## 2 Materials and Methods
### Methods
#### 2.2.1 Data Preprocessing  
To obtain the intensity value of each pixel, the image must be converted from the RGB color space to the HIS color space. The detailed conversion method can be expressed as follows:  
\[\mathrm{i}=\frac{\mathrm{R}+\mathrm{G}+\mathrm{B}}{3} \tag{1}\]  
\[\theta=\cos^{-1}\left\{\frac{\frac{1}{2}[(\mathrm{R}-\mathrm{G})+(\mathrm{R}- \mathrm{B})]}{\left[\left(\mathrm{R}-\mathrm{G}\right)^{2}+(\mathrm{R}-\mathrm{ B})(\mathrm{G}-\mathrm{B})\right]^{\frac{1}{2}}}\right\} \tag{2}\]  
\[\mathrm{h}=\left\{\begin{matrix}\theta\;\mathrm{B}\leq\mathrm{G}\\ 360-\mathrm{\theta}\;\mathrm{B}>\mathrm{G}\end{matrix}\right. \tag{3}\]  
\[\mathrm{s}=1-\frac{\min(\{\mathrm{R},\mathrm{G},\mathrm{B}\})}{\mathrm{i}} \tag{4}\]  
where i, h, and s represent the intensity, hue, and saturation, respectively, and R, G, and B denote the red, green, and blue component values of each pixel, respectively.  
Based on the intensity component values of each pixel, a threshold of 0.2 is used to distinguish between shadow and nonshadow regions, and the distribution range of shadows can be calculated. For shadow area pixels, a fusion algorithm is employed to combine the corresponding pixel values obtained under normal and overexposure conditions. The fusion algorithm determines the weight of the overexposed pixel values in the fusion process based on the intensity values. The strategy of adaptively adjusting fusion weights can better handle images with varying degrees of shadow. This results in reconstructed fusion pixel values with recovered information, thereby generating a shadow-free fused image.  
Figure 3: Flowchart of vegetation extraction under shadow conditions using the double-exposure algorithm. The double-exposure algorithm consists of three parts: data preprocessing, vegetation extraction, and method evaluation.  
\[\text{DN}_{\text{d}}(\text{x},\text{y})=\text{DN}_{\text{n}}(\text{x},\text{y})+ \text{DN}_{\text{o}}(\text{x},\text{y})\times\frac{(0.2-\text{i})}{0.2} \tag{5}\]  
The DN values of the shadow pixels at the spatial position \((\text{x},\text{y})\) in the double-exposure, normal-exposure, and overexposure images are denoted as \(\text{DN}_{\text{d}}(\text{x},\text{y})\), \(\text{DN}_{\text{n}}(\text{x},\text{y})\), and \(\text{DN}_{\text{o}}(\text{x},\text{y})\), respectively. In addition, i denotes the intensity value of the shadow pixels. The fusion effect of the algorithm is shown in Figure 4. The pixel categories in the red box of the fused image also become more distinct because the introduction of pixel information under overexposed conditions allows for the recovery of pixel information in shadow areas. As a result, the boundary information between vegetation and non-vegetation areas is also clearer. However, excessive fusion of overexposed information can affect the accuracy of pixels in weak shadow areas. These pixels become whitish, making it difficult to accurately describe the color information of ground objects. In contrast, incorporating too little overexposure information could lead to failure to fully reconstruct and recover pixel information in intense shadow areas. Therefore, the most suitable fusion approach should be determined based on the actual shadow conditions.