## 2 Materials and Methods
### Methods
#### 2.2.2 Vegetation Extraction  
This study chose to employ a threshold classification method based on vegetation indices, achieving fully automated pixel-level vegetation extraction from vegetation images. This method is an unsupervised approach that can be used directly without relying on manual sample labeling. It features high computational efficiency, fast processing speed, and strong robustness, allowing it to adapt well to different types of vegetation images. Moreover, it does not require additional training data, making it particularly advantageous for rapid FVC calculation in practical scenarios. In addition to this method, machine learning methods such as random forests, support vector machines, and deep learning have also been applied to calculate FVC. However, all of these methods require labeled data to construct datasets for model training, and they need a substantial number of samples to  
Figure 4: Image fusion results for one set of shadow vegetation experimental data under image preprocessing. (**a**) Normal-exposure image. (**b**) Fusion image of the normal-exposure image and overexposed image at gear 1. (**c**) Fusion image of the normal-exposure image and overexposed image at gear 2. (**d**) Fusion image of the normal-exposure image and overexposed image at gear 3. (**e**) Fusion image of the normal-exposure image and overexposed image at gear 4. (**f**) Fusion image of the normal-exposure image and overexposed image at gear 5.  
support the development of the final model for vegetation extraction in images. This process consumes a considerable amount of time and computational resources. Consequently, this strategy was ultimately selected to complete the vegetation extraction task.  
Four vegetation indices based on the RGB color space and the hue component (HUE) of the HIS color space were adopted as the basis for vegetation extraction. The Otsu thresholding method was used to determine the optimal threshold segmentation point, thereby separating the vegetation and non-vegetation parts of the image data. The four vegetation indices used are the excess green index (EXG), color index of vegetation extraction (CIVE), excess red index (EXR), and excess green minus excess red index (EXGR). These indices can be calculated by linearly combining the red component value (R), green component value (G), and blue component value (B) of each pixel in the image as follows:  
\[\text{EXG}=2\text{G}-\text{R}-\text{B} \tag{6}\]  
\[\text{EXR}=1.4\text{R}-\text{G} \tag{7}\]  
\[\text{EXGR}=\text{EXG}-\text{EXR} \tag{8}\]  
\[\text{CIVE}=0.441\text{R}-0.811\text{G}+0.385\text{B}+18.78745 \tag{9}\]  
Otsu thresholding is a widely used adaptive threshold segmentation algorithm designed for image binary classification problems. The algorithm aims to find a threshold value, denoted as t, that maximizes the between-class variance \(\sigma^{2}\). This approach maximizes the difference between the foreground and background, achieving optimal classification results. Ultimately, it generates a binary image that reflects the specific distribution of the two classes. The between-class variance can be calculated as follows:  
\[\sigma^{2}(\text{t})=\text{P}_{\text{a}}(\text{t})\text{P}_{\text{b}}(\text{ t})(\text{u}_{\text{a}}(\text{t})-\text{u}_{\text{b}}(\text{t}))^{2} \tag{10}\]  
where \(\text{P}_{\text{a}}\) and \(\text{P}_{\text{b}}\) denote the proportions of the class a and b distributions, respectively, at a threshold of t. \(\text{u}_{\text{a}}\) and \(\text{u}_{\text{b}}\) are the pixel means corresponding to classes a and b, respectively.