segmentation architecture of 3D U-Net or 3D V-Net. The final segmentation pipeline consists of RORPO and 3D V-Net, which provide the best segmentation results.  
In the paper, several experiments are performed, which test the main parts of the proposed method and make comparisons with alternative state-of-the-art approaches. The first experiment compares five classical vessel enhancement filters separately: Frangi, Hessian, Meijering, RORPO, and Sato. The following two experiments evaluate a fusion of different vessel enhancement filters with two variants of segmentation models (3D U-Net and 3D V-Net). The fusion of the RORPO enhancement filter with the CT image to detect the liver vessel structures supported by the 3D V-Net is proven to be the most efficient. We also suggest the best value of the blending coefficient between the RORPO enhanced image and the raw CT image. In such a setup, we further experiment with different variants of dice loss functions to solve the problem of pixel imbalance between the foreground and background categories. The following experiment then performs the ablation study of the selected architecture. In the last experiment, a comparison between our proposed algorithm and other algorithms is provided.  
The proposed algorithm is proven to be effective, robust, and accurate for liver vessel segmentation, even for images with low contrast and high noise. Experiments are performed on the public 3D-IRCADb [2] dataset; the average dice score and precision are 76.2% and 77.7%, respectively.  
During the work on this topic, we have used 3D Slicer [3] software, for which we have created a software extension that can provide doctors and other healthcare professionals with tools for automatic vessels segmentation, and tools for validating the segmented datasets. Employing deep learning and 3D Slicer, we can segment vascular structures automatically, improve the annotations, automatically collect the annotated datasets, and then fine-tune the neural network models so they can be quickly exposed for further use in automatic segmentation.