## 3 Results  
### Results of Realistic 3D Model and Quality Assessment  
According to the multi-scalar oblique photogrammetric data acquisition scheme, the total number of captured images for each scale (i.e., coarse-scale, meso-scale, and fine-scale) was about 330,000, 89,000, and 6000, respectively. The 3D coordinates of the GCPs were well-distributed in the study area and measured by a Hi-Target GNSS RTK (Guangzhou, China), which can accept full-band satellite signal, affording a horizontal precision between  
Figure 11: Spatial coordinates (1 is the surface, and 2 is the underground coal seam). 1.4 cm and 3.0 cm and vertical accuracy between 3.0 cm and 5.0 cm at each point. To evaluate the real accuracy of the resulting 3D photo-realistic model, some GCPs were selected as CPs, and the ratio of GCPs/CPs is 522/209. All captured images were processed using the SfM-based digital photogrammetry algorithm implemented by Context Capture (CC) [51], which is suitable for oblique photogrammetric image processing and uses the SfM-MVS technique. The resulting 3D photo-realistic model was exported into an OSGB format. Given that the computing task of AT and the 3D reconstruction is enormous, and the improvement of photogrammetry accuracy and the expansion of the measurement range, the total amount of data is massive. Thus, due to the lower efficiency when using a single workstation, it is necessary to perform parallel and distributed calculations on the photogrammetric processing of AT and 3D reconstruction. The hardware setup in this work involved high-frequency computing nodes (CPU (Central Processing Unit): Core i7-8700K with 3.70 GHz, operating system: Win10) with one NVIDIA GeForce RTX 2080 Ti GPU). Related information about the photogrammetric process is summarized in Table 4.  
After the 3D model reconstruction is accomplished, the effect and accuracy of the resulting 3D model should be checked. The precision indexes to evaluate the real accuracy of the 3D model rely on the root mean squared error (\(RMSE\)), including horizontal (\(RMSE_{XY}\)) and vertical (\(RMSE_{H}\)) directions calculated by Equations (8) and (9). \[RMSE_{XY}=\sqrt{\sum_{i=1}^{N}\bigl{(}\Delta X_{i}^{2}+\Delta Y_{i}^{2}\bigr{)} /N} \tag{8}\]  
\[RMSE_{H}=\sqrt{\sum_{i=1}^{N}\bigl{(}\Delta H_{i}^{2}\bigr{)}/N} \tag{9}\]  
where \(N\) is the number of CPs, and \(i\) represents the \(i\)th CP, and \(\Delta X_{i}\), \(\Delta Y_{i}\), and \(\Delta H_{i}\) are the deviations between field survey data and the measured data from a 3D realistic model. Table 5 reports the \(RMSE\)s in the horizontal and vertical positions of the CPs for different scale combinations, highlighting that, compared to the first combination, the second and the third combination significantly improve the geometric accuracy by about 50% in horizontal and vertical directions. In our case study, the accuracies of UAV-based photogrammetric surveys are expected to be 5-10 cm in the horizontal (\(X\), \(Y\)) position and 5-15 cm in the vertical (\(H\)) position. However, the accuracy values obtained in different scales or combinations were all less than 10 cm, indicating that the results are reliable and usable. Figure 12 depicts the 3D model output, which is about 260 gigabytes. Aiming at visual quality inspection, Figure 13 illustrates the photogrammetric surveying results with the graphics format of the two ROIs, including AT processing, 3D realistic models, corresponding local models, and details by merging different photogrammetric scales. By comparing the local 3D models of the same object in the first ROI displayed in Figure 13c (only with coarse-scale) and f (with the combination of coarse- and meso-scale) corresponding to the two local parts labeled with red rectangles in Figure 13b,e, respectively, we observe that multi-scalar oblique photogrammetry can better restore the actual shape for the complex object of the industrial equipment.