## 2 Materials and Methods
### Methodology  
#### 2.3.1 Overview of ST-Cube Model  
(1) Expression and representative significance of ST-cube  
In order to correctly describe the spatial-temporal continuity and distribution of geographical objects, [PERSON] [31] proposed the ST-cube model. ST-cubes can reflect the homogeneous state of geographical objects in a certain continuous spatiotemporal range. This feature allows researchers to obtain the spatiotemporal context quantitatively by analyzing the spatiotemporal neighborhood of the ST-cube. As shown in Figure 2a, cube 4 represents an ST-cube with a duration from 0 to 2. During this period, it is homogeneous and has no change. However, cube 1 changes at t1, because it splits into cube 2 and cube 3 at t2.  
(2) Spatiotemporal neighborhoods  
The main idea of ST-cube model is to express geographic objects using a cube and realize it by merging pixels or cubes. For a cube, the potential merging objects are the surrounding temporal and spatial neighbors. The definition of a spatial neighbor is that it is adjacent in the spatial domain and intersects in the temporal domain. As shown in Figure 2b, cube 2 and cube 4 are both the spatial neighbors of cube 3 and cube 1. The definition of time neighbor is that it is adjacent in the temporal domain and intersects in the spatial domain. For example, cube 3 is the temporal neighbor of cube 1 and cube 4 is the temporal neighbor of cube 2. After comparing different organizational structures, [PERSON] [31] asserted that the most effective way is as follows: the smallest scale cube is first represented by a pixel, while the large scale cube is generated iteratively by merging small cubes. Therefore, the ST-cube model is an independent pixel at the beginning, which is merged with the spatiotemporal neighbors that meet the merging conditions and have the least heterogeneity to form a large-scale cube. When a pixel merges with its neighbors, they will be regarded as a whole large-scale cube for the next merge judgment.  
(3) Spatiotemporal heterogeneity criterion  
Spatiotemporal heterogeneity is used to measure the heterogeneity before and after merger. The judgment basis of spatiotemporal heterogeneity is divided into spatial heterogeneity and temporal heterogeneity. The spatial heterogeneity \(S_{h}\) is defined as a weighted combination of spectral and shape heterogeneity. Temporal heterogeneity \(T_{h}\) is defined  
Figure 2: (**a**) Expression of ST-cube. The X and Y axes represent the spatial domain, and the T-axis represents the temporal domain. (**b**) Schematic diagram of spatiotemporal neighborhoods.  
as the difference of spectral heterogeneity of spatial cubes before and after merging. Two cubes (cube 1 and cube 2) should be merged into cube0, at least to meet the following requirements:  
\[\mathbf{S_{h}}=\mathbf{\omega_{shape}}\cdot\ \ \mathbf{H_{shape}}+\mathbf{(1-\omega_{shape})}\ \ \mathbf{\cdot H_{color}} \tag{1}\]  
where \(\omega_{shape}\) is the weight of the shape heterogeneity difference. \(H_{shape}\) and \(H_{color}\) measure the shape difference and spectral difference before and after merging, respectively.  
\[T_{h}=n_{cb}\cdot\Delta T_{cb}\cdot H_{t}^{cb}-\left(n_{cb1}\cdot\Delta T_{cb1 }\cdot H_{t}^{cb1}+n_{cb2}\cdot\Delta T_{cb2}\cdot H_{t}^{cb2}\right) \tag{2}\]  
Each ST-cube will find the spatiotemporal neighbor that meets the merging condition and has the least heterogeneity to merge with it until no spatiotemporal neighbor meets the merge condition.