## 3 Results and Discussion
### Comparisons of Normalization Results
For site 2, showing a relatively large roof, the radiometric properties normalized through the proposed method show the most similarity with those of the reference image, whereas for site 3, showing several small roofs, the proposed method displays some turbidity when compared to other methods. In other words, roofs are affected by their objective size, which is judged according to its geometric distortion. Large-sized objects can be trained properly, even in the presence of geometric distortion, while small-sized objects acquire the characteristic of other surrounding objects, which adversely affects training. For vegetation areas, phenological properties, such as forests, grass, and crops, are included, and Figure 10 shows the corresponding enlarged areas. In the case of forests, it is confirmed that the areas without vegetation due to the phenological properties in the subject image are normalized to the same phenological properties as the reference image at all sites. For grass and crops, the performance of normalization is somewhat less than that for forests due to the heterogenous characteristics, but it contains the characteristics of the reference image as a whole. Figure 8: Comparison with the results of relative radiometric normalization for site 3: (**a**) proposed method (**b**) MS, (**c**) NC, (**d**) histogram matching, (**e**) RF. Figure 10: Enlargement of the vegetation area marked with a green rectangle: (**a**) site 1, (**b**) site 2, (**c**) site 3. From left to right: reference image, proposed method, MS, NC, histogram matching, and RF. Figure 9: Enlargement of the built-up area marked with a red rectangle: (**a**) site 1, (**b**) site 2, (**c**) site 3. From left to right: reference image, proposed method, MS, NC, histogram matching, and RF. Although visual inspection is a straightforward and direct manner of comparison, it is highly subjective; thus, quantitative evaluations of each method are further performed based on NRMSE. The NRMSE is defined as in Equations (12) and (13):  
\[RMSE\ =\ \ \sqrt{\frac{1}{n}\sum_{j\ =\ 0}^{n}\left(y_{i}^{Nj}-\ y_{i}^{j}\right)^{2}} \tag{12}\]  
\[NRMSE\ =\ \ \frac{RMSE}{\overline{y}_{i}} \tag{13}\]  
where \(y_{i}^{N}\) is RCSSs in the normalized image of band \(i\); \(y_{i}\) is the RCSSs in the reference image of band \(i\); \(n\) is the total number of RCSSs; and, \(\overline{y}_{i}\) is the mean of RCSSs in the reference image of band \(i\). Table 3 shows the NRMSE for the results of the proposed method and the conventional methods. As a result of the quantitative evaluation through NRMSE, although all of the methods show a generally reduced radiometric variation, the proposed method displays the highest performance improvement among them. When compared with the performance of the subject image, on average, the proposed method improves it by 32.85-33.96%, whereas MS, NC, histogram matching, and RF are improved by 18.26-21%, 21.95-24.48%, 20.87-22.87%, and 25.12-28.82%, respectively. This means that the normalized image of the proposed method has the highest accuracy and it is similar to the radiometric and phenological properties of the reference image. In other words, the visual and quantitative evaluations both confirm that it would be useful to carry out normalization with the proposed method when phonological differences exist for the high-resolution images.