# Using an Artificial _Physarum polycephalum_ Colony for Threshold Image Segmentation
## 4 Algorithm Steps of APPCA
### Step 2: Expansion
For DEA [9], the population size was set to \(S=20\), the dimension of the variable to be solved was 20, the crossover factor was \(cr=0.1\), and the initial mutation factor was \(f0=0.4\). For ACO [13; 33], the population size of ants was set to \(S=20\), the parameters contain a pheromone importance of 1.0, a heuristic factor importance of 5.0, and a pheromone volatilization factor of 0.1. For GA [14; 40], the population size of the chromosome was set to \(S=20\), the chromosome length was \(Lind=20\), the crossover probability was \(px=0.7\), and the mutation probability was \(pm=0.01\). For ABC [15; 25], the parameters include the population size of bees \(S=20\), the searching capability limit \(=100\), and the neighborhood size \(Nl=10\). For AFSA [36], the population size of fish was \(S=20\), the maximum number of attempts was 100, the perceptual distance was 1.5, the congestion factor was 0.5, and the fish step was 0.2. For IS [44], the population size of the chromosome was set to \(S=20\), the incentive coefficient included \(alpha=3\) and \(beta=1\), the dimension of the variable to be solved was 10, the concentration threshold \(delta=0.3\), and the mutation probability was \(pm=0.6\). ### Benchmark Test on Pascal VOC 2012 Dataset

The Pascal VOC 2012 segmentation dataset is employed here for the benchmark tests, which is the ancestor of visual recognition competitions. It provides benchmark tests for image segmentation, target detection, object classification, and other image-processing tasks. It contains 20 categories of objects for image segmentation, including people, animals, ships, vehicles, planes, and indoor scenes. Figure 3 shows the experimental results on six original images from the Pascal VOC 2012 dataset. The image IDs of the six images are 2012_001155, 2012_003403, 2012_003438, 2012_004019, 2012_004134, and 2012_004248, and they have 500 \(\times\) 500 pixels, 314 \(\times\) 186 pixels, 500 \(\times\) 332 pixels, 500 \(\times\) 375 pixels, 500 \(\times\) 493 pixels, and 500 \(\times\) 333 pixels, respectively. Figure 3 presents benchmark test results on the Pascal VOC 2012 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. For the fairness of the benchmark test, all the algorithms were tested under the same conditions for comparison. Furthermore, to accurately calculate each algorithm's performance on different benchmark images, all algorithms ran at the same time. At the end of the test, all algorithms can obtain similar experimental results in Figure 3.

Figure 3: _Cont._

After that, Figure 4 showed the fitness convergence curves of APPCA and other artificial intelligence algorithms on the same test images from the Pascal VOC 2012 dataset, where the maximum number of iterations was preset to 200. The convergence curves

Figure 3: Benchmark test on Pascal VOC 2012 dataset. further verified that APPCA obtains lower fitness errors than the other artificial intelligence algorithms in most cases. As we can see, APPCA is less likely to fall into local optima than other algorithms. Other artificial intelligence algorithms can also search for the optimal solution with a certain probability but, usually, they are more likely to fall into local optima too early. Finally, the statistical comparison of the Pascal VOC 2012 dataset is shown in Table 2. Some metrics were explored for performance comparison, including \(MSE\) in Equation (6), _PSNR_ in Equation (7), and _SSIM_ in Equation (13). The optimal solution for each benchmark image is highlighted in bold. From Table 2, it is obvious that the proposed APPCA can obtain better performance in most performance metrics than other artificial intelligence algorithms, including three optimal solutions on image ID 2012_003403, 2012_004019, and 2012_004248.