where
\begin{equation} r=\sqrt{\text{dlx}^{2}+\ \text{dly}^{2}},\nonumber \\ \end{equation}
and k1 , k2 andk3 are the radial distortion coefficients of the lens while p1 and p2 are the tangential distortion coefficients of the lens. These distortion parameters can normally be extracted from the photogrammetry software. If professional camera equipment is used these distortion parameters can normally also be found in the data blade for the lens. A more detailed discussion on lens distortion and equations (2) to (3) can be found in reference [12].
The camera position and viewing angle can be extracted from the Metadata in the image files. The precise location of the TP is also known, this means that the distance DCT from the camera to the TP needed in the equations can be calculated. The 3D world coordinates for all the paint defect/damage pixels in an image calculated using equations 1-3 are represented by the red points and corresponding surface in Figure 4 (a)-(b). These red points are in general placed behind, in front of, or on the TP.
Figure 4 (b) shows the normals with the blue color to the surface given by the red points. The projection of the red points in the direction of the local normal onto the TP surface results in the green points. Both positive and negative normals to the surface must be calculated because the red points can be both in front and behind the large-scale structure. The mapping of the paint damage pixels found in one of the drone images onto the 3D model is given by these green points. The calculated projection points can be anywhere on the mesh, hence also between the vertices of the mesh. A faster but less accurate approach is to find the closest point on the TP for a given point on the red surface. The algorithm is less precise because only the vertices in the mesh can be used but the method can still give very good results if the resolution of the mesh is high and the details of the 2D points that are mapped are relatively coarse. This is illustrated in Figure 5 below where a not-too-detailed drawing of a “blue dog” is mapped using this nearest point method onto the TP. A small drone yaw angle and a placement of the drawing close to the center of the mapped image also contribute to the good result.