## 2 Materials and Methods
### The Adapted Architectures for Brain Tumor Segmentation  
The architectures analyzed and fine-tuned were FCN (Fully Convolutional Network) [40], PSPNet (Pyramid Scene Parsing Network) [41], and DeepLab [42; 43]. For the weight initialization of these encoder-decoder networks, ResNet50 and 101 are used. The ResNet (Deep Residual Networks) architecture was presented in paper [44]. The authors solved the problem of the vanishing gradient. Until this network was introduced, the number of layers of a CNN was limited to below 20-30 convolutional layers. This residual module learns the difference between the input and output of every convolutional layer. The gradient at the output of a layer is equal to the gradient at the input plus the residual. Only the residual part passes through 2 or 3 other CNN layers. Thus, any further layer added does not output worse than previous layers. The architectures created in this way were ResNets 18, 34, 50, 101, and 152. In our experiments, we applied ResNet50 and ResNet101. ResNet50 is based on ResNet34, but instead of 2, each residual block is built out of 3 layers. The first layer is a \(7\times 7\) convolutional layer of a depth of 64, obtaining half of the original image size. After this first layer, the filter size is always \(3\times 3\). Next are the 4 dimension-reduction stages, each reducing into half the size of the previous stage, while at the same time, the layer depth doubles (3 residual blocks 64 depth at size/2, 1 shortcut connection +3 residual blocks depth 128, 1 + 5 depth 256, and 1 + 2 depth 512 at size/32). Instead of 1 + 5 residual blocks between size/8 and size/16, ResNet101 uses 1 + 22 residual blocks. In our case, the dimension of the full size is \(240\times 240\), and the last size/16 is \(15\times 15\) pixels. The original FCN architecture [40] is the fully connected version of the VGG-16 network. The encoder-decoder network leaves the encoder part the same as it is in VGG-16, and the fully connected layers of VGG are replaced by fully convolutional layers to form the deconvolutional part of the architecture (Figure 1). The classification layer is substituted by a bottleneck layer of \(1\times 1\) kernel. Down-sampling is carried out by pooling layers and up-sampling is performed by deconvolution layers. In total, there are 5 stages of halving and a corresponding 5 stages of doubling the previous feature maps from the input size of \(W\times H\) and \(W/2^{5}\times H/2^{5}\) downwards (encoding part) and vice versa in the decoding part until the original size is reached. There are 2 convolutional layers in the full size followed by 2 convolutional layers in the half-size \(W/2\times H/2\) and 3 convolutional layers in the \(W/2^{2}\times H/2^{2}\), \(W/2^{3}\times H/2^{3}\), and \(W/2^{4}\times H/2^{4}\) sizes. The up-sampling upconvolutional layers follow the same pattern. The convolutional kernels are \(3\times 3\) in each layer with corresponding stride and padding to maintain the same output size for each conv-layer. In our experiments, the VGG encoder part is replaced by the ResNet50 and ResNet101 architectures that are incorporated into the FCN architecture (Figure 2). PSPNet Spatial Pyramid Pooling Network [41] idea is combining global and local features in different subregions. First, the image is fed into a convolutional network of  
Figure 1: VGG-FCN Architecture: 15 convolution layers; 5 pooling layers; 5 deconvolution layers (their input is the sum of previous layer and the output of the corresponding convolution layer). Figure 2: ResNet-FCN Architecture: the first part is the encoder module (the ResNet50 or the ResNet101 architectures) and the second part is the 5-times upconvolution. ResNet-based FCN, and then the pyramid module is applied. Here, the features are computed into 4 different scales: a global pooling that generates a single output. Moreover, \(1\times 1\) the \(2\times 2\), \(3\times 3\), and \(6\times 6\) subregions are obtained using the corresponding pooling kernel sizes. Thus, different-sized feature maps are formed.