## 2 Related Work  
The trend of the proposed segmentation methods leads to the automation of liver vessel segmentation [4; 5]. The methods for liver vessel segmentation from CT abdominal images can be divided into several groups: tracking-based algorithms, active contours, and machine learning [6]. The popular approach to segmenting liver vessels is based on machine learning methods and Deep Learning (DL) specifically. The application of 3D U-Net [7; 8; 9; 10] is often used for the segmentation of liver vessels from CT images. The 3D U-Net is composed of analytical and synthetical parts [11], similar to the standard U-Net architecture, but it uses 3D operators instead. [PERSON] et al. [7] described the 3D Residual U-Net technique, which is built on 3D U-Net with a 3D morphological closure operation in the postprocessing phase. The algorithm was tested on their private CT abdominal dataset. [PERSON] et al. [8] used 3D U-Net with a combination of the variant dice loss function. The segmented veins were more continuous and complete when training was carried out using the enhanced manual expert annotations rather than the original dataset. The tests were carried out using the 3D-IRCADb, SLiver007 [12], and private datasets. [PERSON] et al. [9] experimented with three distinct 3D U-Net approaches: basic U-Net, MultiRes U-Net, and Dense U-Net. On the 3D-IRCADb dataset, they determined that MultiRes U-Net architecture was superior for segmenting hepatic blood veins. [PERSON] et al. [10] employed an ensemble technique. They combined the predictions of networks into ensemble E and averaged the resulting probability for each class. Probability maps of all networks (2D U-Net, 3D U-Net, 2D V-Net, and 3D V-Net) and ensembles were resampled back to the original data, resolution and the maximum probability was applied to the data to extract the predicted segmentation. The approach was tested on the publicly available datasets 3D-IRCADb and MICCAI [12], with unsuitable data being excluded. V-Net [13] is the next commonly used neural network architecture that has been studied in recent years for segmenting liver blood vessels. [PERSON] et al. [14] proposed the DV-Net algorithm. DV-Net represents a V-Net with a dense block structure. They utilize a combination of DCDS (dense connection downsampling approach) and D-BCE loss function for capturing blood vessel structure. The method was tested on 3D-IRCADb. [PERSON] et al. [15] used an improved V-Net to segment liver blood vessels on the 3D-IRCADb dataset. Improved V-Net is based on inter-scale dense connections in the decoder. [PERSON] et al. [16] used 2.5D V-Net for the segmentation of liver blood vessels. They trained the method on the 3D-IRCADb dataset and tested it on their dataset. They used Tversky index-based loss function in combination with 2.5D V-Net. The Tversky index ensures a short convergence time due to the unbalanced voxels problem. A different approach than the common utilization of either the U-Net or V-Net architecture is applied in [17; 18]. In [17], the authors propose a fusion network called TransfusionNet. This method is based on a transformer for semantic segmentation. The authors use the 3D-IRCADb and LiTS [19] datasets for pre-training, and their data for fine-tuning the segmentation network. [PERSON] et al. [18] applied a deep neural network based on the bootstrapping technique to the 3D-IRCADb dataset. A convex combination of the model predictions and preliminary predictions with the subsequent application of a noise filter is used to segment the liver blood vessels. There is a full body of work that focuses on image enhancement that can be applied before training the segmentation model. This is especially true if complex structures such as vessels are segmented. [PERSON] and [PERSON] [20] apply a set of preprocessing operations, including filtering via the Frangi filter, to enhance retinal vessels before their segmentation. [PERSON] et al.