## 4 Application of Methodology for Satellite Images
### Subjective Image and Segmentation Method Assessment  
In order to apply the PROMETHEE-IFS method for selecting the best-performing segmentation algorithm for a specific image, developing an initial decision-making matrix is required. This section describes the subjective assessment used to construct the initial decision-making matrix. The subjective assessment consists of two parts:  
1. Evaluation of the sensitivity of the segmentation method according to individual visual image characteristics to obtain segmentation algorithm evaluation matrix \(X_{ij}\). In the initial experiment, five image segmentation algorithms were evaluated: FCM, SFFCM, FRFCM, RSSFCA, and the GMM. The content of the selected images influences the segmentation results. The sensitivity of the algorithms to the image content was evaluated by presenting the segmentation results to the group of ten experts. The experts were asked to assess how each algorithm processes satellite images with specific visual content. The sensitivity measurement was based on a (1-9) rating scale. The mean values of these assessments were calculated as presented in Table 4. The same group of experts provided their opinion on the weights of the visual criteria described in Section 3.4. 2. Evaluation of the presence of visual features in the image content to obtain an image assessment vector \(I_{i}\). The second part of the evaluation was aimed at assessing the content of the images by analyzing their visual features. A set of proposed visual features that characterize satellite images was constructed (in Section 3.2). We have selected images that best represent each visual feature for this test case. Before the image content evaluation process, a group of ten experts was given visual criteria (characteristics) definitions, a rating scale, and information on what is considered to be a minimum and a maximum value of each criterion. A (1-9) rating scale was used to evaluate the image content, and the mean values of the content assessments were subsequently calculated (Table 5). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Features of Images (Criteria)**} & \multirow{2}{*}{**Optimum**} & \multicolumn{5}{c}{**Segmentation Algorithms (Alternatives)**} \\ \cline{3-6}  & & \begin{tabular}{c} **FCM,** \\ \(A_{1}\) \\ \end{tabular} & \begin{tabular}{c} **GMM,** \\ \(A_{2}\) \\ \end{tabular} & \begin{tabular}{c} **SFFCM,** \\ \(A_{3}\) \\ \end{tabular} & \
\begin{tabular}{c} **FRFCM,** \\ \(A_{4}\) \\ \end{tabular} &
\begin{tabular}{c} **RSSFCA,** \\ \(A_{5}\) \\ \end{tabular} \\ \hline Contrast, \(C_{1}\) & max & 9 & 9 & 2 & 8 & 1 \\ \hline Roughness, \(C_{2}\) & min & 4 & 2 & 6 & 5 & 7 \\ \hline Regions of very small size, \(C_{3}\) & min & 4 & 3 & 6 & 5 & 7 \\ \hline Distortions of regions (holes, & & & & & \\ shadows etc.), \(C_{4}\) & min & 4 & 3 & 7 & 5 & 6 \\ \hline Smoothness (continuity) of & & & & & & \\ region edges, \(C_{5}\) & max & 6 & 5 & 9 & 7 & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluation of the segmentation algorithms (1–9). Figure 8: Images from the AID bridge class. (**a**) “bridge_7.png”, (**b**) “bridge_6.png”, (**c**) “bareland_218.png”, (**d**) “desert_41.png”. The FCM and the GMM effectively preserved more details and provided relatively precise boundaries between clusters. However, improved RSSFCA and SFFCM methods returned smoother clusters with reduced noise and artifacts. At the same time, FCM and GMM methods are more sensitive to lossy compression artifacts if present in the image. The FRFCM method was a balanced solution between FCM and the GMM (which overly replicates the original image) and SFFCM and RSSFCA algorithms (clean clusters, but excessive merging). Figure 11: Satellite image “beach_14” after segmentation: (**a**) RSSFCA; (**b**) SFFCM; (**c**) FRFCM; (**d**) FCM; (**e**) GMM; (**f**) original color image from AID. Figure 10: Satellite image “desert_23” after segmentation: (**a**) RSSFCA; (**b**) SFFCM; (**c**) FRFCM; (**d**) FCM; (**e**) GMM; (**f**) original color image from AID.