# 3D Liver and Tumor Segmentation with CNNs Based on Region and Distance Metrics
## 3 Experiment and Discussion
### Experimental Results  
#### 3.2.1 Quantitative Evaluation  
In the LiTS 2017 dataset, 131 scans were used as the experimental data, among which, 102 were used for training, 20 for verification, and nine for testing. In the 3D-IRCADb dataset, 20 scans were selected, including 10 utilized as the training set, five as the validation set, and five as the test set. Three models with HD loss, BD loss, and SDM loss functions were trained on these two datasets, respectively. We utilized the values of Dice Similarity Coefficient (DSC), the 95 th percentile of the Hausdorff Distance (HD) metrics (HD95), the average symmetric surface distance (ASD), together with the True Negative Rate (TNR, specificity) and True Positive Rate (TPR, sensitivity) as the evaluation indicators. The definitions of the indicators were shown as follows:  
\[DSC=\frac{2|TP|}{2|TP|+|FN|+|FP|} \tag{13}\]  
where TP, TN, FP, and FN represent the true positive, true negative, false positive, and negative values, respectively. The HD95 was defined as the 95 th percentile of the Hausdorff distance between the predicted delineation and the ground truth annotation, which was a common indicator in image segmentation tasks. If \(S(A)\) denotes the set of surface voxels of \(A\), then the shortest distance of an arbitrary voxel \(v\) to \(S(A)\) is defined as:  
\[d(v,S(A))=\min_{s_{A}\in S(A)}\|v-s_{A}\| \tag{14}\]  
where \(\|.\|\) denotes the Euclidean distance. The other indicators were calculated according to the following Equation. \[ASD(A,B)=\frac{1}{\big{|}S(A)\big{|}+\big{|}S(B)\big{|}}(\sum_{s_{A}\in S(A)} d(s_{A},S(B))+\sum_{s_{B}\in S(B)}d(s_{B},S(A))) \tag{15}\]  
\[TNR=\frac{|TN|}{|TN|+|FP|} \tag{16}\]  
\[TPR=\frac{|TP|}{|TP|+|FN|} \tag{17}\]  
Note that in the previous studies, researchers used data with different resolutions for training and testing, such as \(512\times 512\)[36], \(256\times 256\)[13], \(224\times 224\)[3], and \(160\times 160\)[26]. Therefore, we firstly trained the original v-net models with different sized data to evaluate the accuracy and computational efficiency. Table 1 summarized the DSC values and runtime of the liver and tumor segmentation task of three original V-net models trained utilizing different resolution data (\(512\times 512\), \(256\times 256\), and \(128\times 128\)), respectively on two databases. The experimental results showed that the model trained with \(512\times 512\) resolution data has a segmentation result improvement of about 2% for the liver and 7% for the tumor compared to the model trained with low resolution. Especially for the tumor segmentation task with a smaller target, down sampling has a greater negative influence. Therefore, we tend to train and test the models utilizing the data with \(512\times 512\) resolution. Table 2 summarizes the results obtained from the LiTS 2017 and 3D-IRCADb datasets. Compared to the models trained using only the region-based loss function (\(L_{Reg}\)), the segmentation results were improved by utilizing the joint loss functions (\(L_{HD}\), \(L_{BD}\), and \(L_{SDM}\)), which were evidenced by the indicators. The best results are shown in bold. For liver segmentation and tumor segmentation tasks, the distance-based loss functions improved the DSC by about 1.2% and 6.5% on the LiTS 2017 dataset, and they improved the DSC coefficients by 1.9% and 5.9% on the 3D-IRCADb dataset, respectively. On the LiTS 2017 test set, the HD95 reduced by 40.6% and 28.2%, while it decreased by 52.5% and 29.6% on the 3D-IRCADb test set. As for ASD, it decreased by 45.3% and 42.4% on the LiTS 2017 test set, and the decrease on the 3D-IRCADb dataset were 29.8% and 24.2%, respectively. Also, those distance-based loss functions improved the TNR of the liver segmentation and tumor segmentation tasks on the test sets. The improvement was 2.5% and 10.6% on the LiTS 2017 dataset, and 3.7% and 11.0% on the 3D-IRCADb dataset.