## 3 Results
### Segmentation of the Myocardium in Tagged CMR Images
#### 3.2.1 Model Architecture  
In this work, two distinct model architectures were implemented and tested: ResNetVAE and nnUnet. Whilst they are both based on an encoder-decoder mechanism, the more commonly used nnUnet has approximately ten times more trainable parameters than ResNetVAE, as detailed in Table 2. Above that, the variational auto-encoder of ResNetVAE ensures that training is regularised to avoid overfitting by constraining the distribution of the latent space. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Architecture** & **No. Parameters** & **Training Time** & **Inference Time** \\ \hline
**ResNetVAE** & 3555891 & 64.3 s/epoch & 112 ms \(\pm\) 28.7 ms \\
**nnUnet** & 34164258 & 163.2 s/epoch & 661 ms \(\pm\) 274 ms \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Training and inference statistics for the trained network architectures. Training is performed on batches of 128 images of size [256; 256] in parallel on two TITAN RTX GPUs with 24 GB of memory each. Inference time statistics are measured on seven runs of a batch of one image. Figure 5: Examples of _cine_ to tagged image transformation performed by (**B**) the physics-driven transformation and (**C**) the trained CycleGAN on (**A**) a set of labeled images from the ACDC dataset, completely disjoint from the dataset used to train the CycleGAN. While all segmentations seem to present a consistent disc-looking shape, the masks produced by the ResNetVAE seem to be physiologically more consistent than the ones produces by the nnUnet (Figures 6 and 7). A common prediction error is the inclusion or exclusion of a short sequence of dark squares delimited by intersecting taglines. An error specific to the nnUnet pretrained with the physics-driven simulated tagged images is the presence of holes within the region of interest. The ResNetVAE outperforms the nnUnet by 4.3 percentage points of average DSC and 1.10 mm of HD-95 (Table 3). Additionally, the training performance metrics are closer to the associated test scores for the ResNetVAE architecture. The nnUnet likely has too much capacity, leading to a tendency to overfit more in comparison to the smaller ResNetVAE with its regularized latent space. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{**DSC (\(\uparrow\))**} & \multicolumn{3}{c}{**HD-95 [mm] (\(\downarrow\))**} \\ \multirow{2}{*}{**Model**} & **Split** & \multicolumn{3}{c}{**Train**} & \multicolumn{3}{c}{**Test**} & \multicolumn{3}{c}{**Train**} & \multicolumn{3}{c}{**Test**} \\  & **Strategy** & **Avg.** & **Std.** & **Avg.** & **Std.** & **Avg.** & **Std.** & **Avg.** & **Std.** \\ \hline \multirow{4}{*}{**nnUnet**} & **Scratch** & 0.894 & 0.021 & 0.771 & 0.084 & 2.519 & 0.554 & 7.219 & 5.075 \\  & **Cine** & 0.895 & 0.020 & 0.770 & 0.078 & 2.325 & 0.545 & 6.700 & 3.435 \\  & **Physics-driven** & 0.895 & 0.020 & **0.785** & 0.054 & 3.115 & 0.871 & **5.846** & 1.625 \\  & **CycleGAN** & 0.894 & 0.020 & 0.779 & 0.074 & 2.385 & 0.569 & 6.117 & 2.087 \\ \hline \multirow{4}{*}{**ResNetVAE**} & **Scratch** & 0.872 & 0.027 & 0.801 & 0.065 & 3.301 & 0.746 & 5.616 & 1.989 \\  & **Cine** & 0.820 & 0.100 & 0.818 & 0.096 & 6.621 & 8.741 & 5.647 & 5.549 \\ \cline{1-1}  & **Physics-driven** & 0.895 & 0.023 & 0.811 & 0.068 & 2.517 & 0.564 & 5.407 & 3.350 \\ \cline{1-1}  & **CycleGAN** & 0.898 & 0.022 & **0.828** & 0.049 & 2.481 & 0.572 & **4.745** & 1.537 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance metrics for the evaluated architectures, training strategies, and data splits. Displayed are the Dice coefficient (DSC) and 95 th percentile Hausdorff Distance (HD-95) for which higher and lower are better, respectively. The average (Avg.) and standard deviation (Std.) statistics are computed over the training and testing data splits containing 1000 and 250 2D SAX tagged MR images, respectively.