## 3 Data Processing and Analyses  
### Image Orientation  
The prerequisite for a successful photogrammetric 3D reconstruction is that both interior and exterior orientations are correctly known. The physical sensor model based on the collinearity condition, describing the geometric relation between image points and their corresponding ground points, yields high accuracies (typically a fraction of one pixel), but is complex, and varies depending on different sensors types. Moreover, information about the camera model, ephemerides, and satellite attitude may not be available to users, since they are kept confidential by some commercial satellite image providers [28]. Usually, in practice, the RFM containing eighty RPCs is used for replacing the rigorous physical model of a given sensor [29]. In our research work, we have used the RFM for the photogrammetric mapping.  
The workflow for DEM extraction from tri-stereo images begins with image block triangulation and geo-referencing, based on provided RPCs and available GCPs. The main steps for the satellite triangulation are:  
1. Image point measurement of GCPs. The number of GCPs is different for the two image sets because of the different data extent and visibility in the scenes. Therefore, 43 GCPs and 22 GCPs were manually measured in each Pleiades and WorldView-3 tri-stereo pair using the multi-aerial viewer, which allows a simultaneous display of the images. This step is performed in order to stabilize the image block and to achieve higher accuracies by improving the given RPCs' values.  
Figure 3: Comparative view of the same area from Pleiades (**a**) and World View-3 images (**b**) with a magnified detail.  
2. Tie points (TPs) extraction and RPC refinement. The orientation of the satellite imagery includes the automatic TPs extraction as well as an automatic and robust block adjustment. During the adjustment, a maximum number of six parameters (affine transformation in image space) can be computed: two offsets, two drift values, and two shear values (for each image). Depending on their significance, only a subset of these corrections could be computed by the software: two shifts (on X and Y) and a scale on Y. TPs were automatically extracted by applying Feature Based Matching using the Forstner operator and refining them with Least Squares Matching [30]. TPs with residuals (in image space) larger than one pixel are considered mistakes (gross errors) and rejected. The RPCs are refined through a subsequent adjustment procedure where the differences between image- and backprojected- (with the RFM) coordinates of the GCPs and TPs are minimized.
3. Geo-positioning accuracy analysis. To evaluate the accuracy of the georeferenced images, 50 CPs were used. They were manually acquired from the available orthophoto at 0.2 m GSD and their heights were extracted at the same locations from the LiDAR DTM (1 m resolution). For CP selection, stable details on the ground such as road marks (e.g., pedestrian crossing lines), road surface changes, corners of paved areas and corners of parking lots were selected. Considering the horizontal accuracy of the orthophoto (0.10 m) and the vertical accuracy of the DTM (0.12 m), these points are less accurate than the RTK point measurements.  
For the current work, the entire photogrammetric workflow was implemented in the Inpho 8.0 software from Trimble [31], designed to perform precise image block triangulation through bundle block adjustment and 3D point cloud reconstruction using dense image matching techniques for push-broom cameras. The same processing line was followed for Pleiades and WorldView-3 tri-stereo images.