## 6 The Proposed ECPSO-MTP for Image Segmentation
### Comparison with Other Clustering Approaches  
In particular, the simple linear iterative clustering (SLIC) technique is first introduced to segment the test images [73] before conducting the clustering experiment. The total number of superpixels is set to 200 for each test image. The segmented images obtained by applying SLIC to the eight test images are given in Figure 6. Then clustering approaches, including the proposed ECPSO-MTP and compared approaches such as K-means, SC, and classic PSO, are employed to cluster the superpixels. The achievable segmentation results of these clustering approaches on the test images are shown in Figures 7-14.  
Figure 5: The labels of eight test images. (**a**) Lawn; (**b**) Agaric; (**c**) Church; (**d**) Castle; (**e**) Elephants; (**f**) Lane; (**g**) Starfish; (**h**) Pyramid.  
Figure 6: Segmentation results obtained by SLIC for eight test images. (**a**) Lawn; (**b**) Agaric; (**c**) Church; (**d**) Castle; (**e**) Elephants; (**f**) Lane; (**g**) Starfish; (**h**) Pyramid.  
Figure 11: Comparison of clustering results on the Elephants image. (**a**) K-means; (**b**) SC; (**c**) PSO; (**d**) ECPSO-MTP.  
Figure 8: Comparison of clustering results on the Agaric image. (**a**) K-means; (**b**) SC; (**c**) PSO; (**d**) ECPSO-MTP.  
Figure 10: Comparison of clustering results on the Castle image. (**a**) K-means; (**b**) SC; (**c**) PSO; (**d**) ECPSO-MTP.  
Figure 7: Comparison of clustering results on the Lawn image. (**a**) K-means; (**b**) SC; (**c**) PSO; (**d**) ECPSO-MTP.  
Figure 9: Comparison of clustering results on the Church image. (**a**) K-means; (**b**) SC; (**c**) PSO; (**d**) ECPSO-MTP.  
The proposed ECPSO-MTP exhibits the best segmentation quality on mostly test images, as shown in Figures 7-14. Furthermore, each test clustering approach was independently implemented 50 times to reduce the influence of random factors. Simple statistical results of Purity from these clustering approaches are presented in Table 6, which validate the effectiveness of the proposed ECPSO-MTP.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Image**} & \multirow{2}{*}{**Statistics**} & \multicolumn{4}{c}{**Comparative Approaches**} \\ \cline{3-6}  & & **K-Means** & **SC** & **PSO** & **ECPSO-MTP** \\ \hline \multirow{4}{*}{Lawn} & Worst & 0.9933 & 0.9937 & 0.9934 & 0.9943 \\  & Best & 0.9933 & 0.9937 & 0.9934 & 0.9943 \\  & Mean & 0.9933 & 0.9937 & 0.9934 & 0.9943 \\  & S.D. & \(2.28\times 10^{-16}\) & \(2.34\times 10^{-16}\) & \(5.61\times 10^{-16}\) & \(3.42\times 10^{-16}\) \\  & Worst & 0.9477 & 0.9517 & 0.9485 & 0.9567 \\  & Best & 0.9477 & 0.9517 & 0.9485 & 0.9567 \\ \multirow{4}{*}{Agaric} & Mean & 0.9477 & 0.9517 & 0.9485 & 0.9567 \\  & S.D. & \(1.24\times 10^{-16}\) & \(2.65\times 10^{-16}\) & \(4.49\times 10^{-16}\) & \(3.16\times 10^{-16}\) \\ \multirow{4}{*}{Church} & Worst & 0.7892 & 0.8902 & 0.7876 & 0.7967 \\  & Best & 0.8646 & 0.8902 & 0.8903 & 0.8962 \\ \multirow{4}{*}{Church} & Mean & 0.8593 & 0.8902 & 0.8641 & 0.8903 \\  & S.D. & 0.0147 & \(1.12\times 10^{-16}\) & 0.0445 & 0.0239 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Performance of four clustering approaches on eight test images (Purity).  
Figure 12: Comparison of clustering results on the Lane image. (**a**) K-means; (**b**) SC; (**c**) PSO; (**d**) ECPSO-MTP.  
Figure 13: Comparison of clustering results on the Starfish image. (**a**) K-means; (**b**) SC; (**c**) PSO; (**d**) ECPSO-MTP.