# Focal Dice Loss-Based V-Net for Liver Segments Classification
## 4 Conclusions and Future Works  
In this paper, we proposed two novel focal Dice loss formulations for liver segments' classification and compared them with the previous one presented in the literature. The problem of correctly identifying liver segments is pivotal in surgical planning, since it can allow more precise surgery, as performing segmentectomies. In fact, according to the Couinaud model [5], hepatic vessels are the anatomic boundaries of the liver segments. Therefore, in current hepatic surgery, the identification of the liver vessel tree can avoid the unnecessary removal of healthy liver parenchyma, thus lowering the risk of complications that can arise from larger reseptions [7]. Despite this, in the literature, many authors that focused on liver segments' classification methods usually only provided visual assessment (as [6,45]), making it difficult to benchmark different algorithms for this task. Thanks to the work of [PERSON] et al. [21], a huge dataset composed of CT scans with liver segments' annotation is now publicly available, using the development and evaluation of algorithms suited for the task. Our CNN-based approach allowed us to obtain reliable results, with the best formulation, \(FDL^{A}\) with \(\gamma=2\), obtaining an average Dice coefficient higher than 83% and an average accuracy higher than 98%. The adoption of a rule-based post-processing, which implements a mechanism for detecting and resolving inconsistencies across axial slice images, allowed slightly improving the obtained results for different models. Given that the difference between the models was exiguous, it may be necessary to exploit a different model to assess a clearer difference between these loss functions. A limitation of this work is the absence of an external validation dataset, which is due to the facts that there is a lack of annotated datasets with liver segments and it is very expensive to create a local one labeled by radiologists. Furthermore, with more GPU memory available, more complex 3D architectures capable of handling a larger context can be exploited, whereas in this work, we limited this to five slices at once. As future work, we note that another possible way to approach this task consists of determining regression planes using a 3D CNN. Even if there are classical approaches (as [PERSON] et al. [45]) devoted to the estimation of these cutting planes, there are actually no DL-based approaches in this direction ([PERSON] et al. [21] and [PERSON] et al. [47], as us, developed a semantic segmentation model), which can be more resilient to overfitting and to the prediction of inconsistent segments' classification. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Paper** & **Method** & **Dataset** & **Dice per Case** \\ \hline \hline \multirow{5}{*}{[PERSON] et al. [21]} & GLC U-Net & & \(92.80\pm 3.80\) \\ \cline{2-4}  & U-Net & & \(83.86\pm 5.44\) \\ \cline{2-4}  & U-Net 2.5D & MSD 08, n = 193 & \(89.04\pm 4.30\) \\ \cline{2-4}  & U-Net 3D & & \(88.93\pm 4.44\) \\ \cline{2-4}  & U-Net with convolutional LSTM & & \(90.06\pm 4.01\) \\ \hline \hline \multirow{5}{*}{[PERSON] et al. [47]} & FCN [48] & & \(82.60\pm 4.29\) \\ \cline{2-4}  & U-Net [46] & & \(83.80\pm 4.01\) \\ \cline{2-4}  & U-Net++ [50] & & \(82.69\pm 4.57\) \\ \cline{2-4}  & nnU-Net [51] & Local Dataset, n = 500 & \(81.70\pm 4.12\) \\ \cline{2-4}  & AU-Net [52] & & \(82.31\pm 4.23\) \\ \cline{2-4}  & PraNet [53] & & \(83.03\pm 4.28\) \\ \hline [PERSON] et al. [45] & Geometric fit algorithm & SLIVER07 [62], n = 20 & N/A \\ \hline [PERSON] et al. [6] & Nearest Neighbor Algorithm & Local Dataset, n = 43 & N/A \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Literature overview for liver segments’ classification. Quantitative results are not available for [6,45], since they only provided visual assessment of the segments’ classification. **Author Contributions:** Conceptualization: B.P., N.A., A.B. and V.B. ; methodology: B.P., N.A., A.B. and V.B. ; software: B.P. and N.A. ; visualization: B.P. and N.A.