# Using an Artificial _Physarum polycephalum_ Colony for Threshold Image Segmentation
## 4 Algorithm Steps of APPCA
### Step 2: Expansion
Hence, the APPC algorithm does not easily deteriorate the solution performance as the scale of the problem increases, and it has great potential for application to other NP-hard problems. ## 6 Conclusions

This paper proposed an artificial _Physarum polycephalum_ colony algorithm to solve threshold image segmentation based on Kapur's entropy fitness function. From an engineering application perspective, the proposed APPCA has a variable population size and can obtain a faster convergence speed, better segmented results, and stronger robustness. In application, the APPCA and Kapur's entropy can be developed and implemented with just a regular personal computer and a general software platform. [PERSON]'s entropy can instruct the artificial _Physarum polycephalum_ colony to expand and contract to obtain good segmentation with high _PSNR_ and low _MSE_. Our benchmark experiment results indicate that the expansion and contraction operations can help APPC improve search performance, and it is less likely to fall into local optima prematurely compared to other algorithms. The \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithms** & **Metrics** & **0105146** & **5000226** & **6000141** & **6000321** & **9000002** & **9005294** \\ \hline \multirow{3}{*}{APPCA} & _MSE_ & **374** & 377 & **351** & 396 & **349** & 382 \\  & _PSNR_ & **22.40** & 22.37 & **22.68** & 22.15 & **22.70** & 22.31 \\  & _SSIM_ & **0.61** & 0.64 & **0.65** & 0.61 & **0.63** & 0.62 \\ \hline \multirow{3}{*}{DL} & _MSE_ & 411 & 1616 & 370 & **354** & 368 & **345** \\  & _PSNR_ & 21.99 & 16.05 & 22.45 & **22.64** & 22.47 & **22.75** \\  & _SSIM_ & 0.59 & 0.46 & 0.62 & **0.62** & 0.61 & **0.64** \\ \hline \multirow{3}{*}{GWO} & _MSE_ & 477 & 615 & 1116 & 1252 & 720 & 768 \\  & _PSNR_ & 21.35 & 20.24 & 17.65 & 17.15 & 19.56 & 19.28 \\  & _SSIM_ & 0.57 & 0.51 & 0.46 & 0.47 & 0.52 & 0.51 \\ \hline \multirow{3}{*}{PSO} & _MSE_ & 1954 & **342** & 751 & 716 & 731 & 1462 \\  & _PSNR_ & 15.22 & **22.79** & 19.37 & 19.58 & 19.49 & 16.48 \\  & _SSIM_ & 0.39 & **0.67** & 0.53 & 0.53 & 0.53 & 0.42 \\ \hline \multirow{3}{*}{DEA} & _MSE_ & 1095 & 568 & 637 & 459 & 694 & 726 \\  & _PSNR_ & 17.74 & 20.59 & 20.09 & 21.51 & 19.72 & 19.52 \\  & _SSIM_ & 0.43 & 0.54 & 0.55 & 0.57 & 0.54 & 0.53 \\ \hline \multirow{3}{*}{ACO} & _MSE_ & 614 & 539 & 990 & 836 & 555 & 657 \\  & _PSNR_ & 20.25 & 20.81 & 18.17 & 18.91 & 20.69 & 19.96 \\  & _SSIM_ & 0.54 & 0.52 & 0.49 & 0.51 & 0.56 & 0.54 \\ \hline \multirow{3}{*}{GA} & _MSE_ & 927 & 425 & 429 & 702 & 572 & 1121 \\  & _PSNR_ & 18.46 & 21.85 & 21.81 & 19.67 & 20.56 & 17.63 \\  & _SSIM_ & 0.47 & 0.57 & 0.58 & 0.54 & 0.55 & 0.45 \\ \hline \multirow{3}{*}{ABC} & _MSE_ & 2628 & 2664 & 1711 & 1692 & 3272 & 1635 \\  & _PSNR_ & 13.93 & 13.88 & 15.80 & 15.85 & 12.98 & 16.00 \\  & _SSIM_ & 0.38 & 0.37 & 0.39 & 0.40 & 0.35 & 0.41 \\ \hline \multirow{3}{*}{AFSA} & _MSE_ & 3063 & 2941 & 1624 & 1570 & 4647 & 3343 \\  & _PSNR_ & 13.27 & 13.45 & 16.02 & 16.17 & 11.46 & 12.89 \\  & _SSIM_ & 0.36 & 0.33 & 0.44 & 0.43 & 0.28 & 0.34 \\ \hline \multirow{3}{*}{IS} & _MSE_ & 3590 & 946 & 865 & 955 & 673 & 3619 \\  & _PSNR_ & 12.58 & 18.37 & 18.76 & 18.33 & 19.85 & 12.54 \\ \cline{1-1}  & _SSIM_ & 0.31 & 0.49 & 0.50 & 0.49 & 0.54 & 0.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical comparison on Stanford background dataset. quality of segmented images on benchmark datasets verifies that the APPCA has great potential for application in various image scenarios, such as medical image processing, autonomous navigation of robots, object recognition, plant detection in agricultural planting, pest and disease recognition, moving object detection, etc. There are also some shortcomings in our work. First, the natural Physarum can optimize the foraging networks with millions of hyphae in a real parallel, while it is very difficult to implement on a classic computer.