## 3 Methods
### Feature Hierarchical Selection  
Variable importance (VI) of image features was calculated by random forest algorithm, as shown in Equation (1):  
\[VI=\sum_{t=1}^{N_{tree}}\frac{E_{OOB2}-E_{OOB1}}{N_{tree}} \tag{1}\]  
where \(E_{OOB1}\) is the out-of-bag (OOB) error of decision trees, \(E_{OOB2}\) is the OOB error when the image feature \(F_{i}\) is replaced, \(N_{tree}\) is the number of decision trees. After the image \begin{table}
\begin{tabular}{c c c} \hline \hline
**Vegetation Indexes** & **Formula** & **Parameter Explanation** \\ \hline NDVI & \(\text{NDVI}=(\text{NIR}-\text{R})/(\text{NIR}+\text{R})\) & NIR is the near-infrared band and R is the red band \\ NDWI & \(\text{NDWI}=(\text{G}-\text{NIR})/(\text{G}+\text{NIR})\) & G is the green band \\ GR & \(\text{GR}=\text{G}/(\text{B}+\text{G}+\text{R})\) & B is the blue band \\ DVI & \(\text{DVI}=\text{NIR}-\text{R}\) & \\ RVI & \(\text{RVI}=\text{NIR}/\text{R}\) & \\ SAVI & \(\text{SAVI}=\frac{\text{NIR}-\text{R}}{\text{NIR}+\text{R}+\text{P}}(1+ \text{P})\) & p is the percent of vegetation cover \\ OSAVI & \(\text{OSAVI}=\frac{(1+0.16)(\text{NIR}-\text{R})}{(\text{NIR}+\text{R}+0.16)}\) & \\ MSAVI & \(\text{MSAVI}=\sqrt{(\text{NIR}+0.5)^{2}-2(\text{NIR}-\text{R})}\) & \\ PVI & \(\text{PVI}=\frac{\text{NIR}-\text{R}-\text{B}}{\sqrt{1+\text{R}^{2}}}\) & \(a=10.489,\ b=6.604\) \\ EVI & \(\text{EVI}=\text{g}\times\frac{\text{NIR}-\text{R}}{\text{NIR}+\text{C}_{1} \text{R}-\text{C}_{2}\text{B}+\text{L}}\) & \(\text{g}=2.5,\ C_{1}=6,\ C_{2}=7.5,\ L=1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The formula of vegetation indexes. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature Types** & **Image Features** & **Number** \\ \hline Spectral-based & blue, green, red, near-infrared bands, brightness & 5 \\  & mean, variance, homogeneity, dissimilarity, & \\ GLCM-based & contrast, entropy, angular second & 192 \\  & moment, correlation & \\  & morphological profiles (opening and closing), & \\ Morphological-based & different morphological profiles & 80 \\  & (opening and closing) & \\ Transform-based & reconstructed features using non-subsampling & \\  & shearlet transform & 12 \\ Edge-based & Sobel edge feature & 4 \\ Vegetation indexes & NDVI, NDWI, GR, DVI, RVI, SAVI, OSAVI, & 10 \\ Total & MSAVI, PVI, EVI & 303 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Image features extracted from ZY-3 images. feature \(F_{i}\) is replaced, if the \(OOB\) error changes obviously, it indicates that the image feature \(F_{i}\) is more important. Assuming that the data sequence is \(\{X_{1},X_{2},X_{3},\cdots,X_{n}\}\), the statistic that obeys the overall distribution is \(F(x,\theta)\), the number is \(n\), the expectation of the data sequence \(\{X_{1},X_{2},X_{3},\cdots,X_{n}\}\) is \(\widetilde{u}\). \(\widetilde{u}_{k}\) is the point estimate that only depends on the expectation \(\widetilde{u}\), shown as Equation (2), in which \(x_{i}\) is the \(i\)th statistic value, and \(x_{k}\) is the kth statistic value. \[\widetilde{u}_{k}=\frac{\sum\limits_{i=1}^{k}x_{i}+(n-k)x_{k}}{k} \tag{2}\]  
In this paper, the jumping degree \(t_{k}\) was designed for feature hierarchical selection. Firstly, all the extracted image features were sorted in ascending order according to their VI values. Secondly, the jumping degree of each image feature was calculated, shown as Equations (3) and (4). \[t_{k}=\frac{\widetilde{u}_{k+1}}{\widetilde{u}_{k}} \tag{3}\]  
\[\widetilde{u}_{k}=\frac{\sum\limits_{i=1}^{k}s_{i}+(n-k)s_{k}}{k} \tag{4}\]  
where \(t_{k}\) is the jumping degree at point k, \(\widetilde{u}_{k}\) is point estimate at point k, \(\widetilde{u}_{k+1}\) is point estimate at point (k+1), \(s_{i}\) is VI value of image features \(F_{i}\), \(s_{k}\) is VI value of image features \(F_{k}\), and \(n\) is the number of image features.