## 3 Results  
Table 1 shows the results of the statistical indicators of Root mean square error (RMSE), Standard deviation (SDT), Peak Signal to noise ratio (PSNR), Correlation coefficient (CC), and Relative global synthesis error (ERGAS). As mentioned above, for the RSME, CC, and ERGAS statistical indicators, the original Sentinel-2 optical images and the resulting fused image were considered.  
An RSME close to zero means that the difference between the values of the optical image compared with the fused image is very low. A CC close to one indicates very high similarity between the values of the optical image compared with the fused image. The Brovey (BR) method achieved the highest RMSE values. However, it obtained a high correlation of 0.7 compared with the optical image. This means that it presented a significant change in the values of the image; however, it preserves the distribution of the data. The high-frequency modulation (HFM) method showed the lowest RMSE and high CC values, which were very similar to the original optical image. A high SDT value means a high dispersion of the data in relation to its arithmetic mean, showing that the image has  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Fusion Method** & **RMSE** & **SDT** & **PSNR** & **CC** & **ERGAS** \\ \hline BR & 0.00057 & 0.13503 & 12.60602 & 0.70102 & 0.32001 \\ HFM & **0.00002** & 0.03890 & **35.82745** & **0.92981** & **0.00979** \\ GS & 0.00003 & **0.03371** & 26.22411 & 0.68361 & 0.02747 \\ PC & 0.00005 & 0.03449 & 23.02522 & 0.23065 & 0.04880 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results of statistical indicators implemented to measure quality in fusion methods: Brovey (BR), high-frequency modulation (HFM), Gram–Schmidt (GS), and principal components (PC).  
Figure 3: Location of ground truth points for the validation process of land cover classification.  
a high level of contrast. An image with a high level of contrast presents a greater wealth of information [28] that can be used to make a more significant differentiation of coverages, as observed in the Brovey (BR) method.  
A high PSNR value means less noise in the fused image. The highest PSNR was achieved by the HFM method and the lowest by the Brovey (BR) method. The Gram-Schmidt (GS) and principal components (PC) methods presented similar mean values. A low ERGAS value means a better overall fusion result that considers all the bands of the fused image. The high-frequency modulation (HFM) method was observed as having the best ERGAS value, while the Brovey (BR) method presented the highest value in this indicator. The Gram-Schmidt (GS) method showed CC values similar to the Brovey (BR) method, with low values in RSME, SDT, and ERGAS. In the principal components (PC) method, despite obtaining good quality values in RSME, SDT, and ERGAS, the CC was very low compared with the optical image, being 0.23.  
In general, the high-frequency modulation (HFM) method achieved the best fusion evaluation indicators, which means that it did not present significant distortions during the fusion process compared with the original optical image. The Brovey (BR) method presented the lowest indicators, showing significant distortions compared with the original optical image. However, it did obtain a high correlation with the original image.  
Figure 4 shows the histograms of the results of the pixel values obtained by the fusion of optical/SAR images implementing the BR, HFM, GS and PC fusion methods on Sentinel-1 and Sentinel-2 images.  
Figure 4: Histogram by bands of the pixel values of the images fused by the different methods evaluated vs. Sentinel-2 optical image. Values in orange correspond to the fused image; values in blue correspond to the Sentinel-2 optical image.