## 5 Experiments and Results
Figure 9: Comparison of Wilcoxon rank sum test of each heart structure for different architectures on the MMWHS MRI testing dataset. Figure 11: Comparison of the results for four different network architectures. (**a**) the input original MRI images; (**b**) segmentation results of Pre-ResNet without VAE; (**c**) segmentation results of Pre-ResNet with VAE; (**d**) segmentation results of FM-Pre-ResNet without VAE; (**e**) segmentation results of the proposed FM-Pre-ResNet with VAE obtains the most accurate results on the testing dataset. Figure 10: Comparison of the results of four different network architectures. (**a**) the input original CT image; (**b**) segmentation results of Pre-ResNet without VAE; (**c**) segmentation results of Pre-ResNet with VAE; (**d**) segmentation results of FM-Pre-ResNet without VAE; (**e**) segmentation results of proposed FM-Pre-ResNet with VAE obtains the most accurate results on the testing dataset. Furthermore, Pre-ResNet has demonstrated that increasing the depth of the network improves model performance significantly. The addition of two convolutional layers at the top and bottom of the pre-activation residual block introduced in our FM-Pre-ResNet unit allows for the feature fusion block to reach the same depth with fewer parameters which benefits model performance. Therefore, the proposed type of connectivity of the FM-Pre-ResNet unit in terms of depth and number of parameters regarding Pre-ResNet implies no increase in the number of parameters compared to the Pre-ResNet. Time-wise, each training epoch (200 cases) and prediction times on two GPU-s (NVIDIA Titan V) are significantly reduced with architectures with VAE. This shows the computational efficiency of our choice for VAE introduction. Comparison of depth, number of parameters, training times per epoch, and prediction time of one volume for different architectures is shown in Table 5.  
Comparison with State-of-the-Art Methods  
The proposed approach was compared with other similar deep learning approaches in terms of image segmentation accuracy as shown in Tables 6 and 7. An approach that combines atlas registration with CNNs' [12] provides an incremental segmentation that allows user interaction, which can be beneficial in a clinical setting. Nevertheless, the challenges of accurate atlas registration resulted in low accuracy on MRI images. The  
Figure 12: 3D visualization of the best and worse cases of WHS results in the CT and MRI test datasets. \begin{table}
\begin{tabular}{c c c c c} \hline
**Architecture** & **Depth** & **Number of Parameters** & **Training Time** & **Prediction Time** \\ \hline
3D Pre-ResNet & 110 & 23.48 & 10 & 0.7 \\
3D Pre-ResNet + VAE & 110 & 26.18 & 8 & 0.6 \\
3D FM-Pre-ResNet & 218 & 22.54 & 9 & 0.5 \\
3D FM-Pre-ResNet + VAE & 218 & 25.14 & 7 & 0.4 \\ \hline \end{tabular}
\end{table} 
Table 5: Comparison of depth, number of parameters (\(\times 10^{6}\)), training times per epoch (min), and prediction time (s) for one volume for different architectures: Pre-ResNet, 3D Pre-ResNet + VAE, FM-Pre-ResNet, and FM-Pre-ResNet + VAE. deep supervision mechanism [23] and use of transfer learning [21] result in an increase of trainable parameters and overall network complexity. In contrast, we aim to introduce a light-weight network that results in a significantly deep network without increasing the parameter number. Moreover, the authors in [21] report an average WHS DSC of \(0.914\pm 0.075\) on CT images and \(0.890\pm 0.054\) on MRI images using a hold-out set of 10% of training data and evaluate their method with 10-fold cross-validation. Our results report \(0.9039\pm 0.0517\) on CT images and \(0.8950\pm 0.0215\) on MRI images and are evaluated on all unseen 40 subjects, which shows that the VAE stage's introduction significantly helps in overcoming overfitting problems. Therefore, these results highlight the advantages of our proposed method.