# Unsupervised Image Classification Based on Fully Fuzzy Voronoi Tessellation
## 4 Experimental Results
### Simulated Image
solutions for seed points, which can only be optimized through random sampling strategies. In addition, even with sufficient iterations, VT-HMRF-FCM cannot fit the boundary well, as shown in Figure 4(f2). This is because pixels are forcibly assigned to the same polygon based on spatial distance, lacking feedback constraints from classification results, which leads to extremely inflexible polygons and makes it difficult to fit complex boundaries finely. In contrast, the prototype appears at 20 iterations in the classification result of the proposed FVT-FCM, and the best results were obtained with only 300 iterations. It benefits from the hierarchical fuzzy membership model proposed in this paper. It can effectively integrate the flexibility of pixels and the noise resistance characteristics of regions. Additionally, the Voronoi tessellation is explicitly modeled in the objective function, and it can have an analytical solution. FVT-FCM can achieve better classification with fewer iterations. To sum up, the proposed FVT-FCM can flexibly fit boundaries while having strong noise resistance. To quantitatively evaluate the effectiveness of the proposed method, the user accuracy (UA), product accuracy (PA), overall accuracy (OA), and Kappa coefficient are calculated according to the confusion matrix and listed in Table 2. It shows that the weighted image constructed by FGFCM still cannot overcome the random distribution noise, and the accuracy is the same as FCM, at only about 80%. Due to fully considering local constraints, the classification accuracy of RFLICM and GKWFLICM has been improved; OAs reach 92%. Although there is some salt and pepper noise in FCM_S, which affects the visual effect, its accuracy is 96%. MSHLICM's accuracy remains at 96% due to boundary fitting bias issues. VT-HMRF-FCM and the proposed FVT-FCM are both region-based algorithms, they have  
Figure 4: Classification results of the simulated image with region-based comparing algorithm VT-HMRF-FCM and the proposed FVT-FCM algorithm. (**a1**-**e1**) Tessellation results of VT-HMRF-FCM in the initial state, 200, 400, 600, and 3000 iterations. (**a2**-**e2**) Corresponding classification results of VT-HMRF-FCM. (**f1,f2**) Contour line and overlap images of VT-HMRF-FCM. (**a3**-**e3**) Tessellation results of the proposed FVT-FCM in the initial state, 5, 10, 20, and 300 iterations. (**a4**-**e4**) Corresponding classification results of the proposed FVT-FCM. (**f3,f4**) Contour line and overlap images of the proposed FVT-FCM. strong noise resistance. In addition, the flexibility of fuzzy polygons demonstrates strong boundary-fitting ability, making the proposed method superior to VT-HMRF-FCM, and achieving an accuracy of up to 98.6%. To focus on boundary effects, boundary accuracy evaluation criteria is designed based on buffer analysis in this paper. It also includes user accuracy (UA), product accuracy (PA), and overall accuracy (OA), where the UA of boundaries is the probability that the classification boundary accurately falls within the template boundary buffer area. The PA of boundaries is the probability that the template boundary accurately falls within the classification boundary buffer area. The OA is the mean of UA and PA. Figure 5 is the visualization of boundary buffer analysis, where the first row represents UA, the second row represents PA, their corresponding quantitative evaluation results are listed in Table 3. Figure 5(a1,a2,b1,b2,c1,c2,d1,d2,e1,e2,f1,f2,g1,g2,h1,h2) represent FCM, FCM, FCM_S, FGFCM, RFLICM, GKWFLICM, MSHLICM, VT-HMRF-FCM, and the proposed FVT-FCM algorithm, respectively. The black represents the buffer area. The green is correct boundary pixels. The red in the first row represents the deficient boundary in classification results. The red in the second row represents the redundant boundary in classification results. It can be seen that although FCM, FCM_S, FGFCM, RFLICMA, and GKWFLICM have almost no deficient boundaries, there are a large number of redundant boundaries. It results in a larger UA and smaller PA.