## 2 Materials and Methods
### Post-Processing of Change Parcels
#### 2.4.1. Parcel Proximity Evaluation Model  
According to the characteristics of automatically extracted new bare land parcels, a buffer radius of 4-8 pixels is set for each parcel. The buffer intersection region is evaluated; for each parcel within the intersection region, its proximity is calculated in pairs, and the proximity threshold is set for parcel aggregation according to the specific requirement of practical applications.  
(1) Confidence-based semantic similarity  
The closer that the change probability values of two parcels are, the higher the semantic similarity of their categories is. After calculating the buffer, the semantic similarity of any two intersecting parcels \(M\), \(N\) is calculated with the following equation.  
\[\text{P}_{sem\_pre}=1-|p_{M}-p_{N}|/255 \tag{2}\]  
where \(p_{M}\), \(p_{N}\) is the average confidence score of the parcels with the confidence range set to [0, 255].  
The semantic distance between two parcels is calculated as \(d_{sem\_pre}=|p_{M}-p_{N}|/255\). The larger the semantic distance, the smaller the semantic similarity value and the smaller the semantic relationship.  
(2) Spatial proximity  
To calculate the shortest distance between any two parcels in a buffer region \(d_{spa}=Dis(F_{M},F_{N})\), that is, the closest spatial distance between two polygons.The distance threshold \(d_{thresh}\) is set as 2-4-pixel width in the processing of new bare land parcels and the spatial proximity is calculated with the following formula \(\text{P}_{spa\_dis}\):  
\[\left\{\begin{aligned} d_{spa}\leq 0.5*d_{thresh}\,\text{P}_{spa\_dis}=1\\ 0.5*d_{thresh}\ <d_{spa}\leq d_{thresh}\,\text{P}_{spa\_dis}=0.5\\ d_{spa}>d_{thresh}\,\ \text{P}_{spa\_dis}=0\end{aligned}\right. \tag{3}\]  
A shorter spatial distance between two parcels indicates a higher spatial proximity.  
(3) Overlap ratio of buffer areas  
As shown in Figure 5, buffer areas are made for parcels M and N, and the areas where the buffer intersects with the parcel are set as \(s_{1}\) and \(s_{2}\), respectively. The two parcels form a polygon \(s_{0}\) at the intersection, and the overlap ratio of buffer areas is calculated using the following equation:  
\[\text{P}_{are\_lap}=\frac{s_{1}+s_{2}}{s_{0}+s_{1}+s_{2}} \tag{4}\]  
Integrating the confidence-based semantic similarity, spatial proximity, and buffer area overlap ratio, the following model is used to calculate the combined proximity \(\text{P}_{com}\) of any two parcels with overlapping buffers:  
\[\text{P}_{com}[M,\ N]=\delta_{1}\text{P}_{sem\_pre}[M,\ N]+\delta_{2}\text{ P}_{spa\_dis}[M,N]+\delta_{3}\text{P}_{are\_lap}[M,N] \tag{5}\]  
Figure 4: Automatic extraction parcels.  
where \(\delta_{1},\delta_{2},\delta_{3}\) are the weights of the variables, \(\delta_{1}+\delta_{2}+\delta_{3}=1\), and the range of P\({}_{com}\) values is [0, 1]. When equal weights are applied to the three variables, \(\delta_{1}=\delta_{2}=\delta_{3}={}^{1}/_{3}\).  
In actual aggregation processing, according to the distribution characteristics of automatically extracted bare land change parcels, the priority factor to be considered is whether the two parcels belong to the change category semantically, which plays a key role in aggregation. At the same time, the parcels should be close enough in space, and the overlapping area ratio is an additional condition for spatial proximity. Therefore, the proximity model adopts weights as such: \(\delta_{1}>\delta_{2}>\delta_{3}\).