## 2 Materials and Methods
### Build a Monitoring Model
#### 2.5.1 kNDVI-PT-Former Model Construction  
With the development of deep learning, remote sensing (RS) image change detection (CD) methods have made significant progress. However, many convolutional neural network (CNN)-based methods are limited in capturing long-distance dependencies due to receptive domain constraints. Relying on the self-attention mechanism, Transformer effectively implements global information modeling and is widely used in CD tasks. Nevertheless, the Transformer-based CD method still has problems such as pseudo-variation and incomplete edges, which is due to the lack of position and time correlation in dual-temporal RS images. In order to solve this problem, a position-temporal awareness transformer (PT-Former) model [29] has been proposed, which models the relationship between position and time in dual-temporal images. Specifically, the Siamese network connected to the position-aware embedding module (PEM) is used as a feature encoder to extract the features of the changed region. Then, a temporal difference perception module (TDPM) is designed to capture the cross-temporal shift and enhance the difference perception ability during the cross-temporal interaction. At the same time, the context information of the ground object is aggregated by the fusion block, and the spatial relationship is reconstructed under the guidance of the bi-temporal features. However, the PT-Former model performs poorly in extracting the characteristics of ecological restoration vegetation changes in complex environments. Therefore, this study proposes the _kNDVI_-PT-Former algorithm model.  
The _kNDVI_-PT-Former model is based on the PT-Former model. PT-Former uses three channels of dual-phase RS images as input (including label data input channel). The _kNDVI_ calculated by the two images is differentiated to obtain the changed _kNDVI_. The changed _kNDVI_ is used as a new input channel to obtain the _kNDVI_-PT-Former model. By extracting the dual-temporal features and the feature information of _kNDVI_, after the spatial resolution reduction and semantic extraction, the feature map is input into PEM to generate position embedding, and the features are embedded by PEM and flat operation. In order to capture cross-temporal shift and enhance the difference perception ability during cross-temporal interaction, dual-temporal features and _kNDVI_ features are input into TDPM. The features continue to pass through the Transformer cross-encoder with cross-attention, and the features are reshaped. At the same time, the two-phase RS feature map from the residual stem is down-sampled and fused by the pre-fusion block. Next, the features extracted from the Transformer encoder are aggregated by the post-fusion blocks. In this process, the extracted dual-phase RS images are first fused, and then the fused image is fused with the feature map of _kNDVI_. The fusion process is based on the feature map of _kNDVI_. Then, the fused features are input into the Transformer decoder. Then, in the same steps as the original model, in order to enhance the features of the changed region, the features extracted by the Transformer decoder and the post-fusion block are connected. Finally, in order to infer the change map  
\begin{table}
\begin{tabular}{c c} \hline
**Hyperparameter** & **Search Range** \\ \hline Learning Rate & [1 \(\times\) 10\({}^{-5}\), 1 \(\times\) 10\({}^{-3}\)] \\ Batch Size & [16; 64] \\ Dropout Rate & [0.1, 0.5] \\ \hline \end{tabular}
\end{table}
Table 2: Hyperparameter search space for model optimization.  
of the observed scene, the classifier head is introduced to generate the change map. The schematic diagram of the _kNDVI_-PT-Former model is shown in Figure 3.