# Using an Artificial _Physarum polycephalum_ Colony for Threshold Image Segmentation
## 4 Algorithm Steps of APPCA
### Step 2: Expansion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithms** & **Metrics** & **2012\_001155** & **2012\_003403** & **2012\_003438** & **2012\_004019** & **2012\_004134** & **2012\_004248** \\ \hline \multirow{3}{*}{APPCA} & _MSE_ & 395 & **356** & 379 & **387** & 443 & **398** \\  & _PSNR_ & 22.16 & **22.62** & 22.34 & **22.25** & 21.67 & **22.13** \\  & _SSIM_ & 0.63 & **0.65** & 0.65 & **0.63** & 0.59 & **0.62** \\ \hline \multirow{3}{*}{DL} & _MSE_ & **376** & 1214 & 1629 & 391 & **405** & 461 \\  & _PSNR_ & **22.38** & 17.29 & 16.01 & 22.21 & **22.06** & 21.49 \\  & _SSIM_ & **0.64** & 0.46 & 0.41 & 0.61 & **0.61** & 0.58 \\ \hline \multirow{3}{*}{GWO} & _MSE_ & 1602 & 2213 & 1007 & 2166 & 1211 & 856 \\  & _PSNR_ & 16.08 & 14.68 & 18.10 & 14.77 & 17.30 & 18.81 \\  & _SSIM_ & 0.42 & 0.36 & 0.48 & 0.36 & 0.48 & 0.48 \\ \hline \multirow{3}{*}{PSO} & _MSE_ & 739 & 383 & 476 & 502 & 722 & 2353 \\  & _PSNR_ & 19.44 & 22.30 & 21.35 & 21.12 & 19.55 & 14.41 \\  & _SSIM_ & 0.52 & 0.63 & 0.59 & 0.58 & 0.52 & 0.35 \\ \hline \multirow{3}{*}{DEA} & _MSE_ & 584 & 391 & 726 & 718 & 507 & 1829 \\  & _PSNR_ & 20.47 & 22.21 & 19.52 & 19.57 & 21.08 & 15.51 \\  & _SSIM_ & 0.56 & 0.61 & 0.53 & 0.54 & 0.57 & 0.41 \\ \hline \multirow{3}{*}{ACO} & _MSE_ & 827 & 745 & 636 & 2029 & 744 & 661 \\  & _PSNR_ & 18.96 & 19.41 & 20.10 & 15.06 & 19.42 & 19.93 \\  & _SSIM_ & 0.51 & 0.50 & 0.55 & 0.38 & 0.51 & 0.53 \\ \hline \multirow{3}{*}{GA} & _MSE_ & 549 & 574 & 373 & 712 & 588 & 2012 \\  & _PSNR_ & 20.74 & 20.54 & 22.41 & 19.61 & 20.44 & 15.09 \\  & _SSIM_ & 0.57 & 0.55 & 0.65 & 0.55 & 0.54 & 0.39 \\ \hline \multirow{3}{*}{ABC} & _MSE_ & 3216 & 4637 & 1405 & 2683 & 2556 & 409 \\  & _PSNR_ & 13.06 & 11.47 & 16.65 & 13.84 & 14.06 & 22.01 \\  & _SSIM_ & 0.32 & 0.28 & 0.45 & 0.33 & 0.41 & 0.61 \\ \hline \multirow{3}{*}{AFSA} & _MSE_ & 2134 & 3936 & 1982 & 2351 & 425 & 2439 \\  & _PSNR_ & 14.84 & 12.18 & 15.16 & 14.42 & 21.85 & 14.26 \\  & _SSIM_ & 0.35 & 0.33 & 0.39 & 0.34 & 0.60 & 0.35 \\ \hline \multirow{3}{*}{IS} & _MSE_ & 1482 & 4335 & **347** & 417 & 3875 & 746 \\  & _PSNR_ & 16.42 & 11.76 & **22.73** & 21.93 & 12.25 & 19.40 \\ \cline{1-1}  & _SSIM_ & 0.43 & 0.30 & **0.67** & 0.60 & 0.31 & 0.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical comparison on Pascal VOC 2012 dataset. Figure 5: Benchmark test on Stanford background dataset. Figure 5 shows benchmark test results on the Stanford background dataset, including the image ID on the dataset in the first line, the original images in the second line, the 2-D histogram in the third line, and the segmented images of different algorithms in the following lines, respectively. The same as the benchmark test in Section 5.2, all the algorithms were tested under the same conditions for comparison, and all algorithms ran at the same time. The benchmark images in the Stanford background dataset have smaller image sizes than those in the Pascal VOC 2012 segmentation dataset, so all the algorithms tended to need less time to obtain the optimal segmented solutions. At the end of the test, all algorithms can obtain similar experimental results in Figure 5.

After that, Figure 6 showed the fitness convergence curves of APPCA and other artificial intelligence algorithms on the same test images from the Stanford background dataset, where the maximum number of iterations was preset to 200. As we can see, APPCA obtains lower fitness errors than the other artificial intelligence algorithms in most cases. Due to the smaller image size, all algorithms can search for the optimal solution in a shorter time. With the aid of increased population size and more individuals for searching, APPCA is less likely to fall into local optima than other algorithms. According to the convergence curves in Figures 4 and 6, the proposed algorithm to some extent improves the disadvantage of traditional swarm intelligence algorithms that are prone to converge to local optima.