## 4 Experimental Results and Analysis
### Comparative Experiments and Analysis
#### 4.5.1 General Assessment
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline  & \multicolumn{3}{c}{**Otsu**} & \multicolumn{3}{c}{**Tsallis-BE**} & \multicolumn{3}{c}{**Cauchy-TB**} \\ \cline{2-10}
**Group** & **Accuracy** & **JC** & **DSC** & **Accuracy** & **JC** & **DSC** & **Accuracy** & **JC** & **DSC** \\ \hline BrainWeb-1 & 0.9749 & 0.9683 & 0.9839 & 0.9843 & 0.9802 & 0.9900 & **0.9844** & 0.9805 & 0.9902 \\ BrainWeb-2 & 0.9700 & 0.9611 & 0.9802 & 0.9729 & 0.9647 & 0.9820 & **0.9816** & 0.9764 & 0.9880 \\ BrainWeb-3 & 0.9516 & 0.9415 & 0.9698 & 0.9752 & 0.9698 & 0.9847 & **0.9808** & 0.9769 & 0.9883 \\ BrainWeb-4 & 0.9440 & 0.9359 & 0.9669 & 0.9856 & 0.9836 & 0.9917 & **0.9881** & 0.9865 & 0.9932 \\ BrainWeb-5 & 0.9578 & 0.9506 & 0.9747 & 0.9873 & 0.9851 & 0.9925 & **0.9879** & 0.9861 & 0.9930 \\ BrainWeb-6 & 0.9476 & 0.9388 & 0.9684 & 0.9872 & 0.9851 & 0.9925 & **0.9875** & 0.9856 & 0.9927 \\ BrainWeb-7 & 0.8991 & 0.8831 & 0.9347 & 0.9877 & 0.9856 & 0.9927 & **0.9894** & 0.9878 & 0.9938 \\ BrainWeb-8 & 0.6792 & 0.6392 & 0.7798 & 0.9839 & 0.9819 & 0.9909 & **0.9888** & 0.9875 & 0.9937 \\ BrainWeb-9 & 0.8660 & 0.8453 & 0.9097 & 0.9836 & 0.9808 & 0.9903 & **0.9874** & 0.9854 & 0.9927 \\ BW-Average & 0.9100 & 0.8960 & 0.9409 & 0.9831 & 0.9796 & 0.9897 & **0.9862** & 0.9836 & 0.9917 \\ MRBrainS13-1 & 0.8919 & 0.8497 & 0.9185 & 0.9206 & 0.8890 & 0.9409 & **0.9292** & **0.9018** & 0.9480 \\ MRBrainS13-2 & 0.9024 & 0.8623 & 0.9255 & 0.8987 & 0.8561 & 0.9216 & **0.9087** & **0.8710** & 0.9303 \\ MRBrainS13-3 & 0.8959 & 0.8494 & 0.9176 & **0.9137** & 0.8750 & 0.9318 & 0.9134 & **0.8761** & 0.9325 \\ MRB-Average & 0.8967 & 0.8538 & 0.9205 & 0.9110 & 0.8734 & 0.9314 & **0.9171** & **0.8830** & 0.9369 \\ \hline \end{tabular}  
* The accuracy, JC, and DSC were computed for sliced images from the BrainWeb and MRBrainS13 datasets using three methods for binary segmentation. The best result is indicated by the bold number.  
\end{table} 
Table 2: Accuracy, JC, and DSC in comparative experiments for binary segmentation. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Group**} & \multicolumn{3}{c}{**Otsu**} & \multicolumn{3}{c}{**Tsallis-BE**} & \multicolumn{3}{c}{**Cauchy-TB**} \\ \cline{2-9}  & **PSNR** & **FSIM** & **SSIM** & **PSNR** & **FSIM** & **SSIM** & **PSNR** & **FSIM** & **SSIM** \\ \hline BrainWeb-1 & 28.1767 & 0.5917 & 0.7539 & 28.1642 & 0.6001 & 0.7557 & **28.1861** & **0.6084** & **0.7571** \\ BrainWeb-2 & 27.1518 & 0.5933 & 0.6722 & 27.1487 & 0.6049 & 0.6729 & **27.1526** & **0.607** & **0.6761** \\ BrainWeb-3 & 26.4694 & 0.5958 & 0.58  
three metrics. Otsu's performance in sensitivity was the most unstable, showing significant fluctuations in values. Overall, our method performed the best, showing significantly improved results in all metrics except specificity. Figure 9 shows a magnified view of the segmentation results of slice 90 of the BrainWeb dataset, compared with the ground truth image. It can be observed that for complex edge areas, both Cauchy-TB and the Tsallis-BE method outperformed the Otsu method. They could clearly and accurately delineate the target region with fewer misclassifications. However, the Tsallis-BE method showed over-segmentation in edge details, where some background pixels were erroneously classified as foreground, leading to differences from the ground truth in the edge contours. Cauchy-TB represented an obvious improvement in this aspect. Figure 10 demonstrates the results of image thresholding on some slices taken from the BrainWeb and MRBrainS13 datasets. A comparison revealed that the segmentation achieved by the Otsu method was the worst, showing poor stability in the results. Cauchy-TB and Tsallis-BE were more similar to the ground truth, with the Tsallis-BE method performing well but being slightly inferior to ours in some perceptible details. (B) Ternary segmentation  
We compared the results of three-class thresholding between the Tsallis-BE and Cauchy-TB methods on nine groups of images from the BrainWeb dataset.