# Advancing Brain Tumor Segmentation with Spectral-Spatial Graph Neural Networks
## 3 Results and Discussion
Figure (**c**) presents the Histogram of Laplacian Eigenvalues, emphasizing low-frequency components and potential community structures. Together, these visualizations provide a concise overview of the graph’s topology, vital for signal processing and community detection. However, the integration of both spatial and spectral features in the Spectral-Spatial GNN method leads to a remarkable improvement in segmentation accuracy, precision, recall, and other metrics. This integrated approach effectively capitalizes on the complementary strengths of spatial and spectral data representations, facilitating a more comprehensive analysis of MRI scans. Such an approach is especially beneficial in the context of brain tumor segmentation, where the accurate delineation of tumor boundaries is critical for diagnosis and treatment planning. The results not only validate the hypothesis that combining spatial and spectral features can yield superior segmentation performance but also illustrate the potential of GNNs in automating and improving the reliability of medical image analysis. The evaluation of our Spectral-Spatial GNN model against established approaches in the literature reveals its superior performance in brain tumor segmentation on the BraTS dataset. As outlined in Table 5, existing methods, including YOLO2 combined with CNN, DNN integrated with SVM, and a standalone CNN approach, have shown commendable results in terms of accuracy, precision, recall, and other key metrics. However, our Spectral-Spatial GNN model demonstrates a notable enhancement in segmentation accuracy and precision, highlighting its effectiveness and efficiency. Recent studies highlight the effectiveness of machine learning in medical imaging. Object detection with YOLO2 + CNN achieved a 90% accuracy and an 87.4% Dice Score [32]. DNN combined with SVM improved the accuracy to 97.47% and the Dice Score to 93.4% [33]. A standalone CNN approach reported a 96% accuracy and a 96.2% Dice Score, emphasizing deep learning's potential [34]. Despite these advances, our Spectral-Spatial GNN model surpasses these methods with an accuracy of 99.2% and a Dice Score of 98.9%. This improvement can be attributed to the model's ability to effectively integrate spatial and spectral features, leveraging the complementary information for a more accurate segmentation of brain tumors. The model's performance emphasizes the importance of multi-dimensional feature analysis in achieving high precision and recall, critical factors in medical diagnosis and treatment planning. As demonstrated in Tables 6 and 7, the Spectral-Spatial GNN method outshines both Spatial GNN and Spectral GNN across validation and test sets for tumor sub-region segmentation, achieving superior Dice Scores and accuracy for necrotic core, enhancing tumor, and edema. This method's integrated approach, combining spectral and spatial graph analyses, allows for a nuanced representation of tumor structures, evident in its robust performance metrics; while Spatial GNN effectively utilizes local connectivity and Spectral GNN focuses on global patterns, they fall short in capturing the comprehensive tumor landscape as effectively as the Spectral-Spatial GNN. This model's ability to accurately segment \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Metric** & **Spatial GNN** & **Spectral GNN** & **Spectral–Spatial** \\ \hline Accuracy & 92.5\% & 95.3\% & 99.2\% \\ Precision & 91.8\% & 94.6\% & 98.7\% \\ Recall & 92.2\% & 95.0\% & 99.0\% \\ Dice Score & 91.7\% & 94.5\% & 98.9\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of GNN methods for whole tumor segmentation \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Metric** & **[32] YOLO2 + CNN** & **[33] DNN, SVM** & **[34] CNN** \\ \hline Accuracy & 90\% & 97.47\% & 96\% \\ Precision & 91.5\% & 92.3\% & 94.1\% \\ Recall & 94.5\% & 91.4\% & 93.4\% \\ AUC & 95.7\% & 93.4\% & 95.2\% \\ Dice Score & 87.4\% & 93.4\% & 96.2\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of other approaches.