# The Fusion of MRI and CT Medical Images Using Variational Mode Decomposition
## 3 Results and Discussion
### Objective Assessment  
Here, we assess the fused image quality objectively using fusion metrics. Tables 3-5 demonstrate the objective assessment of the three fatal-stroke images proposed and other existing approaches (sets: 7, 11, and 15) subjectively analyzed earlier. In addition, we have presented the average objective metric scores of all the 23 sets (fatal-stroke)in Table 6. Fusion metrics except for RMSE with the first highest values are highlighted in bold font, and the second-highest values are underlined. The first-lowest value of the RMSE is indicated in bold, and the second-lowest value is underlined. A number within the bracket at the end of the quantitative metric scores represents the rank of the fusion algorithm. In these Tables, the ranking scheme is considered for better quantitative analysis of fusion algorithms. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Metrics**} & \multicolumn{8}{c}{**Methods**} \\ \cline{2-9}  & **ASR** & **CVT** & **DTCWT** & **MSVD** & **CSMCA** & **NSST** & **Proposed Method** \\ \hline EI & 85.184 & **91.417 (1)** & 88.853 & 77.183 & 87.219 & 81.907 & 90.390 (2) \\ \hline MI & **3.948 (2)** & 3.548 & 3.656 & 3.490 & 3.811 & 3.703 & **4.079 (1)** \\ \hline VIFF & 0.321 & 0.290 & 0.280 & 0.344 (2) & 0.319 & 0.267 & **0.406 (1)** \\ \hline \(Q_{P}^{AB/F}\) & 0.535 & 0.478 & 0.500 & 0.427 & 0.536 (2) & 0.373 & **0.538 (1)** \\ \hline SSIM & 0.563 & 0.376 & 0.499 & 0.548 & 0.629 (2) & 0.520 & **0.697 (1)** \\ \hline AG & 8.561 & **9.140 (1)** & 8.933 & 8.332 & 8.674 & 8.368 & 9.008 (2) \\ \hline RMSE & 0.034 & 0.034 & 0.034 & 0.034 & 0.035 & 0.027 (2) & **0.020** \\ \hline PSNR & 16.328 & 16.749 & 17.166 & 13.28 & 17.393 (2) & 13.976 & **21.342 (1)** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quantitative analysis of various fusion methods for MRI-CT (set-7). Figure 9: The results of various methods on next 13 pairs of MRI-CT images (fatal stroke). Comprehensively, the proposed framework is the only approach that occupies the first two ranks for all eight metrics among all the seven methods. It indicates that our method has robust performance (i.e., stable and promising performance) than other existing techniques. Specifically, our approach always remains in the first position on VIFF and RMSE for all four data sets, as shown in Tables 3-5. Average quantitative analysis of the proposed and other state-of-the-art methods calculated over 23 pairs of MRI-CT (fatal stroke) are presented in Table 6. The proposed \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Metrics**} & \multicolumn{6}{c}{**Methods**} \\ \cline{2-9}  & **ASR** & **CVT** & **DTCWT** & **MSVD** & **CSMCA** & **NSST** & **Proposed Method** \\ \hline EI & 57.800 & 64.531 & 61.820 & 50.850 & 58.592 & 62.404 & **64.582** \\ \hline MI & 3.666 & 3.360 & 3.446 & 3.694 & 3.657 & 3.740 & **3.830** \\ \hline VIFF & 0.376 & 0.362 & 0.358 & 0.365 & 0.401 & 0.364 & **0.498** \\ \hline Q\({}_{p}^{AB/F}\) & 0.541 & 0.483 & 0.500 & 0.399 & 0.531 & 0.439 & **0.542** \\ \hline SSIM & 0.651 & 0.350 & 0.503 & 0.614 & 0.634 & 0.586 & **0.657** \\ \hline RMSE & 0.029 & 0.029 & 0.029 & 0.029 & 0.029 & 0.022 & **0.020** \\ \hline AG & 5.772 & 6.390 & 6.148 & 5.427 & 5.771 & 6.217 & **6.412** \\ \hline PSNR & 16.803 & 16.972 & 17.242 & 16.000 & 17.757 & 16.021 & **20.291** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Average quantitative analysis of the proposed method (23 pairs of MRI-CT) and other state-of-the-art methods.