## 1 Introduction
### Step 2: NIR, H and I Extraction  
In addition to the often utilized \(R\), \(G\) and \(B\) components of the target image, \(NIR\) information attracts more attention ever than before along with the spectral resolution improvement of HSR remote sensing images by recently launched optical satellites [6; 28; 33]. Theoretically, in accordance with the [PERSON]'s illumination model [19] and the [PERSON]'s imaging model [15], the diffusion part of the incident light maintains the difference between shadow and nonshadow. Based on the diffusion part expression shown in Equation (17) and the electromagnetic wave theory in which the surface albedo is positively proportional to the wavelength, namely, the \(NIR\) component obtains a bigger surface albedo value than those of \(R\), \(G\) and \(B\) components. The decrease values between shadow and nonshadow can be described with Inequation (18) in terms of \(NIR\), \(R\), \(G\) and \(B\) components [34; 35]:  
\[C_{d}=m_{d}\int_{\lambda}f_{c}(\lambda)e(\lambda)c_{d}(\lambda)\text{d}\lambda \tag{17}\]  
where \(C_{d}\) is sensor response to the diffusion part of the incident light, \(m_{d}\) is a parameter only depending on the geometry information, \(f_{c}(\lambda)\) denotes the spectral sensitivity in the function of wavelength \(\lambda\), \(e(\lambda)\) is the quantity of incident light, and \(c_{d}(\lambda)\) is the surface albedo. \[NIR_{d}>\Gamma_{d} \tag{18}\]  
where \(NIR_{d}\) is the decreased value between shadow and nonshadow in terms of \(NIR\) component, and \(\Gamma_{d}\in\{R_{d},G_{d},B_{d}\}\) are the decrease values between shadow and nonshadow in terms of \(R\), \(G\) and \(B\) components, respectively. In order to effectively decouple chromaticity and luminance, input images are at first converted to express in several typical invariant color spaces (i.e., HIS, HSV, CIELCh, YCbCr and YIQ) with the usually utilized \(R\), \(G\) and \(B\) components in the RGB color space. Chromaticity and luminance are usually well decoupled in these invariant color spaces described above. Note that the \(Q\) component in the YIQ color space and the Cr component in the YCbCr color space are often regarded as the equivalent term with the \(H\) component in the HSV, HIS and CIELCh color spaces, which are together denoted as hue-equivalent (\(H\)) component. Similarly, the \(V\) component in the HSV color space, the \(Y\) components in both the YCbCr and YIQ color space, and the \(L\) component in the CIELCh color space are usually regarded as equivalent representations of the \(I\) component in the HIS color space, which will be expressed as intensity-equivalent (\(I\)) components [14; 20]. \(H\) and \(I\) components are respectively extracted from these invariant color spaces. Additionally, [PERSON] et al. [15] provide derivations about hue and intensity components between shadow and nonshadow, as presented in Equations (19) and (20) with which conclusions are drawn that bigger hue values and lower intensity values are usually obtained for shadow compared with the nearby nonshadow shown in Inequations (21) and (22):  
\[H_{slitw}=\tan^{-1}\Biggl{\{}\frac{\sqrt{3}(G_{nsltw}-G_{d})-(B_{nsltw}-B_{d}) }{\left[(R_{nsltw}-R_{d})-(G_{nsltw}-G_{d})\right]+(R_{nsltw}-R_{d})-(B_{nsltw }-B_{d})}\Biggr{\}} \tag{19}\]  
\[I_{slitw}=\frac{1}{3}[(R_{nsltw}-R_{d})+(G_{nsltw}-G_{d})+(B_{nsltw}-B_{d})] \tag{20}\]  
\[H_{slitw}>H_{nsltw} \tag{21}\]  
\[I_{slitw}<I_{nsltw} \tag{22}\]  
where \(H_{slitw}\) and \(I_{slitw}\) are hue and intensity components of shadow, \(R_{nsltw}\), \(G_{nsltw}\) and \(B_{nsltw}\) are \(R\), \(G\) and \(B\) components of the nearby nonshadow. Consequently, a dramatical decrease often appears in terms of _NIR_ component compared with \(R\), \(G\) and \(B\) components for surface features in shadow regions compared with the same type surface features in the nearby nonshadow regions, as illustrated in Figure 2a with samples from typical objects in HSR images (taking the WorldView-3 as an example).