# Optimisation of 2D U-Net Model Components for Automatic Prostate Segmentation on MRI
## 3 Materials and Methods
### Model Architecture
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Phase**} & \multirow{2}{*}{**Network**} & \multicolumn{5}{c}{**Components**} \\ \cline{3-8}  & & **Downsampling** & **Upsampling** &
\begin{tabular}{c} **Skip Connection** \\ **within Conv Block** \\ \end{tabular} & **Drop out** & **Batch Normalisation** & **Activation** \\ \hline \multirow{3}{*}{\(1\)} & & UNet\_S & Max Pooling & Interp+Conv \({}^{*}\) & - & 0.5 & - & Relu \\ \cline{2-8}  & & UNet\_S1 & Max Pooling & Transposed Conv \({}^{*}\) & - & 0.5 & - & Relu \\ \cline{2-8}  & & UNet\_S2 & Strided Conv \({}^{\dagger}\) & Interp+Conv \({}^{*}\) & - & 0.5 & - & Relu \\ \hline \multirow{3}{*}{\(2\)} & & UNet\_S1 & Max Pooling & Interp+Conv \({}^{*}\) & Summation & 0.5 & - & Relu \\ \cline{2-8}  & & UNet\_S1.1 & Max Pooling & Transposed Conv \({}^{*}\) & Summation & 0.5 & - & Relu \\ \cline{2-8}  & & UNet\_S2.1 & Strided Conv \({}^{\dagger}\) & Interp+Conv \({}^{*}\) & Summation & 0.5 & - & Relu \\ \cline{2-8}  & & UNet\_S2 & Max Pooling & Interp+Conv \({}^{*}\) & Concatenation & 0.5 & - & Relu \\ \cline{2-8}  & & UNet\_S1.2 & Max Pooling & Transposed Conv \({}^{*}\) & Concatenation & 0.5 & - & Relu \\ \cline{2-8}  & & UNet\_S2.2 & Strided Conv \({}^{\dagger}\) & Interp+Conv \({}^{*}\) & Concatenation & 0.5 & - & Relu \\ \hline \multirow{3}{*}{\(3\)} & & UNet\_S2.1 & Max Pooling & Interp+Conv \({}^{*}\) & Concatenation & 0 & - & Relu \\ \cline{2-8}  & & UNet\_S2.0.1 & Max Pooling & Interp+Conv \({}^{*}\) & Concatenation & 0.5 & Before Activation & Relu \\ \cline{2-8}  & & UNet\_S2.0.1 & Avg Pooling \({}^{\ddagger}\) & Interp+Conv \({}^{*}\) & Concatenation & 0.5 & Before Activation & Relu \\ \cline{2-8}  & & UNet\_S2.0.1 & RMS Pooling & Interp+Conv \({}^{*}\) & Concatenation & 0.5 & Before Activation & Relu \\ \cline{2-8}  & & UNet\_S2.0.1 & \(\text{L2 Pooling}\) & Interp+Conv \({}^{*}\) & Concatenation & 0.5 & Before Activation & Relu \\ \hline \multirow{3}{*}{\(6\)} & & UNet\_S2.0.1 & \(\text{L2 Pooling}\) & Interp+Conv \({}^{*}\) & Concatenation & 0.5 & Before Activation & Relu \\ \cline{1-1} \cline{2-8}  & & UNet\_S2.0.1 & \(\text{L2 Pooling}\) & Interp+Conv \({}^{*}\) & Concatenation & 0.5 & After Activation & Relu \\ \hline \hline \end{tabular}  
* \({}^{*}\) Interp+Conv refers to nearest-neighbour interpolation and convolution layer. \({}^{*}\) Transposed Conv refers to transposed convolution layer. \({}^{\ddagger}\) Strided Conv refers to strided-convolution layer. \({}^{\ddagger}\) Avg Pooling refers to average pooling layer.  
\end{table} 
Table 1: Model architecture details. In phase 1 of the evaluation, we investigate the performance of the convolution layers in performing upsampling and downsampling. Model UNet_S1 is UNet_S where nearest-neighbour interpolation and convolution (Interp+Conv) is replaced with transposed convolution, while model UNet_S2 is UNet_S where max pooling is replaced with \(2\times 2\), 2-strided-convolution. As can be seen from the DSC results shown in Table 2 phase 1, the UNet_S downsampling and upsampling components produce the highest DSC score and hence are still preferable. For phase 2, we considered the use of a skip connection in each convolution block to improve the performance of the models in phase 1 (i.e., UNet_S, UNet_S1 and UNet_S2). Two configurations of the skip connection are considered in each convolution block of the model. Models UNet_S1, UNet_S1.1 and UNet_S2.1 have skip connections with element-wise summation (Figure 2), whilst models UNet_S2, UNet_S1.2 and UNet_S2.2 have skip connections with concatenation (Figure 2). As can be seen from Table 2 phase 2, the skip connections with element-wise summation decreases the performance of UNet_S1, UNet_S1.1 and UNet_S2.1 models as compared to the UNet_S model. On the other hand, the skip connections with concatenation improves the performance of UNet_S2, UNet_S1.2 and UNet_S2.2 models as compared to UNet_S model.