## 2 Materials and Methods
### Segmentation Method  
Despite frequent proposals of newer architectures and frameworks, current state-of-the-art deep-learning-based methods, including QuickNAT [17] and nnU-Net [35], are based on the U-Net architecture, one of the most popular CNN architectures for medical imaging. We also employed the U-Net [48] architecture to segment the thalamus, as it represents a baseline segmentation result for the proposed benchmark.  
To segment the thalamus using a multimodality dataset, the U-Net model was trained with a multichannel input: each channel received T1w or diffusion images (Figure 7). This is the standard U-Net architecture, which is able to handle any amount of input channels by changing the corresponding hyperparameter [49; 50; 51; 52; 53]. When using more than one channel, the U-Net fuses all input channels in the first convolutional layer, transferring features extracted from all inputs to the inner layers.  
We used image patches throughout the training and fine-tuning procedures, as U-Net is a fully-convolutional neural network (FCNN) [54], whose training and prediction phases do not require images of the same size. This is advantageous for many reasons: it increases the amount of training data; it makes the model more immune to location variance, as the thalamus may be present anywhere within a patch; it balances the amounts of background and foreground present during training; and it simplifies the extraction of 2D images from the 3D MRI to feed the 2D CNN architecture.  
For the output, we employed a softmax activation with two channels for the background and thalamus (foreground), respectively. The target for the output was the thalamus segmentation mask, guided by a soft Dice loss [55]. During fine-tuning, we exploited the encoder-decoder nature of the U-Net, freezing the pre-trained encoder and updating only the decoder weights.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & & & \multicolumn{3}{c}{**Labels**} \\ \cline{3-7}
**Dataset** & **Subjects** & **Freesurfer** & **fsl\_anat** & **QuickNAT** & **STAPLE** & **Manual** \\ \hline Training & 963 & yes & yes & yes & yes & no \\ \hline \multirow{2}{*}{Fine-tuning} & 16 & yes & yes & yes & yes & yes (non-expert) \\ \cline{2-7}  & 24 & yes & yes & yes & yes & yes \\ \hline Testing & 20 & yes & yes & yes & yes & yes (benchmarking) \\ \hline Reserved & 40 & yes & yes & yes & yes & no \\ \hline \hline \end{tabular}
\end{table}
Table 2: Dataset for benchmark, its division for CNN model development and evaluation, and available labels. Manual labels for the testing set exist but are not publicly available on the benchmark platform.  
The aforementioned training strategy can be applied to multiple models. We used a multi-view 2D approach to obtain a volumetric thalamus segmentation (Figure 7). First, we predicted the volumetric segmentation three times using different 2D CNN models trained for each respective slicing orientation (axial, sagittal, and coronal). Subsequently, the three volumetric predictions were combined into a single final prediction volume as follows: \(Seg=((A+S+C)/3)>0.5\). Here, \(A\), \(S\), and \(C\) denote the activations for the axial, sagittal, and coronal networks, respectively. Although such a view aggregation requires more computation than a single-view 2D CNN, it significantly improves segmentation quality, primarily by eliminating low-confidence misclassified voxels from the predictions [56]. Furthermore, it requires considerably less computational resources than an equivalent 3D approach. The latter does not guarantee superior performance to the single-view 2D approach [57]. In fact, prior studies have shown equivalent results when comparing 2D view aggregation with the 3D convolutional approach [17; 58; 59].