## 4 Results
### The Fusion of the Selected Sentinel-2 MSI and Landsat-8 Components  
The validation of the results with granite (locations ML-1-ML-4), MMLs, and field visit locations (P1-P7) of the Shewa Shahbazgarhi and Ambela complexes are shown in Figure 10. The final map (shown in Figure 10a) was obtained by the FCCs of a weighted combination of PC3 obtained from the FPCS of the stretched Sentinel-2 MSI data, PC4 of the raw Landsat-8, and PC3 of the stretched Landsat-8 datasets. PC3 of the stretched Sentinel-2 MSI component was assigned a weight of 1.5, and PC3 of Landsat-8 stretched datasets had more matching with the target (granite/marble) than the raw Landsat-8 data. Therefore, it was assigned \(\frac{3}{4}\) of the remaining 0.5 weight, i.e., 1.125, and PC4 of the raw Landsat-8 datasets was weighted as 0.375. Figure 10b,c shows the results obtained by applying PCA on stacking all bands of the raw and stretched ASTER, Sentinel-2, and Landsat-8 OLI and TIR sensors mentioned in Table 1. The results from the proposed method in Figure 10a showed a good correlation with ground truth locations compared to Figure 10b,c. A binarized normalized difference vegetation index (NDVI) was calculated and overlaid on the final map for comparison, which showed pixels containing of >0.5 NDVIs in black and pixels containing less than 0.5 NDVIs in white color (as seen in Figure 11). Granite having no vegetation cover was visible in sky-blue and sea green. The dark reddish black color at the MML region showed the marble mining areas, while the dark sky-blue color near P4, P5, and ML-3 indicated the granite with scree, clay, and disturbed land area, respectively, due to weathering. The results from our proposed methodology (Figure 10a) correctly identified all granite and marble known locations compared to the FPCS of the stacked raw (Figure 10b) and stretched (Figure 10c) bands, identifying 5 and 10 out of the 11 locations, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Sentinel-2**} & \multicolumn{2}{c}{**Blue Band 2**} & \multicolumn{2}{c}{**Green Band 3**} & \multicolumn{2}{c}{**Red Band 4**} & \multicolumn{2}{c}{**NIR Band 8**} & \multicolumn{2}{c}{**SWIR1 Band 11**} & \multicolumn{2}{c}{**SWIR2 Band 12**} \\  & & **(490 nm)** & **(560 nm)** & **(665 nm)** & **(842 nm)** & **(1570-1650 nm)** & **(2115-2290 nm)** \\ \hline \multirow{11}{*}{**FPCS**} & Raw & \(0.558\) & \(-0.387\) & \(-0.187\) & \(0.280\) & \(0.481\) & \(0.441\) \\ \cline{2-9}  & Str & \(-0.211\) & \(-0.272\) & \(-0.363\) & \(-0.253\) & \(-0.573\) & \(-0.598\) \\ \cline{2-9}  & Raw & \(0.494\) & \(0.674\) & \(0.114\) & \(0.303\) & \(0.199\) & \(-0.395\) \\ \cline{2-9}  & Str & \(0.056\) & \(-0.001\) & \(0.160\) & \(-0.929\) & \(-0.050\) & \(0.325\) \\ \cline{2-9}  & Raw & \(0.278\) & \(-0.434\) & \(0.183\) & \(-0.516\) & \(0.257\) & \(-0.607\) \\ \cline{2-9}  & Str & \(0.501\) & \(0.525\) & \(0.468\) & \(0.008\) & \(0.038\) & \(0.038\) & \(0.038\) \\ \cline{2-9}  & Str & \(0.257\) & \(-0.392\) & \(-0.122\) & \(0.492\) & \(-0.644\) & \(-0.329\) \\ \cline{2-9}  & Str & \(0.098\) & \(0.122\) & \(-0.184\) & \(-0.266\) & \(0.737\) & \(-0.572\) \\ \cline{2-9}  & Raw & \(-0.106\) & \(0.095\) & \(-0.941\) & \(-0.104\) & \(0.130\) & \(-0.257\) \\ \cline{2-9}  & Str & \(0.317\) & \(0.485\) & \(-0.764\) & \(-0.017\) & \(-0.122\) & \(0.255\) \\ \cline{2-9}  & Raw & \(0.538\) & \(0.212\) & \(-0.133\) & \(-0.557\) & \(-0.481\) & \(0.326\) \\ \cline{2-9}  & Str & \(-0.769\) & \(0.632\) & \(0.077\) & \(-0.042\) & \(-0.019\) & \(-0.027\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Eigenvector loadings after applying FPCS to raw (Raw) and stretched (Str) Sentinel-2 MSI data. The highlighted components were used in generating the final image shown in Figure 10a.