## 3 Methodology
### Ortho-Rectification and 3D Visualization  
Compared with D-InSAR, another advantage of PS-InSAR technology is that it cannot only estimate the deformation rate but can also obtain the height error of each PS. Combined with the external DEM, the SAR image pixel can be accurately located in a three-dimension space. Medium-resolution images are limited by resolution. They can acquire little semantic information on the ground, making it difficult to display a single building. However, under a high resolution, there will be multiple PS points on a single building, which makes it possible to measure the deformation of a single building. In this case, the traditional two-dimensional InSAR can no longer meet the application needs of urban three-dimensional information display, and a 3D visualization of building deformation emerges, as required.  
After geocoding, determining how to \"stand\" PSs in a three-dimensional space (despite the side-looking imaging features of the SAR satellite) is a problem that must be considered in high-resolution PS-InSAR. In the geometry of SAR imaging, the height of a building is the main reason for side-looking projection. By correcting the coordinates of PSs projected to the ground in a three-dimensional space, the real spatial position can be restored. Supposing a spatial coordinate system \(\mathrm{O}-\mathrm{XYZ}\), \(\mathrm{h}\) is the building height, with a PS point at the top of the building (Figure 2). The local incident angle of the radar wave is \(\theta\), which produces a projection along the ground range direction, and \(\alpha\) is the angle between the projection of the building and the \(\mathrm{X}\) axis, which we also call the azimuth. The real spatial coordinates of the PS point are \((\mathrm{x},\mathrm{y},\mathrm{h})\), and the projected ground coordinates are \((\mathrm{x}1,\mathrm{y}1,0)\). According to the relationship expressed in Figure 2, the following formula can be established:  
\[\left\{\begin{array}{l}\mathrm{x}=\mathrm{x}1+\mathrm{h}\cdot\cos\alpha/ \tan\theta\\ \mathrm{y}=\mathrm{y}1+\mathrm{h}\cdot\sin\alpha/\tan\theta\end{array}\right. \tag{6}\]  
Finishing the above operation, the height of the PS points on the building can be restored. This is also called ortho-rectification of the PS points.  
Three-dimensional visualization is a tool for describing and understanding the characteristics of many geological phenomena on the ground and underground and is widely used in all fields of geology and geophysics. InSAR 3D visualization is conducive to accurately and rapidly describing various complex ground deformation phenomena. Most of the previous PSI monitoring results are displayed in a two-dimensional plane, which is inconsistent with the characteristics of urban three-dimensional buildings, so it is difficult to correctly explain the causes of deformation. In high-resolution images,  
Figure 2: Schematic diagram of ortho-rectification.  
PS points can be densely distributed in various parts of the building (excluding the shadow surface), making PS points convenient to analyze the stress and strain status of buildings. After ortho-rectification, accurate longitude, latitude, and height coordinates for the PS points can be obtained, and we can use these coordinates on the building. Combined with an actual 3D building model, the temporal and spatial characteristics of the building deformation can be analyzed. The main flow is as shown in Figure 3. In addition to conventional PSI operations, we have also added ortho-rectification and 3D visualization, which are unique to high-resolution SAR data processing.