# High-Brightness Image Enhancement Algorithm
## 3 Proposed Method
### Guidance Map Configuration  
In the linear optimization framework introduced before, the image processing quality is determined by the guidance map \(c\). We next mainly describe how to obtain an appropriate guidance map \(c\). The coefficient \(m_{i}\) directly affects the local contrast of the image. To retain the visual information in the image, we reduced the value of \(m_{i}\) where the local contrast was significant and increased the value of \(m_{i}\) where the local contrast was slight. The standard deviation \(\sigma_{i}\) of \(l^{h}\) is a measure of the local contrast of the image in each window. However, \(c_{i}\) is inversely proportional to \(\sigma_{i}\), which has a bad effect on the results. We defined the guidance map as:  
\[c_{i}=\left(\sigma_{i}^{\theta_{2}}+\kappa\right)^{-1} \tag{13}\]  
To improve the visual quality of the resulting image, we calculated the Gaussian filtered image and the \(\sigma_{i}\) of the Gaussian filtered image to reduce noise. In Figure 3b,c show the radiance map of \(l^{h}(i)\) and the radiance map of the mean value \(\mu\), respectively. Since the local mean value \(\mu\) and the radiance map \(l^{h}(i)\) represent the radiance information of the image, we could see that the information contained in any one of the images was sufficient to contain all the information from the original image completely. If the two factors are added to the guidance image, the local contrast details of the image can be retained as much as possible. We also found that the contrast of the local window radiance is related to the absolute variance. Considering these factors, we add \(\mu\) and \(l^{h}(i)\) to the guidance map. We redefine \(c_{i}\) as:  
\[c_{i}=\left[\mu_{i}^{\beta_{1}}\sigma_{i}^{\beta_{2}}l^{h}(i)^{\beta_{3}}+ \kappa\right]^{-1} \tag{14}\]  
where \(\kappa\) is a small weight coefficient. We set it to 0.5 in our experiments to prevent \(c_{i}\) from being divided by zero. Normally, \(\beta_{1}\in[0.4-0.9]\), \(\beta_{2}\in[0.1-0.4]\), \(\beta_{3}=0.1\).  
Figure 3 shows the visual image of each parameter and the effect of our newly defined guidance map \(c_{i}\) on the output image. Figure 3a is the input image with a large extensive exposure, in which background information can hardly be seen. Only the colors of some personnel's clothes can be seen in this picture, and the visual effect is inferior. Figure 3b,c show the image brightness and mean radiance after performing \(5\times 5\) window processing, respectively. Figure 3d shows our measure for the local contrast based on the standard deviation of the radiance \(\sigma_{i}\). This step can preserve and strengthen the gradients and edges of the image. Figure 3h shows the image generated by the proposed algorithm, which is produced by the guidance map generated by Formula (7); its visual image is Figure 3f. We can see that compared with the output image produced by the standard deviation, average value and average brightness of a single image, the visual image of the proposed method contains all the information in the original image, which can significantly improve the restoration quality of the image. Compared with Figure 3g generated by Formula (6),  
Figure 3h generated by our algorithm is better in terms of its color, visual effect and detail processing. The detailed comparison is shown in Figure 3i-1.  
Figure 3: (**a**) Original image; (**b**) original radiance map \(l^{h}(i)\); (**c**) map of the mean radiance \(\mu_{i}\); (**d**) map of the standard deviation \(\sigma_{i}\); (**e**) the guidance map generated by (6); (**f**) the visualized guidance map \(c_{i}\); (**g**) the result obtained using the guidance map shown in (**e**); (**h**) the result obtained using the guidance map shown in (**f**); (**i–1**) the comparison of the details of figures (**g.h**), respectively.