# Parallel Compact Differential Evolution for Optimization Applied to Image Segmentation
## 3 Parallel Compact Differential Evolution
The mathematical definition is as follows:

\[DICE=\frac{2|R_{gt}\cap R_{seg}|}{|R_{gt}|+|R_{seg}|},DICE\



Figure 4:3 (**a–c**) image after threshold segmentation, (**d–f**) image after morphological processing, (**g**) original image, (**h**) noisy image. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Segmentation Method** & **Original Image** & **Noisy Image** \\ \hline Otsu & 0.9210 & 0.9531 \\ \hline minimum error thresholding & 0.9732 & 0.9093 \\ \hline pcDE & 0.9738 & 0.9684 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: DICE values obtained by different image segmentation methods. Figure 12: Contour marked image. Figure 13: Ground truth segmentation. Through analyzing the experimental results, we can see that, in the absence of noise, the minimum error thresholding and pcDE algorithm have a better segmentation effect, with Otsu's segmentation effect being weak. After that Gaussian noise is added, the pcDE algorithm can still achieve better segmentation effect, while the minimum error thresholding segmentation effect becomes unsatisfactory. Considering the two situations, the pcDE performs better than the other two methods with or without noise, and could be extensive in prospects for application. ## 6 Conclusions

This paper proposes a parallel compact DE algorithm. The parallel communication strategy achieves faster convergence speed and can find a better solution in a short time. Two different parallel communication strategies are proposed and compared, which are optimal elite strategy and mean elite strategy. In general, the former is better than the later one. Compared with the previous algorithms, the parallel algorithm has obvious advantages in terms of performance and stability. It is applied to image threshold segmentation. Compared with the previous method, we can see that the threshold found by the pcDE algorithm has a better segmentation effect, which has a positive impact on subsequent image processing operations. It can adapt to some weak computing power environment, such as medical equipment, micro robot and so on. In these environments, pcDE algorithm can still maintain good performance and stability, and achieve a balance between accuracy and speed. It has a good application prospect for those optimization problems that need to be solved in the environment with weak computing power. Conceptualization, S.-C.C. and J.-S.P. ; Formal analysis, X.S. ; Methodology, H.L. ; Software, X.S. ; Supervision, S.-C.C. and J.-S.P. ; Writing--original draft, X.S. ; Writing--review & editing, J.-S.P. All authors have read and agreed to the published version of the manuscript. This research was funded by National Natural Science Foundation of China (grant number NSF 61872085) and Natural Science Foundation of Fujian Province (grant number 2018)01638). The authors declare no conflict of interest. ## References

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