UNNELS 
Portugal - 
res, such as tunnels, 
ems, which produce 
s acquired by laser 
'sentation of the 3D 
ion. 
| images that can be 
.in highway tunnels 
tation where image 
is likely that points 
being described by 
the same way as a 
hen transformed in 
ribed by their (x,y) 
nce to the reference 
to the original 3D 
der is the simplest 
in a plane, without 
cross-section is not 
ame. The resulting 
distance along the 
3-section. 
hat they are curved 
ns of a torus, in a 
) sections of a torus 
  
uxtaposition of two 
5 a point cloud and 
0 the cross-sections 
ns, mapping it then 
ially in railways, is 
ral kilometres. The 
not degrading the 
perception of dimensions in the rectified image of the tunnel 
surface. 
This method was developed in cooperation with Artescan-3D 
Scanning, a Portuguese company that owns a Riegl VMX-250- 
CS6 mobile laser scanning system (figure 2). This system has 
been applied in long tunnel surveying, both motorway and 
railway (Boavida et al., 2012). These can be as-built surveys of 
tunnels, or can be made with the purpose of monitoring and 
maintenance. Many of these surveys span along distances of 
several kilometres, producing very large amounts of data. The 
availability of methodologies that automatically produce 
rectified, planar images of the tunnels, was found an essential 
tool for analysis of these data. 
  
Figure 2. Riegl VMX-250-CS6 mobile laser scanning system in 
operation in a tunnel survey. 
The method was tested with data of railway tunnels, first in 
small samples of the underground of the city of Porto, and then 
with data collected in the survey of a 25 km long high-speed 
railway tunnel (Pajares tunnel in Asturias, Spain). Figure 3 
shows a profile of the terrain and the tunnel in a distance of 
more than 1 km. Tunnel slope is approximately 1.7 %. 
  
  
  
  
  
1200 
1000 
Terrain 
T 800 mE 
= Tunnel 
= 
> 600 
X 
400 
0 200 400 600 800 1000 
Distance (m) 
Figure 3. Profile of the terrain and the tunnel in Asturias. 
2. DESCRIPTION OF THE ALGORITHM 
The goal of this algorithm is to project a 3D tunnel surface into 
a plan, or in other words cut the tunnel longitudinally and 
unfold it to make it flat. The input is a point cloud acquired by 
laser scanning inside a tunnel. 
The algorithm was programmed in PostgreSQL/PostGIS, 
making use of some of its capabilities of spatial search and 
analysis. 
The algorithm is composed by the following 5 stages. 
STAGE 1 
The first stage is to recalculate the tunnel axis. The original axis 
can be acquired in different ways. It can be extracted from the 
vehicle trajectory (obtained by the inertial navigation system); 
109 
from a traverse or other survey network; from a manual 
procedure or from a semi automatic process involving a 
skeletonization algorithm. Once a planar representation of the 
axis is available, a set of points, with constant spacing, will be 
generated along the axis (figure 4). This spacing (e.g. 10 
meters) is a parameter defined by the user. 
" 3 in M Moters 
fear} 
Figure 4. Tunnel axis with the original points (larger squares) 
and the equally spaced points (small dots). 
For each one of these points a line is created, locally 
perpendicular to the axis. The direction of the axis in a point is 
considered to be the direction defined by the previous point and 
the next point, as shown in Figure 5. 
"m 
A. — 
ji 3 
ry gai 
ee 
pp 
0 5 18 26 Meters 
Figure 5. The perpendicular line (green line) at point 3 is 
calculated perpendicularly to the direction defined (blue line) by 
the previous (2) and the next point (4). 
Now a buffer around this perpendicular line is created, with 
parameters specified by the user. Then, all the points from the 
point cloud that are inside this buffer are averaged to calculate 
the central point of the tunnel at the respective location (the 
central point is a 3D point calculated with the average values of 
the three coordinates of the selected points from the point 
cloud). The final 3D tunnel axis is composed by all this 3D 
points. This process can be recursively repeated until the 
differences between the old and the new axis are negligible. 
STAGE 2 
The second stage is to rectify the tunnel axis that was 
automatically created. It is possible that the axis calculated in 
the previous stage has errors or unwanted points. In these cases, 
it is crucial to examine the result and make the desired changes 
manually, before continuing to the next stage. This step is 
essentially a visual inspection and possibly a manual adjustment 
of few points. It is not time consuming and may increase the 
results quality in irregular parts of the tunnel. 
STAGE 3 
The third stage is the segmentation of the point cloud. For each 
vertex of the axis a plan perpendicular to the trajectory is 
calculated (direction defined as before, between the previous 
point and the next point). These plans can be materialized with 
their dimension defined by user (Figure 6). 
en n 
Figure 6. The tunnel axis (red line) is cut by perpendicular plans 
(green plans) crossing the axis in its vertices, segmenting it. 
The tunnel axis is cut in n — 1 segments (n is the number of 
axis vertices). For each segment, comprehended between two