## 6 Conclusions  
This study presents a novel approach to the accurate Quality Assessment of graph-based images in 3D ECT. By adopting state-of-the-art GQA methods and developing a 3D ECT tomography-based dedicated benchmarking system, we established a robust framework for evaluating the quality of graph-based 3D ECT reconstructions. Specifically, we proposed tailored Graph Quality Assessment (GQA)-based methods, and we demonstrated their effectiveness in evaluating the quality of graph-based 3D Electrical Capacitance Tomography (ECT) image reconstructions. By adapting various image Quality Assessment methods to the graph-based image representation, resulting in our proposed Group Peak Signal-to-Noise Ratio (G-PSNR), Group Structural Similarity Index Measure (G-SSIM), and Histogram Comparison (HC), we have shown that these methods can accurately assess the similarity between reconstructed and reference images. Specifically, our results indicate that the G-SSIM method with node grouping depths of 1 and 2 achieves the most effective error reduction, while the PSNR method is the fastest among the examined GQA methods.  
The experimental results presented in this paper highlight the robustness of the proposed GQA methods in evaluating the quality of graph-based 3D ECT image reconstructions. Specifically, the visual and numerical results for the selected examples of various-shaped phantoms demonstrate the effectiveness of these methods in accurately assessing the similarity between reconstructed and reference images. These findings could contribute to advancing 3D ECT imaging by providing a reliable and effective means for evaluating the quality of graph-based image reconstructions.  
Future work could build upon this study by exploring the development of methods that can directly compare graph structures, rather than relying on image-based Quality Assessment metrics. This could involve adapting graph-comparison algorithms, such as graph edit distance or graph kernel methods, to the specific requirements of 3D ECT image reconstruction. The development of new GQA methods that can handle complex graph structures and varying node densities could further enhance the accuracy of Quality Assessment in 3D ECT. Furthermore, the integration of GQA methods with machine learning algorithms could enable the development of automated quality control systems for 3D ECT imaging. By continuing to advance the field of Quality Assessment for 3D ECT, researchers and practitioners can work towards improving the reliability and accuracy of this imaging modality, ultimately leading to better process monitoring and control in industrial settings.  
**Author Contributions:** Conceptualization, R.B. and A.F.; methodology, M.B.; software, M.B.; validation, R.B., M.B. and A.F.; formal analysis, R.B., M.B. and A.F.; investigation, M.B.; resources, R.B.; data curation, M.B.; writing--original draft preparation, M.B.; writing--review and editing, R.B. and A.F.; visualization, M.B.; supervision, R.B. and A.F.; project administration, R.B. and A.F. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The raw data supporting the conclusions of this article will be made available by the authors on request.  
**Conflicts of Interest:** The authors declare no conflicts of interest.