# Learning-Based Colorization of Grayscale Aerial Images Using Random Forest Regression
## 3 Results and Discussion
### Implementation and Performance
These colorization algorithms use millions of images for training neural networks, which are based on ImageNet and convolutional neutral networks (CNN). Both results contain color information that is completely different from the ground-truth or reference color images, as shown in Figures 6-9. For example, although the colors of the tree are somewhat predicted, the colors of the buildings or the roads are not predicted at all, which suggests that artifacts are more obvious when the structure is complex. In other words, it is impossible to colorize aerial images through a model that is trained with natural images. As can be seen in Figures 6-9, our approach more accurately predicts colors than do the other methods, producing results with fewer artifacts. In Figure 6, the color determined by our method is much clearer, especially in the red portion of the ground that is correctly recovered without artifacts. Figure 7 is a site with many human-made objects, and our method demonstrates remarkably high performance in color prediction, while other methods completely fail to correctly predict colors or contain halo effects. Figure 8 also has many human-made objects that contain multiple colors in the area of vegetation, which makes it more difficult to predict the color values at this site. Except for our method and that of [PERSON] et al. [22], the colors of human-made objects are not correctly predicted, which indicates that our method is robust for color prediction. Figure 9, the urban area, contains the most complex structure and the greatest variety of colors for prediction. Although the results of the proposed method also contain slightly turbid colors, our method produces significantly better results than do the other methods. In other words, our method retrieves more color values with fewer artifacts from the reference image; these details can be confirmed in Figures 10-13. Figure 11: Enlargement of site 2: our method retrieves color values well in this region, compared with other methods. Figure 12: Enlargement of site 3: our method retrieves color values well in this region, compared with other methods. Figure 10: Enlargement of site 1: our method retrieves color values well in this region, compared with other methods. Although visual inspection is a simple and direct way of appreciating the quality of the colorization results, it is highly subjective and cannot accurately evaluate the results of the various colorization methods. Therefore, for quantitative evaluation of the results, we employ the standard peak signal-to-noise ratio (PSNR) and normalized color difference (NCD). The PSNR, which is expressed in terms of the decibel (dB), is an estimate of the quality of the reconstructed (colorization) image compared with the ground-truth color image [54]. Given an \(m\times n\) ground-truth color image \(u_{0}\) and a colorization result \(u\), PSNR is defined as:  
\[\text{PSNR}=10\cdot\log(\frac{3 mn\ (MAX)^{2}}{\sum_{RGB}\sum_{i=0}^{m-1} \sum_{j=0}^{n-1}\left[u(i,j)-\ u_{0}(i,j)\right]^{2}}) \tag{9}\]  
where \(MAX_{I}\) is the maximum possible pixel value of the image (i.e., 255 with standard 8-bit samples), and \(\sum_{\text{RGB}}\)(0) denotes summation over the red, green, and blue bands. The higher the PSNR value, the better the reconstruction process. Normalized color difference is used to measure the color quality degradation in color images [55]. For the NCD calculation, Lab space is used and is defined as:  
\[\text{NCD}=\ \frac{\sum_{i=0}^{m-1}\sum_{i=0}^{n-1}[\ (\Delta L)^{2}+\ (\Delta a)^{2}+\ ( \Delta b)^{2}]^{1/2}}{\sum_{i=0}^{m-1}\sum_{i=0}^{n-1}[\ (L_{u0})^{2}+\ (u_{u0})^{2}+\ (b_{u0})^{2}]^{1/2}}, \tag{10}\]  
where \(\Delta L\), \(\Delta a\) and \(\Delta b\) are the differences between the components of the ground-truth color image and the colorization result, and \(L_{u0}\), \(a_{u0}\), and \(b_{u0}\) are each component values of the ground-truth color image [56]. The lower the NCD value, the better the color quality. The PSNRs and NCDs of the various algorithms are shown in Tables 1 and 2.