‘the point cloud to a 
Jd the nearest cross- 
o one). Then, the two 
ained, as well as the 
, as shown in Figure 
aon oM n 
e 
ross-section and its 
oints) for the point 
D). 
determination of the 
oint in analysis is 
points of the section 
tion) until the top of 
for the other section 
oint in analysis and 
he weighted average 
along the sections, 
tween the point and 
  
in analysis and the 
ross-sections (black 
the two distances. 
analysis (red point) 
ted with the average 
(1) 
d cross-sections 
1€ Cross-sections 
tion at the axis 
distance larger than 
are considered not 
discarded from the 
its (2D points) have 
nel axis and the Y 
coordinate as the length of the arc (along the tunnel's wall), 
from the top of the tunnel to the point. The points from the point 
cloud are now projected in a plane. Laser return intensity values 
can then be resampled in order to generate a continuous image. 
Some examples are shown in the following section. 
3. RESULTS AND DISCUSSION 
This section describes some tests of the algorithm with real 
data. The initial tests were done with small subsamples of data 
collected in Portugal. A second test was done with the full data 
set acquired in Spain, but in subsamples of 1 km. The choice of 
several parameters is justified. 
3.1 Tests with small samples 
The generation of an axis for a tunnel is a relatively simple 
process, by skeletonization, that can be achieved fully 
automatically. The definition of perpendicular plans in order to 
divide the tunnel in segments (in general with 10 m length) is 
also a simple and automatic process. 
Once points in a segment are extracted there is an important 
parameter to chose, that depends on the shape of the cross- 
section. The first example is for a tunnel in the region of Porto, 
that has a rather irregular shape. 
Figure 12(a) represents the points in a cross section, for which 
polar coordinates are calculated. In order to create a set of 
points that define the polyline of the cross-section, points are 
grouped in angle intervals, such as 5° 10° or 20°. This 
corresponds to the cross-section being modelled by 72, 36 or 18 
points, respectively. Figure 12(b) represents, in green, blue and 
red these situations. 
  
  
(b) 
Figure 12. Points of a cross-section, in polar coordinates (a); 
adjustment of polylines at angular steps of 5°, 10° and 20° 
At the smoother part, the top of the tunnel, an angle step of 20° 
was enough. However, since in some parts the orientation of the 
line changes significantly, the adjusted line lies a few 
decimetres apart form the points. A 5° step was chosen in order 
to do a better modelling of the cross-section. 
Another important step is the elimination of points that do not 
belong to the tunnel surface, such as cables. The rule that was 
adopted was that, once a polyline was adjusted to the cross- 
section, any point that is more than half meter away from the 
polyline is not on the tunnel surface. Figure 13 shows a few 
points in cables. This step is important in order to avoid 
obstacles in the final unfolded image of the tunnel surface. 
111 
  
  
Figure 13. Elimination of points not on the surface. 
Finally comes the planar projection. All points in the point 
cloud identified as belonging to the tunnel surface were mapped 
to a tunnel segment. Within the segment each point was located 
by a distance along the axis, and by a distance along the cross- 
section, in order to plot the segment as a planar image. 
Figure 14 shows a segment of the tunnel in Porto, with grey 
values representing intensity. After unfolded it shown as a 
planar image of laser intensity, with the railways in the centre. 
The left and right parts of the image represent the top of the 
tunnel. 
  
Figure 14. Unfolding of a tunnel segment 
3.2 Tests with larger datasets 
The Pajares tunnel, in Spain, with 25 km length, and a point 
spacing of a few mm, corresponds to an extremely large dataset 
that has to be treated partially. It was divided in 1 km parts and 
also these were decimated in the Riegl software in order to keep 
points in an average density of 1 point per square decimetre. 
This was enough for the definition of the surface, but all the 
data can be later processed for the planar images. 
A few important differences existed in this case. First, the radius 
of curvature of this tunnel is very large (more than 4 km), and 
so the tunnel segments could be increased to more than 10 
meters without any problems with deformations. 
Another fact for this tunnel is that its cross-section is nearly 
circular, with the bottom flat. A total of 36 points per cross- 
section are enough to have an approximation of 1.5 cm in a 
tunnel with 8 m diameter. 
Although the tunnel surface is very regular in some parts it has 
some derivations that may cause some irregularities in the 
automatic determination of the tunnel axis. These very few 
situations were corrected by a manual editing, in a few points 
only, of the axis.