## 4 Experimental Results and Analysis
### Comparative Experiments and Analysis
#### 4.5.2 Comparison with State-of-the-Art Methods
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Slice** & **No. of Thresholds** & **PSNR** & **SSIM** & **FSIM** \\ \hline \multirow{3}{*}{Z1} & 1 & 27.34 & 0.340 & 0.843 \\  & 2 & 27.39 & 0.598 & 0.905 \\  & 3 & 28.24 & 0.704 & 0.992 \\ \hline \multirow{3}{*}{Z2} & 1 & 27.43 & 0.335 & 0.836 \\  & 2 & 27.50 & 0.596 & 0.902 \\  & 3 & 28.46 & 0.700 & 0.990 \\ \hline \multirow{3}{*}{Z5} & 1 & 27.45 & 0.325 & 0.822 \\  & 2 & 27.47 & 0.587 & 0.904 \\  & 3 & 28.34 & 0.682 & 0.998 \\ \hline \multirow{3}{*}{Z10} & 1 & 27.63 & 0.320 & 0.803 \\  & 2 & 27.61 & 0.566 & 0.910 \\  & 3 & 28.38 & 0.648 & 0.983 \\ \hline \multirow{3}{*}{Z36} & 1 & 28.07 & 0.342 & 0.877 \\  & 2 & 28.05 & 0.580 & 0.885 \\  & 3 & 28.51 & 0.676 & 0.991 \\ \hline \multirow{3}{*}{Z72} & 1 & 28.32 & 0.478 & 0.745 \\  & 2 & 27.61 & 0.546 & 0.842 \\  & 3 & 27.59 & 0.641 & 0.819 \\ \hline \multirow{3}{*}{Z108} & 1 & 29.34 & 0.513 & 0.773 \\  & 2 & 29.00 & 0.568 & 0.858 \\  & 3 & 29.35 & 0.679 & 0.829 \\ \hline \multirow{3}{*}{Z144} & 1 & 31.40 & 0.665 & 0.931 \\  & 2 & 31.53 & 0.685 & 0.859 \\ \cline{1-1}  & 3 & 31.63 & 0.809 & 0.992 \\ \hline \end{tabular} The PSNR, SSIM, and FSIM were computed for sliced images from the BrainWeb datasets using one, two, and three thresholds.  
\end{table} 
Table 6: Segmentation results of Cauchy-TB on a small subset of the BrainWeb database where the number of the image slice indicates the Z-plane of the analyzed image. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **No. of Thresholds** & **PSNR** & **SSIM** & **FSIM** \\ \hline \multirow{2}{*}{HHO [63]} & 2 & 18.80 & **0.716** & 0.755 \\  & 3 & 20.48 & **0.772** & 0.815 \\ \hline \multirow{2}{*}{LSHADE [64]} & 2 & 18.80 & 0.716 & 0.755 \\  & 3 & 20.48 & 0.770 & 0.815 \\ \hline \multirow{2}{*}{DE [50]} & 2 & 18.75 & 0.696 & 0.725 \\  & 3 & 20.44 & 0.750 & 0.795 \\ \hline \multirow{2}{*}{PSO [65]} & 2 & 18.67 & 0.706 & 0.732 \\  & 3 & 20.36 & 0.747 & 0.805 \\ \hline \multirow{2}{*}{GWO [66]} & 2 & 18.74 & 0.678 & 0.731 \\  & 3 & 20.39 & 0.732 & 0.790 \\ \hline \multirow{2}{*}{SCA [67]} & 2 & 18.55 & 0.638 & 0.724 \\  & 3 & 20.36 & 0.739 & 0.737 \\ \hline \multirow{2}{*}{WOA [68]} & 2 & 18.80 & 0.716 & 0.755 \\  & 3 & 20.48 & 0.770 & 0.815 \\ \hline \multirow{2}{*}{ALO [69]} & 2 & 18.80 & 0.716 & 0.755 \\  & 3 & 20.48 & 0.770 & 0.815 \\ \hline \multirow{2}{*}{CSA [70]} & 2 & 15.69 & 0.600 & 0.664 \\  & 3 & 18.94 & 0.726 & 0.772 \\ \hline \multirow{2}{*}{Cauchy-TB} & 2 & **28.27** & 0.591 & **0.883** \\  & 3 & **28.81** & 0.692 & **0.948** \\ \hline \end{tabular} The best result is indicated by the bold number.  
\end{table} 
Table 7: The proposed method is compared with other state-of-the-art metaheuristic methods on the BrainWeb dataset; these values represent the mean on eight brain slices. \begin{table}
\begin{tabular}{c c} \hline
**Slice** & **2 Thresholds** & **3 Thresholds** \\ \hline Original Image & Thresholded Image \\ \hline \end{tabular}
\end{table} 
Table 8: _Cont._ \begin{table}
\begin{tabular}{c c} \hline
**Slice** & **2 Thresholds** & **3 Thresholds** \\ \hline Original Image & Thresholded Image \\ \hline \end{tabular}
\end{table} 
Table 8: _Cont._