## 2 Materials and Methods
root mean square error (RMSE) measures the error associated with two data sets; i.e., the values of the fused image versus the original image (in this case, the optical image); standard deviation (SDT) estimates image contrast, where a high contrast represents greater information available in the image; the peak signal-to-noise ratio (PSNR) measures the noise present in the fused image compared with the original image, where a high value represents lower noise in the fused image; the correlation coefficient (CC) evaluates the degree of correlation, a high correlation means high similarity with the original image (in this case, the optical image); and the relative global synthesis error (ERGAS) measures the overall quality of the image fusion process, taking into account the total number of bands of the fused image and considering the pixel size of the optical images and the image to be fused (in this case, the SAR image). Once the fused images were generated, the random forest (RF) classification algorithm was implemented using a parameter of 100 decision trees, without limiting the number of nodes per leaf in each tree. This algorithm was implemented to determine the land cover types in the study area. This process was performed on the Sentinel-2 optical image and on the Sentinel-1 SAR image, with each of the images fused by the methods mentioned above and on the image formed by the compilation of Sentinel-2 optical bands and Sentinel-1 SAR. Regarding the SAR image, both the vertical-vertical (\"VV\") and vertical-horizontal (\"VH\") polarization bands were selected. Six SAR indices commonly implemented in the literature were also added to increase the classification accuracy [56]. SAR indices allow us to obtain more information on land cover characteristics. Their application significantly increases the identification and differentiation of land covers, such as oil palm crop areas and natural forests [57; 58]. The SAR indices implemented were: division ratio (DR) (1), cross-ratio (CR) (2), difference (DIF) (3), normalized difference bands (NDB) (4), radar vegetation index (RVI) (5), and radar square index (RSI) (6). \[\text{Division Ratio }(\text{DR})=\frac{\text{VV}}{\text{VH}} \tag{1}\]  
\[\text{Cross Ratio }(\text{CR})=\frac{\text{VH}}{\text{VV}} \tag{2}\]  
\[\text{Difference }(\text{DIF})=\text{VV}-\text{VH} \tag{3}\]  
\[\text{Normalized Difference Bands }(\text{NDB})=\frac{\text{VV}-\text{VH}}{\text{VV}+\text{VH}} \tag{4}\]  
\[\text{Radar Vegetation Index }(\text{RVI})=\frac{\text{4*VH}}{\text{VV}+\text{VH}} \tag{5}\]  
\[\text{Radar Square Index }(\text{RSI})=\frac{\text{VV}^{2}}{\text{VH}} \tag{6}\]  
In addition, textural indices from the gray-level co-occurrence matrix (GLCM) [59] were calculated using a \(5\times 5\) pixel moving window (kernel) for both SAR image polarization bands \"VV\" and \"VH\". These textural indices have been widely found in the literature to increase the accuracies of SAR image classification, obtaining more information associated with the characteristics of the interaction of radar waves on different types of coverages [14; 38; 39; 60]. The GLCM textural indices implemented were: second angular momentum, average, contrast, correlation, variance, homogeneity, entropy, and dissimilarity. In total, 28 bands were implemented by the random forest (RF) classification algorithm for SAR imagery (2 original bands \"VV\" and \"VH\", 6 SAR indices, and 20 GLCM textural indices); 11 bands were used for optical imagery and optical/SAR fusion methods (\"B2\", \"B3\", \"B4\", \"B5\", \"B6\", \"B7\", \"B8\", \"B8A\", \"B9\", \"B11\", \"B12\"); and for the optical and SAR band stack, 39 bands (a union of the abovementioned) were employed. Subsequently, an adaptive median filter with a moving window (kernel) of 3 \(\times\) 3 pixels was applied to each classification to homogenize the result.