# Illuminant Adaptive Wideband Image Synthesis Using Separated Base-Detail Layer Fusion Maps
## 3 Proposed method
### Base Layer Synthesis  
The base layers of the separated visible-light and near-infrared images are synthesized by forming different weight maps according to the infrared natural and auxiliary light characteristics. In the case of daytime images, the intensity and diffusion of IR natural light in the near-infrared images are secured compared to visible images in distant, fog, and shade areas. In contrast, at night, IR auxiliary light is used to compensate for the low-light conditions, long-range IR infiltration is weak in the nighttime infrared images, and the near-distance luminance saturation is relatively strong due to the IR flash. The main purpose of base layer synthesis is local background tone compression through synthetic ratio control of visible-light images and near-infrared images. This compresses the local tone range of the base layer within the limited luminance range of the display, thereby improving the expression performance of the detailed layer and enhancing the clarity. Therefore, in low-light areas, such as backlight and shade, which inhibit visibility, the synthesis ratio of an infrared image with a relatively large luminance value must be increased, and in a high-light area, such as the anterior saturation area caused by night auxiliary lights, the ratio of visible images with a relatively small luminance value should be increased. As shown in Figure 6a,b, the left-side visible-light luminance image has low-level shading information on average, and the right-side near-infrared luminance image is bright on average and has many saturated regions owing to the extended band component. The image synthesis ratio needs to be adjusted for these regions. A bilateral filter with edge preservation is used to divide local regions according to strong boundary components and compress tones from the synthetic map, from which details are removed. The structural formula of the bilateral filter used in each synthesis map and the VIS-IR joint bilateral filter blurred by the boundary information of the near-infrared image is as follows:  
\[MAP_{B}(i,j)=N[B[L_{VIS}(i,j)]] \tag{6}\]  
\[MAP_{B}(i,j)=N\big{[}JB_{L_{IR}}[L_{VIS}(i,j)]\big{]} \tag{7}\]  
\[N[I(i,j)]=\frac{I(i,j)-\min(I(i,j))}{\max(I(i,j))-\min(I(i,j))} \tag{8}\]  
Figure 5: Image decomposition by the bilateral filter. where \(MAP_{B}\) is a bilateral filter map, which is an image of applying a bilateral filter by substituting visible-light luminance images \(L_{VIS}\) into the input image \(I\) in Equation (1). In addition, in Equation (2), \(MAP_{B}\) is a joint bilateral filter map obtained by substituting a visible-light luminance image \(L_{VIS}\) into the input image \(I\) and a near-infrared luminance image into the input image \(F\) to determine the blur weight using boundary information. \(N\) is a min-max normalization function that normalizes the image to a value between 0 and 1. However, when the two images are synthesized using a bilateral filter map to preserve the strong boundaries of the object, the results include distorted objects because the object details are reflected in the synthetic map, as shown in Figure 6c. In the low-brightness areas of visible light, the synthetic ratio of near-infrared images is increased, and the high-brightness areas of near-infrared images are excessively synthesized in dark letters. When creating a synthetic map using a joint bilateral filter, the strength of near-infrared images is reflected in the visible-light low-brightness areas, which increases the ratio of near-infrared images. Therefore, the VIS-IR joint bilateral filter, which includes the boundary information of the near-infrared image of Equation (7), was used. Figure 6d shows the synthesis results using the joint bilateral filter map. It is confirmed that the internal area of the object of the synthetic map is blurred according to the strength of the neighboring pixel image of the near-infrared image, and the details of the information are well-synthesized as the local tone increases in the resulting image.