## 2 Materials and Methods
### Property Analysis
#### 2.1.1 Analysis of Chromaticity and Luminance
Thus, the decreasing response of the near infrared, red, green and blue sensor to shadow areas against the corresponding nonshadow areas follow the inequation relationship shown in Equation (3):  
\[NIR_{d}>R_{d}>G_{d}>B_{d} \tag{3}\]  
where \(NIR_{d}\), \(R_{d}\), \(G_{d}\), and \(B_{d}\) are the surface albedo in terms of the near infrared (NIR), red (R), green (G), and blue (B) bands, respectively. Meanwhile, both the hue component of chromaticity and the intensity component of luminance are functions of R, G, and B in RGB color space, as shown in Equations (4) and (5) [26; 37]:  
\[I=\frac{1}{3}(R+G+B) \tag{4}\]  
\[H=\tan^{-1}\Bigg{(}\frac{\sqrt{3}(G-B)}{(R-G)+(R-B)}\Bigg{)} \tag{5}\]where \(I\) and \(H\) denote the intensity and hue components, respectively, and \(R\), \(G\), and \(B\) are reflectivity values of the red, green, and blue bands, respectively. Additionally, [PERSON] et al. calculated the hue value under shadow using [26]:  
\[H_{shadow}=\tan^{-1}\Bigg{(}\frac{\sqrt{3}(G_{shadow}-B_{shadow})}{(R_{shadow}-G_{ shadow})+(R_{shadow}-B_{shadow})}\Bigg{)} \tag{6}\]  
where \(H_{shadow}\), \(R_{shadow}\), \(G_{shadow}\), and \(B_{shadow}\) are hue, red, green, and blue values of shadow regions, respectively. According to the analysis of the difference in illumination of shadow and nonshadow regions, the hue value \(H_{shadow}\) under shadow conditions can be converted into the format corresponding to that under nonshadow conditions, as shown in Equation (7):  
\[H_{shadow}=\tan^{-1}\Bigg{(}\frac{\sqrt{3}((G-G_{d})-(B-B_{d}))}{((R-R_{d})-( G-G_{d}))+((R-R_{d})-(B-B_{d}))}\Bigg{)} \tag{7}\]  
where \(R\), \(G\), and \(B\) denote reflectivity values of the red, green and blue bands of nonshadow regions, respectively, and \(R_{d}\), \(G_{d}\), and \(B_{d}\) are the reflectivity values of the diffusion part of the incident light in terms of the red, green, and blue bands, respectively. Consequently, a conclusion is drawn that the hue value \(H_{shadow}\) of shadow regions is usually higher than that of nonshadow areas based on Equation (3) [26]:  
\[H_{shadow}>H_{nonshadow} \tag{8}\]  
where \(H_{shadow}\) and \(H_{nonshadow}\) are the hue values of shadow and nonshadow regions, respectively. Apart from the hue value, the intensity value of shadow regions can be obtained using Equation (9):  
\[ \begin{array}{l}I_{shadow}=\frac{1}{3}(R_{shadow}+G_{shadow}+B_{shadow})\\ =\frac{1}{3}((R-R_{d})+(G-G_{d})+(B-B_{d}))\\ =I-\frac{1}{3}(R_{d}+G_{d}+B_{d})\end{array}  \tag{9}\]  
where \(I_{shadow}\) is the intensity value of the shadow regions, \(R\), \(G\), and \(B\) denote reflectivity values of the red, green and blue bands of nonshadow regions, respectively, and \(R_{d}\), \(G_{d}\), and \(B_{d}\) are the reflectivity values of the diffusion part of the incident light in terms of the red, green, and blue bands, respectively. Obviously, the intensity value \(I_{shadow}\) of the shadow regions is lower than the intensity \(I_{nonshadow}\) of nonshadow areas, as shown in Equation (10). \[I_{shadow}<I_{nonshadow} \tag{10}\]  
When the hue component and the intensity component are normalized into the range of [0,1], a conclusion can be deduced for the difference values between the hue and the intensity components, i.e.,\(H_{shadow}-I_{shadow}\) for shadows and \(H_{nonshadow}-I_{nonshadow}\) for nonshadows, as shown in Equation (11), according to the unequal relation of the hue component between shadows and nonshadows shown in Equation (8), and the unequal relation of the intensity component between shadows and nonshadows, shown in Equation (10).