# Guided Facial Skin Color Correction
## 4 Results and Discussion  
In this section, we show the results obtained through the proposed process. The experiment tests our algorithm on various sets, which are available from our website [[http://wwwell.cs.shinshu-u.ac.jp/~keiichi/projects/auto_album](http://wwwell.cs.shinshu-u.ac.jp/~keiichi/projects/auto_album)]([http://wwwell.cs.shinshu-u.ac.jp/~keiichi/projects/auto_album](http://wwwell.cs.shinshu-u.ac.jp/~keiichi/projects/auto_album)) (accessed on 14 August 2021). The range of RGB values is normalized to \([0,1]\). The prescribed scale factor \(l\) in Section 3.1 is set to 2.0. The filter window sizes used in Section 3.4 and Appendix A are \(19\times 19\) and \(31\times 31\), respectively. \(\eta_{\mathcal{S}}=5|\Omega_{\mathcal{S}}|\times 10^{-4}\) and \(\eta_{\mathcal{B}}=5|\Omega_{\mathcal{B}}|\times 10^{-10}\) are used, where \(|\Omega_{(\cdot)}|\) indicates the number of pixels contained in the region \(\Omega_{(\cdot)}\). \(L\) in MFISTA is set to 500.  
Our filtering often flattens the gradation of the input images caused by shadows. It yields unnatural images as shown in the top of Figure 6, where the input image is input to our algorithm, and the filtered image is a result of our guide image filtering. For the luminance correction, each pixel color value of the image is decomposed into a color component \(\mathbf{x}_{i}^{C}\in\mathbb{R}^{3}\) and an intensity component \(x_{i}^{I}\in\mathbb{R}^{1}\) as follows:  
\[\begin{split} x_{i}^{I}&=\frac{x_{i}^{R}}{\|\mathbf{x }_{i}\|_{1}}x_{i}^{R}+\frac{x_{i}^{G}}{\|\mathbf{x}_{i}\|_{1}}x_{i}^{G}+\frac{ x_{i}^{B}}{\|\mathbf{x}_{i}\|_{1}}x_{i}^{B},\\ \mathbf{x}_{i}^{C}&=\frac{\mathbf{x}_{i}^{I}}{x_{i} ^{I}},\end{split} \tag{16}\]  
where the superscripts \(R\), \(G\) and \(B\) indicate each color component. This decomposition procedure is the same as [10].  
The input image and the filtered image are decomposed into the two components by (16), and then the intensity component of the input image \(y_{i}^{I}\) and the color component of the filtered image \(\mathbf{x}_{i}^{C}\) are combined as follows:  
\[\mathbf{x}_{i}^{\prime}=y_{i}^{I}\mathbf{x}_{i}^{C}. \tag{17}\]  
Figure 6 shows this procedure and its effectiveness.  
Figure 7 shows the result of our skin color correction. The area around the face in the input image has color distortion due to the lighting conditions and background color. Our result has a white balanced facial skin color similar to the target facial skin color. Sometimes, when we take a photograph in dark surroundings, the results sometimes have unnatural face colors (Figure 8b) due to the camera flash. Hence, we apply our proposed method to flash images in dark surroundings to reduce undesirable effects of artificial lights. Figure 8c shows the flash image editing results using our method. One can see that unnatural colors of the original image are corrected to natural colors by our method.  
Figure 6: Simple luminance correction. Input image and filtered image are decomposed into intensity components and color components, respectively, by (16), then the intensity component of the input image and the color component of the filtered image are combined by (17).