## 3 Methodology  
Figure 2 depicts the global data processing workflow. With the aid of a priori information coming from GNSS trajectories, tie points were extracted solely on overlapping images with the algorithm SIFT (Scale Invariant Feature Transform) [24]. A first BBA procedure including only tie points was performed to recover the observed scene. At this step, we get information of the camera attitudes and the tie points are completed by taking this into account. A second BBA procedure including complete tie points was performed for estimating camera poses in a relative scale. GNSS-derived camera positions were used to transform the estimated relative camera poses to absolute ones by estimating a spatial similarity. Afterwards, the tie points, the GCPs, the GNSS-derived camera positions and the image measurements were used as observations for an absolute BBA. Finally, the accuracy was evaluated with CPs. The bundle block adjustment was carried out with bootstrap solutions. Performing direct algorithm on a single image, a pair or a triplet of images, the global orientation was deduced sequentially starting from a seed image pair [25]. The camera was self-calibrated during the relative BBA process with a two-step procedure. Firstly, the center of distortion (CD) and the  
Figure 2: Data processing workflow. radial symmetric distortion (RSD) were estimated (the latter with a polynomial up to \(R^{15}\)). Then, the RSD and the CD parameters were fixed, and the asymmetric radial distortion was estimated. The objective of the second phase was to model the sensor and lens discrepancies that have no physical explanations. The refined camera model, especially the high degree polynomial for radial distortion correction, mitigates significantly the recurrent \"dome effect\" without over-parameterizing [4; 26]. The estimated parameters of the camera model then served as input for an absolute bundle block adjustment and can be either re-estimated or fixed within the procedure. This absolute BBA procedure takes tie points, GNSS-derived camera positions, GCP coordinates and image measurements as observations. Aforementioned observations being redundant, the cost function was minimized with least square method. The mathematical model of the performed bundle block adjustment is presented as follows. The cost function to minimize is:  
\[\mathcal{E} =\sum_{l=1}^{L}\sum_{m=1}^{M}\frac{\left(p_{l,m}-\zeta(\pi(R_{m}( P_{l}-C_{m})))\right)^{2}}{\sigma_{im}^{A}} \tag{1}\] \[+\sum_{z=1}^{Z}\sum_{k=1}^{K}\frac{\left(R_{k}(C_{k}-C_{\text{gnss},k})-\vec{\theta}_{z}\right)^{2}}{\sigma_{gnss}}\] (2) \[+\sum_{n=1}^{N}\frac{\left(P_{n}-P_{\text{gcp},n}\right)^{2}}{ \sigma_{gcp}}^{2}\] (3) \[+\sum_{n=1}^{N}\sum_{m=1}^{M}\frac{\left(p_{n,m}-\zeta(\pi(R_{m} (P_{\text{gcp},n}-C_{m})))\right)^{2}}{\sigma_{im}^{H}} \tag{4}\]  
where: \(l\) is the index of tie points;  
\(m\) is the image index;  
\(z\) is the index of image blocks assorted by lever-arm;  
\(k\) is the index of images with GNSS measurements;  
\(n\) is the index of GCPs;  
\(\zeta\) is the camera model;  
\(\pi\) is the projection function;  
\(p_{l,m}\) is the 2D position of tie point \(l\) in image \(m\);  
\((R_{m},C_{m})\) is the pose of image \(m\);  
\(P_{l}\) is the 3D position of tie point \(l\);  
\(C_{k}\) is the camera projection center of image \(k\);  
\(C_{\text{gnss},k}\) is the phase center of GNSS antenna of image \(k\);  
\(R_{k}\) is the world to camera rotation;  
\(\vec{\theta}_{z}\) is the lever-arm of image block \(z\);  
\(P_{n}\) is the pseudo-intersection position of GCP \(n\);  
\(P_{\text{gcp},n}\) is the ground measurement of GCP \(n\);  
\(p_{n,m}\) is the image measurement of GCP \(n\) in image \(m\);  
\(\sigma_{int}^{A}\) is the weight of tie points in images;  
\(\sigma_{gnss}\) is the weight of GNSS measurements;  
\(\sigma_{gcp}\) is the weight of GCPs; and  
\(\sigma_{int}^{A}\) is the weight of image measurements of GCPs.