## 2 Materials and Methods
### Multi-Scalar Realistic 3D Modeling and Data Format Conversion
#### 2.4.2 SfM-Based Photogrammetric Processing  
The images were processed using the SfM-based photogrammetry algorithm [20]. The SfM was applied to obtain camera parameters and reconstruct the 3D model from a set of feature matches simultaneously. Indeed, if the calibration matrix \(K\) is known, the rotation matrix R and translation vector \(t\) can be deduced. Given \(m\) perspective images of \(n\) fixed points, the 2D image projection is related to the 3D point in the scene and can be calculated by triangulation with the calibration, rotation, and translation matrices, as follows [20]:  
\[\widetilde{x}_{ij}=\ M_{ij}\widetilde{X}_{j},i=1,\ldots,m;j=1,\ldots,n \tag{1}\]  
where \(\widetilde{x}_{ij}\) is the image point coordinate of the 3D point \(\widetilde{X}_{j}\) projected onto the \(i\)th camera image plane and \(\widetilde{x}_{ij}\sim\left[u_{ij},\,v_{ij},\,1\right]^{\mathrm{T}}\) and \(\widetilde{X}_{j}\sim\left[X_{j},\,Y_{j},\,Z_{j},\,1\right]^{\mathrm{T}}\) are homogeneous coordinate versions, respectively. The symbol\(\sim\)means equality up to scale. \(M\) is the projection matrix, expressed as:  
\[M\,=\, \begin{bmatrix}K&0\end{bmatrix}\begin{bmatrix}R&t\\ 0^{\mathrm{T}}&1\end{bmatrix}  \tag{2}\]  
Figure 5: Optional combination strategy and its corresponding specifications for multi-scalar oblique photogrammetry. Figure 6: Flight path for oblique photogrammetry. (**a**) Zigzag flight path with an oblique camera comprising five lenses, (**b**) cross shape of the flight path with a single camera, and (**c**) circular flight path with multi-levels using a single camera of adjusted shooting angle. To minimize the distance between the projected and observed image points, an optimization method known as the BA algorithm is used over the collective set of camera and scene parameters, which is expressed as:  
\[g\left(C,\,\widetilde{X}\right)=\sum_{i=1}^{n}\sum_{j=1}^{m}\omega_{ij}\left\| \widetilde{x}_{ij}-P\left(C_{i},\,\widetilde{X}_{j}\right)\right\|^{2} \tag{3}\]  
where \(\omega_{ij}\) is an indicator variable: \(\omega_{ij}\)\(=1\) if camera \(i\) observes point \(j\), otherwise, \(\omega_{ij}\)\(=0\). \(C\) is the collection of camera parameters for a single camera with \(C_{i}=\{M,\,R,\,t,\,K\}\), \(P\) is the projection equation, and \(P\left(C_{i},\,\widetilde{X}_{j}\right)\) is the projected image point. The objective function \(g\) is the sum of the squared projection errors. BA is used to calculate the camera calibration parameters and posture of images that minimize this objective function. This procedure is repeated until the parameters are suitable for all photos, and the results can be used to generate a relatively sparse set of 3D points. After BA, a dense point cloud is constructed using multi-view stereo (MVS) algorithms that create a 3D mesh with triangles and texture into a 3D photo-realistic model. On the other hand, before conducting the flight mission, a specific number of ground control points (GCPs) must be deployed on the target region as a constraint to refine the model reconstruction in the SfM processing step and to generate the UAV-based model with the geolocation and scale. At the same time, a certain amount of GCPs should be selected as checkpoints (CPs) to assess the accuracy of the final 3D model. The 3D location (\(X,\,Y,\,H\)) of GCPs is measured by real-time kinematic (RTK) mode based on global navigation satellite system (GNSS) in the predefined coordinate system, and the observation time at each point is about 15 s. This topographic and geodetic instrument measures the coordinates of the center of the GCPs with a horizontal precision between 0.014 m to 0.030 m, and vertical accuracy between 0.030 m to 0.050 m at each point. To ensure this level of accuracy, RTK corrections are carried out by using the closest national permanent GPS reference stations around the research site [40]. In this study, (\(X,\,Y\)) is referred to as Gauss planar rectangular coordinate in the China Geodetic Coordinate System 2000 (CGCS2000) framework [41].