## 3 Method
### Quantitative Description of Crop Early Growth Characteristics  
This section describes the growth differences of crops in different periods by constructing differential temporal-phase features. The multi-temporal features are superimposed to increase the amount of early-stage crop information. Each crop has a unique phenology [48; 49]. As the crop grows, the spectral reflectance of the crop varies at different periods (Figure 3). The trend of corn and soybean is similar, with a faster growth rate in the early stage, a gradual increase in the middle stage, and a rapid increase or decrease in the later stage, but there are differences in the rate of increase or decrease between the two at different stages. Due to its unique characteristics, the spectral properties of rice are more different from those of the previous two, with a gradual increase in the early stage, followed by a gradual decrease and an upward trend in the later stage. The three crops \begin{table}
\begin{tabular}{c c c} \hline \hline
**Vegetation Index** & **Formula** & **Reference** \\ \hline NDVI & \(\frac{\text{B}_{8}-\text{B}_{4}}{\text{B}_{8}+\text{B}_{4}}\) & [36] \\ LSWI & \(\frac{\text{B}_{8}-\text{B}_{4}}{\text{B}_{8}+\text{B}_{4}}\) & [37] \\ EVI & \(2.5\frac{\text{B}_{8}-\text{B}_{4}}{\text{B}_{8}+\text{B}_{4}}-1-7.5\text{B}_{ 2}\) & [38] \\ RESI & \(\frac{\text{B}_{8}-\text{B}_{4}}{\text{B}_{8}+\text{B}_{4}+\text{B}_{5}}\) & [39] \\ RENDVI & \(\frac{\text{B}_{8}-\text{B}_{8}}{\text{B}_{8}+\text{B}_{4}}\) & [40] \\ NDRE1 & \(\frac{\text{B}_{8}-\text{B}_{8}}{\text{B}_{8}+\text{B}_{4}}\) & [41] \\ NDRE2 & \(\frac{\text{B}_{8}-\text{B}_{8}}{\text{B}_{8}+\text{B}_{4}}\) & [42] \\ NDRE3 & \(\frac{\text{B}_{8}-\text{B}_{8}}{\text{B}_{8}+\text{B}_{4}}\) & [43] \\ VIgreen & \(\frac{\text{B}_{8}-\text{B}_{8}}{\text{B}_{8}+\text{B}_{4}}\) & [44] \\ OSAVI & \(1+0.16\frac{\text{B}_{8}-\text{B}_{8}}{\text{B}_{8}+\text{B}_{4}+\text{B}_{4} +\text{B}_{4}}\) & [45] \\ NDTI & \(\frac{\text{B}_{1}-\text{B}_{2}}{\text{B}_{1}+\text{B}_{2}}\) & [46] \\ SR & \(\frac{\text{B}_{4}}{\text{B}_{4}}\) & [47] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Vegetation Index used in this study. Figure 2: Workflow for early crop identification based on multi-temporal difference information. have different growth rates and show different remote sensing information at different periods [50], indicating that crops can be distinguished by different time phase characteristics. Therefore, the multi-temporal and spectral features were considered together to construct an index of the early growth characteristics of crops. Specifically:  
(1) The spectral features of crops are not obvious or easy to distinguish based on a single image of early crop growth [44]. Based on all the remote sensing images collected in the early stages, the different image features were constructed to amplify the performance of crops in different periods. To facilitate understanding, Figure 4 represents the different information in different periods, while Table 4 defines the meaning of each character in the figure represents. The formula for the constructed temporal difference images (\(TSDVI_{T_{1}T_{2}}\)) is:  
\[TSDVI_{T_{1}T_{2}}=V_{T_{2}}-V_{T_{1}} \tag{1}\]  
where \(V\) comes from the 12 vegetation indices collected in Table 4 and the 10 original bands, \(T_{2}\) represents the current image, \(T_{1}\) represents the prior image, and \(T_{1}\) and \(T_{2}\) were acquired on 28 April, 8 May, 13 May, 28 May; and 12 June, 7 July. (2) Multi-temporal features can describe the growth characteristics of different crops, which can help improve the accuracy of crop identification [51; 52; 53]. All possible combinations of images were exhausted based on each period's different images using the permutation method (\(C_{n}^{m}\)). The band combination was performed according to the \(m\) combination type and used as input for uncombined-type image features for that period.