# Retinal Vessel Segmentation Using Math-Inspired Metaheuristic Algorithms
## 3 Results
### Convergence Analysis
Furthermore, the GNDO algorithm stands out, as it does not contain any control parameters, while the GOBC-PA algorithm stands ou as it contains only one control parameter. In general, it can be expressed that all of the considered algorithms provide high performance in terms of segmentation. On the other hand, the Se, Sp, and Acc values obtained for the CSA, TSA, AOA, GNDO, GOBC-PA, and SCA implementations indicate that each algorithm is able to produce effective results in  
Figure 8: Convergence speeds of the algorithms. (**a**) Diseased retinal image taken from the DRIVE database (see Figure 1b); (**b**) healthy retinal image taken from STARE database (see Figure 2a). terms of correctly and incorrectly classified vessel and background pixels. However, the performances of the algorithms in terms of Se seem a bit worse when compared to the Sp- and Acc-based performances. The lowest standard deviation values produced by the GOBC-PA algorithm for both the DRIVE and STARE databases prove that this algorithm is stabler and more robust when compared to the other algorithms. On the other hand, the TSA and AOA produced the highest standard deviation values for the DRIVE and STARE databases, respectively. On the DRIVE database, the GOBC-PA algorithm reached the minimum MSE value with the highest convergence speed. However, on the STARE database, the GNDO algorithm reached the lowest error value while the GOBC-PA algorithm exhibited the best performance in terms of convergence speed. Furthermore, for both databases, the worst MSE value was obtained for the TSA, while the worst convergence speed performance was observed for the AOA. Finally, although it produced relatively worse results in terms of other performance metrics, it was found that the TSA had the most effective performance in terms of CPU time. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Algorithms**} & \multirow{2}{*}{**Total NFEs**} & **DRIVE** & **STARE** \\  & & **(Figure 1b)** & **(Figure 2a)** \\ \hline \multirow{2}{*}{**CSA**} & \multirow{2}{*}{1010} & 2.1720 s & 2.6960 s \\  & & (77.28\% of the total CPU time) & (77.72\% of the total CPU time) \\ \hline \multirow{2}{*}{**TSA**} & \multirow{2}{*}{110} & 0.2820 s & 0.3440 s \\  & & (67.92\% of the total CPU time) & (70.64\% of the total CPU time) \\ \hline \multirow{2}{*}{**AOA**} & \multirow{2}{*}{1010} & 2.0740 s & 2.6720 s \\  & & (77.82\% of the total CPU time) & (78.02\% of the total CPU time) \\ \hline \multirow{2}{*}{**GNDO**} & \multirow{2}{*}{2000} & 3.9220 s & 5.1320 s \\  & & (74.61\% of the total CPU time) & (76.85\% of the total CPU time) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance comparison in terms of the NFEs convergence analysis. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **DRIVE** & **STARE** \\  & **(Figure 1b)** & **(Figure 2a)** \\ \hline \multirow{2}{*}{**CSA**} & Minimum MSE & 0.6631 & 0.5953 \\  & CPU Time & 2.8103 & 3.4689 \\  & (seconds) & 2.8103 & 3.4689 \\ \hline \multirow{2}{*}{**TSA**} & Minimum MSE & 0.7077 & 0.6189 \\  & CPU Time & 0.4152 & 0.4869 \\ \hline \multirow{2}{*}{**AOA**} & Minimum MSE & 0.6803 & 0.6138 \\  & CPU Time & 2.6651 & 3.4248 \\ \hline \multirow{2}{*}{**GNDO**} & Minimum MSE & 0.6576 & 0.5918 \\  & CPU Time & 5.2565 & 6.6776 \\ \hline \multirow{2}{*}{**GOBC-PA**} & Minimum MSE & 0.6562 & 0.5920 \\  & CPU Time & 6.4216 & 8.3765 \\ \hline \multirow{2}{*}{**SCA**} & Minimum MSE & 0.6687 & 0.5996 \\  & CPU Time & 2.6980 & 3.4260 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance comparison of the CSA, TSA, AOA, GNDO, GOBC-PA, and SCA implementations on the DRIVE and STARE databases.