## 2 Materials and Methods
### Proposed Model Architecture
Deep supervision introduces supervision into the neural network's hidden layers to directly influence their parameters in favor of highly discriminative features [37]. To achieve this, two loss functions, Cross Entropy Loss and Dice Loss, are combined for each of the four semantic labels [38]. Atrous convolution effectively enables feature maps to be computed at the desired resolution without significantly increasing computational costs. It achieves this by utilizing a kernel with spaces between values, as defined by the dilation rate, offering an increased field of view without added computational expenses [39]. Spatial pyramid pooling is a type of pooling layer that can accommodate input images of varying sizes, by pooling the features into a fixed-length representation of the initial input vector in spatial bins. The bins' outputs are kM-dimensional, where k represents the number of filters in the final convolutional layer, and M denotes the number of spatial bins [40]. To alleviate any potential increase in computational complexity associated with spatial pyramid pooling, atrous convolution is integrated into the approach [41]. Four parallel atrous convolutional layers of varying dilation rates capture multi-scale information. As the dilation rate increases, the number of valid filter weights diminishes, and global average pooling is employed on the last feature map of the model. The resulting features are subsequently fed into a 1 \(\times\) 1 convolution. Finally, depthwise separable convolution encompasses depthwise convolution, performing a spatial convolution for each input channel, followed by pointwise convolution, where the outputs from the depthwise convolution are combined. In the proposed model, atrous convolution is incorporated into depthwise convolution, effectively reducing computational complexity while maintaining performance levels. To provide interpretation of the behavior of the deep learning models, gradient-weighted class activation mapping [42], a visual XAI method, is employed, as illustrated in the architecture diagram in Figure 3. This method leverages the gradients of a specific class, in this case, the water class, as they flow into a target layer to generate a heatmap where the regions of the input image that were most influential in the model's decision-making are highlighted. The heatmap \(L^{c}\) is generated by first determining the target class \(c\) with respect to the feature map activations \(A^{k}\) of the target layer \(\frac{\partial y^{c}}{\partial A^{k}}\). Global average pooling is then applied over the width \(i\) and height \(j\) of the image, to provide the weight of importance for each neuron, as in Equation (3). \[\alpha_{k}^{c}=\frac{1}{Z}{\sum_{i}}{\sum_{j}}\frac{\partial y^{c}}{\partial A _{ij}^{k}} \tag{3}\]  
ReLU is then applied to a weighted combination of the activation maps computed from the forward pass of the model, so that the highlighted pixels are only those that have a positive influence on the prediction of the target class, resulting in the final heatmap as shown in Equation (4). \[L^{c}=ReLU\left(\sum_{k}\alpha_{k}^{c}A^{k}\right) \tag{4}\]