## 5 Discussion  
### Principal Findings  
The full method was trained using four cascaded FCNN networks (3D U-net, V-net, SegResNet, and HighResNet) and evaluated on the validation dataset by segmentation metrics and their improvement using the cascade approach (Table 1). All four networks improved the segmentation metrics after the cascade network was applied. The methods based on the U-net (such as 3D U-net, V-net, and SegResNet) did not contain tumors within the initial segmentation mask, which could be due to a significant class imbalance and  
Figure 11: Two of the worst cases from the test set segmentation produced by the method in terms of the tumor Dice score: test#11—first row, test#12—second row. Red—segmentation from our method, Green—correction provided by the expert.  
the downsample nature of the U-net architecture. HighResNet, despite the smallest input size (128 \(\times\) 128 \(\times\) 92) and the lowest amount of parameters to train, was able to find tumors from the uncropped data. After the liver region was cropped, all networks could detect lesion representations from the MRI input. In the method based on the HighResNet, despite the Dice score and precision improvement, the sensitivity for the tumor class decreased from 0.948 \(\pm\) 0.209 to 0.915 \(\pm\) 0.258. This indicates that the detection ability of the HighResNet slightly decreased, while segmentation became more accurate. That could be due to the huge variation in the tumor shape and texture representation and the possible discharging of true-positive lesions due to overfitting on the samples from the training dataset. The lowest segmentation results were achieved by V-net, which could be also due to low liver segmentation after the first stage. Compared to other networks, this network used kernels of 5 \(\times\) 5 \(\times\) 5 matrix, while others are using 3 \(\times\) 3 \(\times\) 3 kernels; maybe changes in the filter kernel size have this influence. In general, comparing all four networks, HighResNet achieved the best Dice score with a more stable mean value for both liver and tumor segmentation. We also marked a slight reduction in time for the method based on HighResNet compared to other networks, even though all were able to produce the segmentations in less than 7 s per volume.  
On the test dataset evaluation (Table 2), we observe higher tumor segmentation metrics on test set #1, with similar liver parenchyma segmentations. As in the validation subset, this could be caused by the inconsistent tumor shape and texture appearances throughout the whole dataset. Within the CLRM tumors, there are different subtypes of tumor growth patterns, and the representation of the tumors could also vary even within the same sequence and modality [52].  
Visualization of our results demonstrated that the cases with the lowest Dice score network tend to predict similar tumor shapes with a bit of over-segmentation. The misclassified vessel on the first row of Figure 9 was connected to the missed tumor, which might be a reason for the method's failure. On the second row of Figure 9, in the two tumors that were located very close to each other, the second was missed. On the other hand, in the first row of Figure 10, the network made a false-positive prediction of the completely isolated tumor while segmenting two other tumors with high accuracy. On the second row of the same figure, we can also see that the network reached the highest Dice score for liver tumor (0.809), and the 3D model and 2D contour overlap were close to each other.  
In Figure 11, we can observe similarities between test#8 and test#11 (first row). The missed tumor was in close contact with another tumor that was correctly predicted and segmented by the network. In contrast, in the second row, missed tumors were located on the borders of the liver parenchyma. Despite that, the correction time for the tumors was almost the same as for the liver parenchyma due to the small volume of the tumors compared to the liver.