# 3D Liver and Tumor Segmentation with CNNs Based on Region and Distance Metrics
## 3 Experiment and Discussion
### Experimental Results
#### 3.2.1 Quantitative Evaluation
It was also found that the TPR of all models has reached more than 99.7%, which shows that for the liver segmentation task, the existing models have already obtained high sensitivity [37]. The models on the 3D-IRCADb database didn't perform as well as it did on the LiTS 2017 database. It was mainly due to the small scale of the 3D-IRCADb database, resulting in insufficient model training. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Category** & **Dataset** & **Resolution** & **Dice Similarity Coefficient (DSC)** \\ \hline \multirow{4}{*}{Liver} & & 512*512 & **0.953** \\  & LiTS 2017 & 256*256 & 0.947 \\  & & 128*128 & 0.936 \\ \cline{2-4}  & \multirow{2}{*}{3D-IRCADb} & 512*512 & **0.929** \\  & & 256*256 & 0.924 \\  & & 128*128 & 0.91 \\ \hline \multirow{4}{*}{Tumor} & & 512*512 & **0.699** \\  & LiTS 2017 & 256*256 & 0.655 \\  & & 128*128 & 0.615 \\ \cline{1-1} \cline{2-4}  & \multirow{2}{*}{3D-IRCADb} & 512*512 & **0.623** \\  & & 256*256 & 0.597 \\ \cline{1-1}  & & 128*128 & 0.567 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the results of models trained with different resolution data. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Category**} & \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Loss Function**} & \multirow{2}{*}{**DSC**} & **95 th Percentile of the Hausdorff (Distance Metrics)** & \multicolumn{2}{c}{**Average**} & **True** & **True** \\  & & & & **(HD95) (mm)** & & **(mm)** & **(**)** & **Negative** & **Positive** \\ \hline \multirow{4}{*}{Liver} & & \(L_{Reg}\) & 0.953 & 5.44 & 1.61 & 0.957 & 0.998 \\  & & \(L_{HD}\) & 0.962 & 3.60 & 1.05 & 0.971 & 0.998 \\  & & \(L_{BD}\) & 0.963 & 4.24 & **0.88** & 0.973 & 0.999 \\  & & \(L_{SDM}\) & **0.965** & **3.23** & 1.07 & **0.982** & **0.999** \\ \cline{2-6}  & \multirow{4}{*}{3D-IRCADb} & \(L_{Reg}\) & 0.929 & 8.74 & 2.58 & 0.921 & 0.997 \\  & & \(L_{HD}\) & 0.942 & 6.97 & 2.17 & 0.949 & 0.998 \\  & & \(L_{BD}\) & 0.947 & **4.15** & 1.87 & 0.955 & 0.998 \\  & & \(L_{SDM}\) & **0.948** & 4.68 & **1.81** & **0.958** & **0.998** \\ \hline \multirow{4}{*}{Tumor} & & \(L_{Reg}\) & 0.699 & 9.36 & 2.17 & 0.655 & 0.998 \\  & & \(L_{HD}\) & 0.731 & 8.77 & 1.82 & 0.682 & 0.999 \\ \cline{1-1}  & & \(L_{SDM}\) & 0.745 & 8.14 & 1.68 & 0.708 & 0.999 \\ \cline{1-1}  & & \(L_{SDM}\) & **0.764** & **6.72** & **1.25** & **0.761** & **0.999** \\ \cline{1-1} \cline{2-6}  & \multirow{4}{*}{3D-IRCADb} & \(L_{Reg}\) & 0.623 & 13.46 & 3.72 & 0.564 & 0.999 \\ \cline{1-1}  & & \(L_{HD}\) & 0.648 & 11.25 & 3.08 & 0.587 & 0.999 \\ \cline{1-1}  & & \(L_{BD}\) & 0.677 & 9.88 & 2.88 & **0.674** & 0.999 \\ \cline{1-1}  & & \(L_{SDM}\) & **0.682** & **9.47** & **2.82** & 0.654 & **0.999** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: A summary of the results on LiTS 2017 and 3D-IRCADb datasets. Some studies have shown that utilizing additional data for training will significantly improve the performance of the 3D-IRCADb database [8; 9; 24; 27]. Generally, the traditional region-based segmentation methods measure the affinity of the network probability Softmax output-defined region to related ground truth regions. It assumes that all samples and classes have the same importance distribution. Therefore, it requires a training set with balanced classes to get good generality. However, for unbalanced data, the regional loss-based approaches lead to training instability and biased decision boundaries to most categories. Adding a distance-based loss function to the regional loss function for joint training can mitigate the issues. Instead of utilizing the imbalanced integrals on these regions, the distance-based loss function used integrals on the inter-regional boundaries. Therefore, it was easily combined with a regional loss for joint training to solve the problem of imbalanced data for the liver and tumor segmentation task. In addition, the cross-validation experiments were also conducted on the LiTS 2017 and 3D-IRCADb datasets.