## 5 Result and Discussion
### Application for MRI-Based Brain Tumor
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multirow{2}{*}{**Dataset**} & \multicolumn{8}{c}{**Number of Clusters (K)**} \\ \cline{3-10}  & & & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline \multirow{8}{*}{**Normal**} & \multirow{4}{*}{**GMM**} & IM01 & 0.5498 & 0.3488 & 0.539 & 0.4553 & 0.6949 \({}^{*}\) & 0.6936 & 0.654 \\  & & IM02 & 0.904 & 0.9133 \({}^{*}\) & 0.748 & 0.6909 & 0.758 & 0.795 & 0.748 \\  & & IM03 & 0.7924 & 0.803 & 0.836 \({}^{*}\) & 0.8034 & 0.7654 & 0.7497 & 0.7138 \\  & & IM04 & 0.8875 & 0.9275 \({}^{*}\) & 0.8764 & 0.8759 & 0.8437 & 0.7868 & 0.7745 \\ \cline{2-10}  & \multirow{4}{*}{**GGMM**} & IM01 & 0.8021 & 0.8263 \({}^{*}\) & 0.7412 & 0.7406 & 0.6824 & 0.6211 & 0.5488 \\  & & IM02 & 0.7682 & 0.8487 & 0.8935 \({}^{*}\) & 0.8204 & 0.7581 & 0.6328 & 0.7004 \\  & & IM03 & 0.9002 \({}^{*}\) & 0.895 \({}^{*}\) & 0.7324 & 0.7101 & 0.6048 & 0.5545 & 0.6266 \\  & & IM04 & 0.8333 & 0.8859 \({}^{*}\) & 0.8479 & 0.8022 & 0.7643 & 0.7614 & 0.7321 \\ \hline \multirow{8}{*}{**Neo-Normal**} & \multirow{4}{*}{**FSSN-MM**} & IM01 & 0.8725 \({}^{*}\) & 0.6412 & 0.6752 & 0.6351 & 0.5897 & 0.6325 & 0.6606 \\  & & IM02 & 0.8109 & 0.8636 \({}^{*}\) & 0.8464 & 0.812 & 0.8467 & 0.7929 & 0.8292 \\ \cline{1-1}  & & IM03 & 0.9145 \({}^{*}\) & 0.8014 & 0.7512 & 0.7049 & 0.6854 & 0.7046 & 0.6699 \\ \cline{1-1}  & & IM04 & 0.8347 & 0.9010 \({}^{*}\) & 0.9009 & 0.8794 & 0.8695 & 0.8529 & 0.7558 \\ \cline{1-1} \cline{2-10}  & \multirow{4}{*}{**MSNBurr-MM**} & IM01 & 0.9300 \({}^{*}\) & 0.8349 & 0.7412 & 0.7218 & 0.714 & 0.7331 & 0.7435 \\ \cline{1-1}  & & IM02 & 0.8428 & 0.9119 \({}^{*}\) & 0.9106 & 0.7729 & 0.7322 & 0.6731 & 0.7091 \\ \cline{1-1}  & & IM03 & 0.9157 \({}^{*}\) & 0.8014 & 0.7491 & 0.7072 & 0.6938 & 0.6931 & 0.6912 \\ \cline{1-1}  & & IM04 & 0.8364 & 0.9230 \({}^{*}\) & 0.8647 & 0.8009 & 0.801 & 0.7647 & 0.7577 \\ \hline \hline \end{tabular}  
* indicates the maximum \(OSC\) value.  
\end{table} 
Table 1: The summary of overall silhouette coefficients (\(OSCs\)) for the sample image. GMM: Gaussian mixture model; GGMM: generalized Gaussian mixture model. The parameter of the Nenomimo for optimum clusters is shown in Table 2. In Table 2, the ROI for each dataset is denoted by the last cluster. For example, in IM01, for the FSSN-MM, the ROI had a cluster center at a grayscale intensity of 165 with the range of intensity dispersion at about 6.719. The pixel in the ROI was about 5.4% from all MRI areas. Different results were provided by the MSNBurr-MM, which had a cluster center at a grayscale intensity of about 163, an intensity dispersion of 7.138, and the ROI pixel just 6.3% from the MRI areas. Both the FSSN-MM and the MSNBurr-MM had skewness parameters \(\gamma>1\) in the first and third clusters, indicating that the distribution of the  
Figure 10: The comparison of the \(MCR\) for each image and each method. Figure 9: The region of interest (ROI) of (**a**) input slice in different layers compared with (**b**) the ground truth (GT) for the (**c**) GMM, (**d**) GGMM, (**e**) FSSN-MM, and (**f**) MSNBurr-MM algorithms.