# 3D Liver and Tumor Segmentation with CNNs Based on Region and Distance Metrics
## 4 Comparison and Discussion
As such, it can be concluded that the overall performance of our algorithm outperforms other similar algorithms in the table on the two databases. Spatial information was not used in models based on regional metrics, and the prediction errors were treated equally. This meant that voxel errors in objects that had already been detected were as important as errors that occurred within objects that had missed totally. By contrast, because the distance-based loss was on the basis of a distance map relative to the true boundary, such cases were penalized, thus assisting in recovering the far and small regions. Therefore, our algorithm will have advantages in the tasks which need to segment a large number of small objects. It is worth noting that for the models jointly trained with two or more loss functions, it was generally necessary to discuss the weight of each loss function. Our experimental results also showed that as the weight of the distance-based loss function increases, the performance did not continue to improve, and even showed a downward trend, which required special attention during the model training stage. In addition, it was also important that the distance-based loss function was gradually \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Training Strategy**} & \multirow{2}{*}{**Category**} & \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**DSC**} & **HD95** & **ASD** & \multirow{2}{*}{**TNR**} & **TPR** \\ \cline{5-8}  & & & & **(mm)** & & **(mm)** & \\ \hline \multirow{3}{*}{Joint training at the beginning} & \multirow{3}{*}{Liver} & LiTS 2017 & 0.951 & 4.17 & 2.1 & 0.967 & 0.999 \\  & & 3D-IRCADb & 0.937 & 7.28 & 2.49 & 0.951 & 0.998 \\ \cline{2-8}  & \multirow{3}{*}{Tumor} & LiTS 2017 & 0.742 & 8.03 & 2.38 & 0.623 & 0.999 \\  & & 3D-IRCADb & 0.633 & 12.22 & 3.55 & 0.602 & 0.999 \\ \hline \multirow{3}{*}{Our training strategy} & \multirow{3}{*}{Liver} & LiTS 2017 & **0.965** & **3.23** & **0.88** & **0.982** & **0.999** \\  & & 3D-IRCADb & **0.948** & **4.68** & **1.81** & **0.958** & **0.998** \\ \cline{2-8}  & \multirow{3}{*}{Tumor} & LiTS 2017 & **0.764** & **6.72** & **1.25** & **0.761** & **0.999** \\  & & 3D-IRCADb & **0.682** & **9.47** & **2.82** & **0.654** & **0.999** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The results on two datasets with a different training strategy. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Approach**} & \multirow{2}{*}{**Dataset**} & \multicolumn{2}{c}{**Liver**} & \multicolumn{2}{c}{**Tumor**} \\ \cline{3-6}  & & **DSC** & **ASD (mm)** & **DSC** & **ASD (mm)** \\ \hline U-Net [39] & LiTS 2017 & - & - & 0.650 & - \\ ResNet [40] & LiTS 2017 & - & - & 0.670 & 6.66 \\ DenseNet [41] & LiTS 2017 & 0.912 & 6.49 & 0.492 & 1.44 \\ FCN+ACM [42] & LiTS 2017 & 0.943 & 2.30 & - & - \\ GIU-Net [43] & LiTS 2017 & 0.951 & 1.80 & - & - \\ ResNet [44] & LiTS 2017 & 0.959 & - & 0.500 & - \\ RA-Unet [13] & LiTS 2017 & 0.961 & 1.21 & 0.595 & 1.29 \\ H-DenseUNet [3] & LiTS 2017 & 0.961 & 1.45 & 0.722 & **1.10** \\ CDNN [45] & LiTS 2017 & 0.963 & 1.10 & 0.657 & 1.15 \\ ours & LiTS 2017 & **0.965** & **0.88** & **0.764** & 1.25 \\ \hline MPAM [46] & 3D-IRCADb & - & 2.24 & - & - \\ ASM [47] & 3D-IRCADb & - & 1.66 & - & - \\ U-Net [3] & 3D-IRCADb & 0.923 & 4.33 & 0.510 & 11.11 \\ ResNet [3] & 3D-IRCADb & 0.938 & 3.91 & 0.600 & 6.36 \\ CFCNs [48] & 3D-IRCADb & 0.943 & **1.50** & 0.560 & - \\ H-DenseUNet [3] & 3D-IRCADb & 0.947 & 4.06 & 0.650 & 5.29 \\ ours & 3D-IRCADb & **0.948** & 1.81 & **0.682** & **2.82** \\ \hline \hline \end{tabular} Note: - denotes the result is not reported.  
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Table 5: The comparison of our approach with similar approaches. added for joint training, only after the performance of the model on the validation set entered the platform period.