## 3 Results and Discussions
After this stage, using the histograms of the two images, the Bhattacharyya distance is calculated according to the following formula:  
\[\text{BC}(\text{H1},\text{H2})=-\text{ln}\left(\sum\text{i}=\sqrt{\text{nh}_ {\text{i1}}\text{h}_{\text{2i}}}\right) \tag{3}\]  
where:  
H1 and H2 are the histograms;  
\(\text{h}_{\text{1}i}\) and \(\text{h}_{\text{2}i}\) are histogram values for the region. Examples of test images improved using the model trained with two different datasets are presented in Figure 6a,b. Metric values obtained for the test images are illustrated as examples. The average of the metric values obtained for all test images are provided in Table 1.  
Figure 6: (**a**) Comparison between LR, HR, and improved images and (**b**) comparison between LR, HR, and improved images. The SR application was carried out with a scale factor of 4. Images of different sizes in the training dataset were arranged as 256 \(\times\) 256 and accepted as HR. The four times smaller versions of these with the interpolation technique were accepted as LR with a size of 64 \(\times\) 64. Depending on these values, the SR application was performed on two different datasets. Dataset-1 included the approach recommended in this study. Dataset-2 kept the brightness values within a limited range and contains cropped images of size 512 \(\times\) 512. When the LR image, HR image, and improved images are evaluated based on visual interpretation, it can be clearly seen that dataset-1 is closer to the HR images. The negative effect that occurs in the images improved in SR studies involves a smoothing effect. The proposed approach aims to obtain higher metric values by minimizing this effect. When the images enhanced with dataset-2 are examined in both images, it can easily be observed visually that they contain more of a smoothing effect than the images enhanced with dataset-1. At this point, it is suggested specifically for historical aerial photographs that the same region has to be represented by images from different years and features extracted from three different bands. The intensity values of the images vary in a wide range, meaning that they are distributed homogeneously, and the image sizes that have to be included in the training phase are larger than those used in the literature, leading to a positive impact on the results. However, the smoothing effects which remain present in dataset-1 can further be eliminated with models using different learning strategies. When the results based on image quality metrics are examined, the values obtained in both improved test images exert consistent results with visual interpretation. The differences between the mutually obtained values for the improved images are lower than those obtained in the literature. However, this is an expected situation, as a single model was used on different datasets. In addition, as the scale factor increases in SR studies, the metric values presented by different models grow closer to each other [1; 2; 3; 4; 5]. The differences between PSNR and SSIM values for the two enhanced images in Figure 6 would be greater if the scale factor was 2. In this study, 4 was used as the scale factor, as suggestions for solving a real-world problem were presented. This is one of the reasons why the differences between the metric values were relatively low. In historical aerial photographs, the distortion amount detected when downsampling the original HR image to LR was more than the distortions observed when conducting the same downsampling on natural images such as Set5 [24] and Set14 [25]. This situation limits the features that the model can learn during training. Therefore, the ability to improve the test image may have been limited. Consequently, there was positive progress both in pixel-based metrics and in metrics that underline structural similarity. The conducted study is distinguished by the use of the UIQI and Bhattacharyya metrics, which are not used in most SR studies. The results for the UIQI metric showed a similar trend to the SSIM.