# Unsupervised Image Classification Based on Fully Fuzzy Voronoi Tessellation
## 4 Experimental Results
### Simulated Image  
To demonstrate the effectiveness of the proposed method in noise reduction and boundary fitting more clearly, a simulated image with Gaussian distribution is generated according to the template, as shown in Figure 2. The Gaussian distribution parameters used for generating the simulated image are listed in Table 1. To simulate complexity and diversity, classes III and IV have similar means, and classes II and III, and classes IV and V have similar standard deviations. Figure 3 shows the classification results of the simulated image with pixel-based comparing algorithms, where Figure 3(a1-f1) shows FCM, FCM_S, FGFCM, RFLICM, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{5}{c}{**Classes**} \\ \cline{2-6}  & **I** & **II** & **III** & **IV** & **V** \\ \hline Mean & 20 & 50 & 100 & 150 & 200 \\ Std. & 30 & 20 & 20 & 10 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Gaussian distribution parameters used for generating the simulated image. Figure 2: (a) Template image; (b) simulated image. GKWFLICM, and MSHLICM, respectively; Figure 3(a2-f2) shows the corresponding contour line images, where the content of contour lines can reflect the noise resistance level of the algorithm. Figure 3(a3-f3) shows the corresponding contour line overlay images, where the proportion of red can reflect the degree of misclassification, and the red line can also indicate the degree of fit between the classification results and the real boundaries. According to Figure 3, it can be seen that FCM is unable to classify areas with a standard deviation greater than 20, such as region I-III, as shown in Figure 3(a1-a3). FCM_S has good noise resistance, but there is still a salt and pepper phenomenon in the classification results, as shown in Figure 3(b1-b3). The classification performance of FGFCM and RFLICM are unstable. There are a large number of misclassified pixels. Additionally, due to the influence of weighted images, the classification boundaries are relatively blurry, as shown in Figure 3(c1-c3,d1-d3). GKWFLICM has overcome the salt and pepper and boundary-blurring phenomenon, but there are a large number of misclassifications in region II, as shown in Figure 3(e1-e3). MSHLICM strengthens the local constraint of neighbors through a double-layer neighborhood system, which can effectively overcome noise. However, the boundary fitting is not tight enough, as shown in Figure 3(f1-f3). To sum up, even if considering the local neighborhood constraint effect through various ways, the pixel-based clustering algorithm still yields unsatisfactory classification results. Figure 4 shows the classification result of simulated images with region-based comparing algorithm VT-HMRF-FCM and the proposed FVT-FCM, where Figure 4(a1-e1) shows the tessellation results of VT-HMRF-FCM in the initial state, 200, 400, 600, and 3000 iterations. Figure 4(a2-e2) shows the corresponding classification results. Figure 4(f1,f2) shows the contour line and overlap images of VT-HMRF-FCM, respectively. Figure 4(a3-e3) shows the tessellation results of the proposed FVT-FCM in the initial state, 5, 10, 20, and 300 iterations. Figure 4(a4-e4) shows the corresponding classification results. Figure 4(f3,f4) shows the contour line and overlap images of the proposed FVT-FCM, respectively. It can be seen that both the Voronoi tessellations and the classification results are chaotic and disorganized at the initial time. As the model iterating, the classification results gradually optimize in the correct direction. However, the optimization process of VT-HMRF-FCM is slow. The prototype appeared at 600 iterations, as shown in Figure 4(d2). This is mainly due to the lack of analytical  
Figure 3: Classification results of the simulated image with pixel-based comparing algorithms. (**a1–f1**) Classification results with FCM, FCM_S, FGFCM, RFLICM, GKWFLICM, and MSHLICM, respectively. (**a2–f2**) The corresponding contour line images. (**a3–f3**) The corresponding contour line overlay images.