## 4 Three-Dimensional Modelling by the SfM-MVS Approach
### Direct and Indirect Georeferencing
The calibration procedure allows the determination of the rotation matrix (\(\mathbf{R}_{c}^{b}\)), which can be determined by the product between the rotation matrix provided by the IMU (\(\mathbf{R}_{b}^{l}\)) and the rotation matrix provided by the conventional beam adjustment using the control field of frame l. Specifically, the rotation matrix (\(\mathbf{R}_{c}^{b}\)) is expressed by the following relationship [74]:  
\[\mathbf{R}_{c}^{b}=\mathbf{R}_{l}^{b}\mathbf{R}_{c}^{l}. \tag{4}\]  
The vector between the GPS phase centre and the IMU centre is determined through a survey process. The vector and boresight angle can be calculated by comparing the position and trim differences between the EO parameters and the interpolated INS/GPS solutions:  
\[r_{bc}^{b}=\mathbf{R}_{l}^{b} \begin{pmatrix}X_{oc}^{l}&X_{ob}^{l}\\ Y_{oc}^{l}&Y_{ob}^{l}\\ Z_{oc}^{l}&Z_{ob}^{l}\end{pmatrix} , \tag{5}\]  
where:  
\(r_{bc}^{b}\)--vector to be estimated;  
\((X_{ob}^{l},Y_{ob}^{l},Z_{ob}^{l})\)--positional vector of the INS centre in the l-frame provided by integrated INS/GPS POS solutions;  
\((X_{oc}^{l},Y_{oc}^{l},Z_{oc}^{l})\)--positional vector of the camera centre in the l-frame provided by the beam adjustment adjustment. A sketch of the DG acquisition scheme and several frames is shown in Figure 6.  
Indirect photogrammetry is the traditionally most widely used procedure, and it is a particularly robust method that uses a series of ground points of known coordinates, called ground control points (GCPs), and \"tie points\" between individual frames to perform orientation. In general, GCPs are reference points easily recognisable on the images, such as intersections, manholes, antennas (Figure 7a), marks made by tracing an X shape on the ground with spray paint (Figure 7b), panels made of waterproof, high-contrast material (black and white or yellow and black), with a matt finish to reduce reflections and improve visibility (Figure 7c), and coded targets (Figure 7d). Target sizes are variable depending on the design GSD; however, their size must be such to ensure that they can be identified at the flight height from which they are detected. GCPs should be distributed evenly over the area to be surveyed and, depending on the terrain morphology, positioned at different altitudes. More information regarding the use and impact of the GCPs in UAV photogrammetry can be found in refs. [75,76]. Subsequently, within the photogrammetric processing software, GCPs must be manually identified on the individual photos and their associated coordinates in the appropriate reference system used. Currently, various photogrammetric processing software can automatically identify GCPs (coded targets) within the project area through the use of machine learning and computer vision algorithms. The use of GCPs makes it possible to define a relationship between the reference system of the object and that of the image. In fact, GCPs are known to coordinate points in both reference systems, capable of making the parameters within the collinearity equations the only unknown elements. Figure 6: DG: Acquisition scheme (**a**) and representation of several frames (**b**). Figure 7: Ground control design: natural points (**a**), marks made with spray paint (**b**), high-contrast targets (**c**), and coded targets (**d**). The collinearity equations are the constitutive equations of photogrammetry, useful in the transition from image space to object space, and express the alignment between the object point, the image point, and the point of the camera:  
\[ \begin{split} x^{0}&=-c\frac{r_{11}(\hat{x}-\hat{x}_{ 0})+r_{12}(\hat{y}-\hat{y}_{0})+r_{13}(\hat{z}-\hat{z}_{0})}{r_{31}(\hat{x}- \hat{x}_{0})+r_{32}(\hat{y}-\hat{y}_{0})+r_{33}(\hat{z}-\hat{z}_{0})},\\ y^{0}&=-c\frac{r_{21}(\hat{x}-\hat{x}_{0})+r_{22}(\hat{y}- \hat{y}_{0})+r_{23}(\hat{z}-\hat{z}_{0})}{r_{31}(\hat{x}-\hat{x}_{0})+r_{32}( \hat{y}-\hat{y}_{0})+r_{33}(\hat{z}-\hat{z}_{0})},\end{split}