## 5 Conclusions  
In this paper, a new cascaded 2.5D FCNs learning framework based on the boundary loss function is proposed to segment the liver and tumor of 3D medical images. Specifically, we integrate distance, area and boundary information as a boundary loss to optimize the parameters of the networks. Boundary loss will force the cascaded 2.5D FCNs to learn more boundary and contour features, so as to improve the segmentation performance of the network. To accurately extract the shapes of the liver and tumor, two types of post-processing for the liver and tumor are adopted for the results with the 2.5D learning framework. Compared with the 2D model and 3D model, the proposed 2.5D network framework can explore sufficient 3D context information while minimizing computing resource requirements. The boundary loss function can optimize the network to learn the features of the boundaries in the observed objects to achieve a smoother segmentation effect for the target boundary.  
Although our method can explore specific 3D spatial characteristics, it is still inadequate compared with some 3D models. In addition, the boundary loss function cannot learn the boundary features effectively if the boundary is staggered and too complicated. Therefore, in the future, we will try to plug a dual path attention mechanism module [59] into our model. Dual path attention can incorporate the position and channel feature information and capture more spatial information in the intra-slices and inter-slices of the 3D medical data. At the same time, we will revise the 2.5D network to a lightweight 3D deep learning network. A 3D surface loss based on boundary loss will be implemented and embedded in a lightweight 3D deep learning network. In fact, we have implemented most of the work, but the details of the work are still to be tested for a better segmentation performance.  
Writing--original draft, X.L.; Writing--review--editing, X.L. and Y.H.; Software, X.L.; Validation, X.L.; Visualization, X.L.; Funding acquisition, Y.H.; Supervision, B.W. and L.W.; Formal analysis, X.L.; Methodology, X.L.; Investigation, X.L. All authors have read and agreed to the published version of the manuscript.  
This research is sponsored by the National Key Research and Development Program of China (Grant Nos. 2020 YFB074503, 2018 YFB0704400, and 2018 YFB0704402), and the Program for  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Tumor**} & \multicolumn{2}{c}{**Liver**} \\ \cline{2-5}
**Loss** & **Dice Per Case** & **Dice Global** & **Dice Per Case** & **Dice Global** \\ \hline
2D UNet [16] & 65.0 & - & - & - \\
2D FCN [9] & 67.0 & - & - & - \\
3D V-Net [43] & - & - & - & 93.9 \\ [PERSON] et al. [17] & 0.680 & 0.796 & - & - \\ [PERSON] et al. [54] & 65.7 & 82.0 & **96.3** & **96.7** \\
3D H-DenseUNet [18] & 72.2 & 82.4 & 96.1 & 96.5 \\
3D AH-Net [55] & 63.4 & **83.4** & - & - \\ Med3D [56] & - & - & - & 94.6 \\
3D-DenseUNet [57] & 69.6 & 80.7 & 96.2 & 96.7 \\ [PERSON] et al. [58] & - & 70.2 & - & 95.1 \\ our method & **74.5** & 77.2 & 94.3 & 96.1 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of liver and tumor segmentation results on the LiTS dataset (Dice: %).  
Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, Natural Science Foundation of Shanghai (Grant No. 20 ZR1419000).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** All data used in this work were obtained from open-source, publicly-available repositories.  
**Conflicts of Interest:** The authors declare no conflict of interest.