# [PERSON]'s Entropy Based Multilevel Thresholding Using a Novel Meta-Heuristics Algorithm
## 4 Simulation Results and Discussion
### Quantitative Evaluation of Segmented Results
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Test** & **k** & **HRO-Renyi** & **ALO-Renyi** & **DE-Renyi** & **SSA-Renyi** & **WOA-Renyi** & **PSO-Renyi** & **GA-Renyi** \\ \hline  & 2 & **11.4686** & **11.4686** & **11.4686** & 11.4684 & **11.4686** & **11.4686** & 11.468 \\ baboon & 4 & **16.5897** & 16.588 & 16.5874 & 16.5779 & 16.5791 & 16.5854 & 16.5549 \\  & 6 & **21.0589** & 21.0585 & 21.0371 & 21.0303 & 20.9759 & 21.053 & 20.8251 \\  & 8 & **24.8839** & 24.4965 & 24.7552 & 24.3798 & 24.6572 & 24.7754 & 24.3504 \\  & 2 & **12.4864** & **12.4864** & **12.4864** & **12.4864** & 12.4863 & **12.4864** & 12.4863 \\ cameraman & 4 & **18.4057** & 18.3471 & 18.4052 & 18.3909 & 18.3975 & 18.4009 & 18.3846 \\  & 6 & **23.7795** & 23.7200 & 23.7729 & 23.7570 & 23.7473 & 23.7475 & 23.6548 \\  & 8 & **28.6612** & 28.5974 & 28.6348 & 28.6437 & 28.5839 & 28.6417 & 28.3456 \\  & 2 & **11.8064** & **11.8064** & **11.8064** & **11.8064** & 11.80616 & **11.8064** & 11.80631 \\ house & 4 & **17.3329** & **17.3329** & 17.33224 & **17.3329** & 17.32379 & 17.33291 & 17.30065 \\  & 6 & **22.0218** & 22.02141 & 22.00228 & 22.01171 & 21.97924 & 22.01973 & 21.89545 \\  & 8 & **26.1522** & 25.69837 & 26.0066 & 25.33308 & 26.04371 & 25.76974 & 25.77073 \\  & 2 & **12.5218** & **12.5218** & **12.5218** & **12.5218** & **12.5218** & **12.5218** & 12.5217 \\ pepper & 4 & **18.3199** & **18.3199** & 18.3194 & 18.3178 & 18.3185 & 18.3198 & 18.3047 \\  & 6 & **23.4910** & 23.4909 & 23.4846 & 23.4854 & 23.463 & 23.4888 & 23.3293 \\  & 8 & **28.0391** & 27.9952 & 28.0121 & 27.9978 & 27.9937 & 28.0289 & 27.6193 \\  & 2 & **12.5460** & 12.5458 & **12.5460** & 12.5456 & 12.5458 & 12.5459 & 12.5456 \\ image1 & 4 & **18.7229** & 18.7222 & 18.7223 & 18.7208 & 18.7188 & 18.7217 & 18.6988 \\  & 6 & **24.0641** & 24.0617 & 24.0522 & 24.0527 & 24.0385 & 24.0604 & 23.9386 \\  & 8 & **28.8219** & 28.8078 & 28.7710 & 28.6861 & 28.7250 & 28.7597 & 28.4813 \\  & 2 & **11.3539** & **11.3539** & **11.3539** & **11.3539** & 11.3521 & **11.3539** & 11.3533 \\ image2 & 4 & **16.6878** & 16.6855 & 16.6869 & 16.6874 & 16.6810 & 16.6841 & 16.6592 \\  & 6 & **21.4421** & 21.2219 & 21.3739 & 21.1208 & 21.3276 & 21.4302 & 21.1757 \\  & 8 & **25.4777** & 25.2385 & 25.2277 & 24.4738 & 25.2488 & 24.8811 & 24.9524 \\  & 2 & **11.3417** & **11.3417** & **11.3417** & **11.3417** & 11.3413 & **11.3417** & 11.3416 \\ image3 & 4 & **16.6759** & **16.6759** & 16.6741 & 16.6757 & 16.6687 & 16.6757 & 16.6499 \\  & 6 & 21.0103 & 20.8263 & 21.0759 & 20.7750 & **21.0994** & 20.7757 & 20.9413 \\  & 8 & **25.1005** & 25.0947 & 25.0833 & 25.0896 & 25.0238 & 25.0923 & 24.8731 \\  & 2 & **11.8064** & **11.8064** & **11.8064** & **11.8064** & 11.8063 & **11.8064** & 11.8063 \\ image4 & 4 & **17.3329** & **17.3329** & 17.3327 & 17.3329 & 17.3277 & 17.3329 & 17.3053 \\  & 6 & **22.0218** & 21.9362 & 22.0032 & 22.0133 & 21.9971 & 22.0198 & 21.8579 \\  & 8 & **26.1522** & 25.7859 & 25.9856 & 25.4901 & 26.0444 & 25.7597 & 25.7633 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The average fitness values of each algorithm under Renyi’s entropy. Figure 4: The proportion of optimal average fitness value obtained by each method in the total number of experiments. When the threshold-level k = {2,4}, all the optimization algorithms have good performance and can get better solutions, but when the number of thresholds increases, HRO is more stable and the optimization ability is better than other methods. HRO can effectively find the optimal threshold. Figure 5 shows the convergence curve of the optimal fitness values with 8 thresholds (\"house\" and \"image2\"). These threshold methods are HRO-Renyi, DE-Renyi, PSO-Renyi, SSA-Renyi, ALO-Renyi, WOA-Renyi, GA-Renyi. It could be seen that some algorithms are prone to fall into a local optimum or not converge to the maximum entropy, resulting in a lower average fitness value.