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.