## 3 Materials and Methods
### Mapping in Dense Vegetation by the Fusion of FPCS Components from Different Data Sources Using GEE
#### 3.3.1 Pre-Processing and Selection of Suitable Multispectral Bands  
First, filtered images with the least vegetation, noise, clouds, and shadows were acquired from the earth engine database within the ROI shown in Figure 2. This figure is the base map for evaluating the results that indicated the leased areas for marble/granite quarries and low, medium, and dense vegetation areas. Landsat-8 data were collected from the Level-1 collection 1 Tier 1 (precision and terrain corrected) suite of Landsat-8 OLI and TIRS images scaled and calibrated at the sensor level. The SWIR bands of the Sentinel-2 MSI L2A data with the bottom of atmosphere reflectance in cartographic geometry were atmospherically corrected using Sen2 Cor processor and the PlanetDEM digital elevation model (DEM). True-color composites (TCCs) and FCCs were used for filtering data of any discontinuities, cloud, noise, vegetation, and shadows in the image. The median value for each pixel was obtained from all the images of these datasets over the past five years for selecting pixels with the minimum vegetation, clouds, and other variations in a pixel at a different time from Landsat-8 and Sentinel-2 MSI data. GEE's \"Clip\" function was used to crop the area of interest to avoid mixing the spectral response of granitic rock bodies with the surrounding residential areas and agricultural fields. This helped process only the desired location in the study region, which allowed faster computational time and better results. Granite and marble bodies showed significant spectral variations in 0.9 \(\upmu\)m, 1.4 \(\upmu\)m, and 2.3 \(\upmu\)m high-spatial-resolution NIR and SWIR regions [4,10]. Granite-associated minerals such as muscovite showed discriminative spectral signatures responses in the SWIR range between 1.400 \(\upmu\)m and 2.200 \(\upmu\)m [13]. On the other hand, alkaline rocks emit larger wavelength radiations, specifically the TIR range of 8-12 \(\upmu\)m [56]. Therefore, the corresponding bands, i.e., 0.88 \(\upmu\)m, 1.600 \(\upmu\)m, and 2.430 \(\upmu\)m, of the three datasets (the Landsat-8 OLI, the ASTER, and the Sentinel-2 MSI) were used to carry out further investigations (see Table 1). Calcite (a main mineral constituent of marble) shows diagnostic spectral absorptions in the SWIR region of electromagnetic radiation. Since the SWIR bands of ASTER are no longer functional and have previously produced poor results [57]; hence, the SWIR bands from the Landsat-8 OLI and Sentinel-2 data were utilized. The 15 m VNIR (B01, B02, and B3N) and the 90 m TIR (B10, B11, and B12) bands of the ASTER, the NIR (B5), SWIR (B6 and B7) of the Landsat-8 OLI, and TIR (B10 and B11) bands of the Landsat-8 TIRS, and the visible (B2, B3, and B4), NIR (B8), and SWIR (B11 and B12) bands of the Sentinel-2 were selected. The red-green-blue (RGB) bands of the Landsat-8 OLI were not used due to their lower resolution. Based on the spectral response of granite (in SWIR and TIR bands) and marble (1.6 \(\upmu\)m and 2.3 \(\upmu\)m) [58], suitable bands for FPCS were identified, as shown in Table 1. The schematic representation of the detailed methodology is also shown in Figure 3.  
Figure 2: Locations of granite leases (ML-1 and ML-2) at Shewa Shahbazghari, granite leases (ML-3 and ML-4), and marble mining leases (MMLs) at Ambela Complex. The regions of dense vegetation (DV) and light vegetation (LV) are overlaid on the Sentinel-2 Multispectral Instrument (MSI) mosaicked image. Seven points P1–P7 show different validation points during the field visit. The bands' spatial resolution variation was automatically handled by nearest neighbor resampling while processing the scale provided (i.e., 15 m in this study). The TCCs from Landsat-8 OLI data had the least shadows, but a relatively greater vegetation cover than Sentinel-2 TCCs. The Sentinel-2 images were level 2A-corrected; therefore, they were rich in contrast, free of clouds and had less vegetation than the Landsat-8 OLI images.