# Multi-Task Learning for Small Brain Tumor Segmentation from MRI
## 3 Materials and Method
### Proposed Network Architecture  
Our proposed method is based on two observations. Firstly, the size of brain tumors is various. Secondly, the U-Net cannot detect the tumor with a small size, especially the enhancing tumors, which have the smallest size. Some of the previous methods, they just focus on improving the performance.  
There are still some unsolved issues including missing tumors and poor detection/segmentation performance on small-sized tumors. For small object segmentation, context is one of the most important elements [6]. In a typical U-Net, the down-sampling layers are useful for feature extraction and extending receptive fields. However, they lose an important element, which is the resolution. Through downsampling layers, the feature resolution is gradually reduced. As a result, the features of small objects can be lost. Once those features are lost, they are difficult to recover in spite of the effort of skip connection [5;6]. Therefore, we need a method to be able to retain the features of small objects, even if the resolution is reduced. The architecture of our model is shown in Figure 1. Our model employed a multi-task learning with two tasks. The main task was brain tumor segmentation and additional feature reconstruction was used for an auxiliary task. The model inputted four MRI modalities and outputted a segmented mask of regions including whole tumor, tumor core, and enhancing tumor. In particular, we added an upsampling layer and an MF unit for reconstructing features after encoder layers. By applying this technique, important features were retained in the following layers and reduced the side effects of downsampling layers on small tumors. As shown in Figure 1, U-module was formed by 3 DMF units, one MR unit, and an upsampling layer. The first DMF unit will reduce the size of the feature map. After two DMF units, the feature map resolution was the same and we added an upsampling layer and an MF unit to upsample the feature map to create a reconstructed feature map with the same size as the previous feature map. In detail, the operation of the U-module is described as the following formula:  
\[\varphi:F\to Z \tag{1}\]  
\[\rho:Z\to F \tag{2}\]  
\[\varphi,\rho=\begin{array}{c}argmin\|F-\left(\varphi^{\circ}\rho\right)F\|^ {2}\\ \varphi,\rho\end{array} \tag{3}\]  
where the \(\varphi\) and \(\rho\) transitions present the encoder and decoder of the U-module. The encoders compress the original feature map \(F\) into a smaller feature map \(Z\). The decoder using the upsampling layer and MF unit to recover the original feature map. The difference between the reconstructed map and the features map is minimized so the small feature map can represent the large feature map. This way, the most important and relevant features of the previous layer will be retained in the next layer. In our model, we used two U-modules at the first and second encoder layers because those layers had the largest feature resolution to be kept. In addition to helping our model retain the properties of small tumors, the U-module can also improve parameter initialization as its original purpose.