## 4 Results
### Application on the Test Subsets
#### 4.2.1 Quantitative Results  
Segmentation metrics from obtained inferences for both test sets were presented in Table 2. Binary masks of the liver and tumors were compared to GT and expert manual corrections.  
The proposed method based on the HighResNet achieved a Dice score of 0.944 \(\pm\) 0.009 for the liver and 0.780 \(\pm\) 0.119 for the tumor segmentation on the first test set. Out of 17 tumors defined on the GT annotation, the HighResNet found 15, while pixel-wise tumor sensitivity was 0.832 \(\pm\) 0.163. The precision of 0.699 \(\pm\) 0.124 and two false-positive tumors segmented by the network leads to many of false-positive pixels on the DL tumor prediction mask. On the second test subset (compared to expert manual corrections) the same method achieved a Dice score of 0.994 \(\pm\) 0.003 for liver and 0.709 \(\pm\) 0.171 for tumor segmentation. Among nine tumors presented in this subset, six were detected, and the average sensitivity was 0.667 \(\pm\) 0.257. The method predicted no false-positive tumors, and the average precision for tumor segmentation was 0.882 \(\pm\) 0.146. The average Dice score for both datasets for the liver segmentation was 0.958 \(\pm\) 0.024, and for the CLRM tumor segmentation, the Dice score achieved was 0.724 \(\pm\) 0.130.  
Figure 7 presents segmentation results on each of the test samples in terms of the Dice score for the tumor and liver parenchyma.  
On the test subset with GT (Figure 7a), the highest Dice score for tumors was 0.831 (test#1), and the lowest was 0.466 (test#6). For the tumors that were found, the mean Dice score was 0.780 \(\pm\) 0.119. The liver segmentation Dice remained high for all cases, with the lowest result of 0.925 (test#5) and the highest of 0.960 (test#9). The average inference time was 4.82 \(\pm\) 1.30 s per volume.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Network** & **Subject** & **Sensitivity** & **Precision** & **Dice** \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} Test set \#1 \\ compared to GT \\ \end{tabular} } & Liver & 0.988 \(\pm\) 0.003 & 0.903 \(\pm\) 0.019 & 0.944 \(\pm\) 0.009 \\ \cline{2-5}  & Tumors & 0.832 \(\pm\) 0.163 & 0.699 \(\pm\) 0.124 & 0.780 \(\pm\) 0.119 \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Test set \#2 \\ compared to expert \\ corrections \\ \end{tabular} } & Liver & 0.996 \(\pm\) 0.003 & 0.993 \(\pm\) 0.006 & 0.994 \(\pm\) 0.003 \\ \cline{2-5}  & Tumors & 0.667 \(\pm\) 0.257 & 0.882 \(\pm\) 0.146 & 0.709 \(\pm\) 0.171 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Liver parenchyma and tumor segmentation results on the test set.  
First, expert manual corrections were required to calculate the Dice score and other metrics on the test subset without GT (Figure 7b). The inference time to achieve DL segmentation was 5.35 \(\pm\) 1.25 s per case. The average time to correct the volumes (both liver and tumor segmentation masks) was 21.15 \(\pm\) 10.6 min. For the liver parenchyma, the average correction time was 10.6 \(\pm\) 4.5 min. In all cases, the time required for tumor correction was similar as for all parenchyma. The longest time per volume was 32 min (test#11). The highest Dice score for tumors was 0.916 (test#14), and the lowest was 0.500 (test#11). The liver parenchyma's lowest Dice score was 0.989 (test#11) and the highest was 0.996 (test#13 and test#14).  
Figure 8 demonstrates the confusion matrix for the detected tumors by the HighResNet based methods and tumors presented on the GT. For the second test subset, the number of tumors was checked with annotations provided by the radiologist to guide and confirm expert segmentation correction.  
From the boxplots, we can see that in both datasets, there were five tumors that were missed by our method. Three false-positive tumors were detected in total in both test datasets. Out of 23 lesions annotated on the dataset, 18 were segmented using our method.