# Visible and Near-Infrared Image Synthesis Using PCA Fusion of Multiscale Layers
## 4 Radiance Map Generation
\[rad_{base}=P_{rad_{base}}\times NIR_{base}+(1\ -\ P_{rad_{base}})\times base_{fused}, \tag{12}\]  
where \(P_{rad_{base}}\) is the base weighting map of the PCA weights applied using the soft-mixing method in Figure 5b for improving the local contrast, and \(NIR_{base}\) is the NIR image obtained from the Laplacian pyramid, and \(base_{fused}\) is the fusion image obtained using Equation (11). Equation (13) shows a radiance map that applies the PCA image-fusion algorithm and the reconstruction process of the Laplacian pyramid:  
\[ \begin{array}{c}\text{Radiance map}=\ \sum_{n=0}^{l}\{rad_{n}+\ Expand(rad_{n+1})\}\\ (\text{base layer for }n=l,\text{ detail layer for }n=0\ \sim l-1),\end{array}  \tag{13}\]  
where \(rad_{n}\) denotes the result of the fusion algorithm of the PCs calculated using Equations (10) and (12). \(Expand(rad_{n+1})\) represents the reconstruction process of the Laplacian pyramid (Equation (3)), and the radiance map denotes the radiance map obtained through the PCA and the Laplacian pyramid reconstruction process. Figure 5a shows the results of applying the soft-mixing method for the edge layer. If the PCA weight is less than \(th_{1}\), the weight shall be used only for the NIR image pixel value, and then the pixel value should be 1. Conversely, if the PCA weight exceeds \(th_{2}\), the weight should only be used as the pixel value of the VIS image, and then the pixel value should be 1. The PCA weighting map is multiplied by two base-layer images and is adapted to the PCA fusion algorithm given in Equation (12). Figure 5b shows the results of applying the soft-mixing method for the base layer. The PCA fusion algorithm is run differently from the detail-layer fusion algorithm because the base layer has low contrast. The PCA fusion is lower than the contrast of the VIS image only if the PCA weight of the base layer is used. Therefore, the base layer is considered in two stages of the PCA fusion algorithm. In the first step, the PCA fusion algorithm is used in a manner similar to edge-layer PCA fusion. The VIS base layer and NIR base-layer images are implemented by the PCA fusion algorithm, as shown in Equation (11). In the second step, the PCA fusion algorithm used in Equation (12) employs the PCA fusion base obtained from Equation (11) and the NIR base layer. Here, the NIR base layer was used because it contained edge information and higher contrast than the PCA fusion base and the VIS image. Moreover, if it were used with the VIS images, the fused image would have contained shade or reverses light. This would have reduced the tone compression effect. To generate a radiance map, the Laplacian pyramid algorithm was reconstructed following Equation (13): the lower layer was upsampled and then combined with the previous layer. The lowest layer was an image comprising the base fusion of Equations (11) and (12), which upsampled this composed image and added an edge layer image. The images comprising the base and edge images were also upsampled, and then, the next edge-layer images were added. However, the Laplacian pyramid-based multiscale image fusion algorithms are difficult for preserving details. It is necessary to use the detailed enhancement component on the Laplacian pyramid [11; 12]. Thus, Based on the Stevens effect [6], which is the human visual characteristic of local contrast, a gamma value that changes locally according to regional adaptation luminance was applied to the detail layer to improve local contrast. After generating the radiance map, the proposed algorithm was used to realize the Stevens effect to increase the contrast. The Stevens effect increases local perceptual contrast in the detail layer, and the Stevens effect power function determines the luminance-dependent local contrast enhancement. \[k=1/(5L_{A}+1), \tag{14}\]where \(L_{A}\) is a function of 20% of the adaptation luminance  
\[F=0.2k^{4}(5L_{A})+0.1\Big{(}1-k^{4}\Big{)}^{2}(5L_{A})^{1/3}, \tag{15}\]  
where \(F\) is a prediction of a variety of luminance-dependent appearance effects in CIECAM02.