# 3D Liver and Tumor Segmentation with CNNs Based on Region and Distance Metrics
## 4 Comparison and Discussion  
As mentioned in Equations (1)-(3), \(\alpha\) is regarded as a hyperparameter that adjusts the function proportion based on regional loss and distance-based loss. According to the previously mentioned rules, the value of this parameter maintained at 1 during the first 400 epochs, and it gradually dropped to 0.01 during the next 1000 epochs. Considering that the models were tested on the test set for every 40 epochs, the setting of \(\alpha\) is discussed based on the results of each test. Typically, the set interval of the \(\alpha\) value for similar problems could be summarized according to the \(\alpha\) value of the optimal model on different databases. As observed from Figure 5, the DSC coefficients of the joint training model were improved on the two databases with the decrease in the \(\alpha\) value. The best results for each model were obtained at the \(\alpha\) value of 0.4-0.6. However, as \(\alpha\) continues to decrease, the DSC coefficients of all models did not continue to improve, but even exhibited a downward trend in some columns. When the value of \(\alpha\) is between 1.0-0.7, the loss function is mainly based on the regional loss. As mentioned above, it may affect the training stability and performance due to the highly imbalanced data. However, when the value of \(\alpha\) is less than 0.4, the loss function is dominated by the distance-based loss, which may make the function fall into a local minimum. In general, Thus, the recommended interval for the distance-based loss weight (1-\(\alpha\)) in the joint training strategy is 0.4-0.6. Figure 4: The visual comparison of segmentation results. The ground-truths are denoted in red, and the results are in blue. The first three rows are the results of liver segmentation; the last three rows are the results of tumor segmentation. Each column represents the results obtained, utilizing different loss functions. Some studies point out that the earlier use of distance-based loss may lead to convergence to a local minimum or saddle point [30]. In this paper, the solution for this problem was to utilize the regional loss function only in the first period of training to avoid falling into local minima. Then, after the training entered the platform period, the distance-based loss weight gradually increased to fine-tune the results. This strategy was conceptually similar to the energy on the basis of the classical contour for the segmentation of the level set, such as the active geodesic contour [38], which also required additional regional terms to avoid trivial solutions. Taking the model based on SDM loss function as an example, according to our experimental findings in Table 4, the models utilizing the training strategy proposed in this paper achieved higher results on two databases, respectively. A comparison of our approach with similar approaches is given in Table 5. Some values were missing because they were not available in the original article. On the LiTS 2017 dataset, compared with the other methods in the table, the algorithm in this paper obtained the best results in the liver segmentation task. It also surpassed most methods in the tumor segmentation task. Our algorithm achieved the highest DSC score, while our ASD score was slightly higher than the ASD scores in [3, 45]. Figure 5: The test results on two databases with different \(\alpha\) values. (**a**) The test results of models with HD loss on LiTS 2007. (**b**) The test results of models with HD loss on 3D-IRCADb. (**c**) The test results of models with BD loss on LiTS 2007. (**d**) The test results of models with BD loss on 3D-IRCADb. (**e**) The test results of models with SDM loss on LiTS 2007. (**f**) The test results of models with SDM loss on 3D-IRCADb. On the 3D-IRCADb dataset, the algorithm in this paper obtained the highest DSC score in the liver segmentation task, and the ASD score was only higher than the results in [47; 48]. As for the tumor segmentation task, our method obtained the best results on the two indicators of DSC and ASD.