In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C.. Tournaire O. (Eds). 1APRS. Vol. XXXVIll. Part ЗА - Saint-Mandé, France. September 1-3. 2010 
Ebridge in order to show the benefits of using this information 
(Figs. 3). The weights used in this and all the following 
examples are given in Tab. 1; these values were determined 
empirically. Tab. 2 and 3 illustrate the RMS of the point to line 
distances of the results for the four examples shown in Fig. 3. 
Generally, if the initialisation is located within the borderline of 
the bridge the quality of the results without bridge information 
is similar to the other. However, the algorithm converges faster 
with the integration of the bridge detection method. If the initial 
position of the road network is situated outside the bridge due to 
large differences between the landscape model and the height 
data the snake is not able to jump across the strong edges along 
the bridge using only E ALS and E hw i d and thus can not move to 
the correct position. However, in all examples in Fig. 3 the 
bridge energy supports the adaptation of the small road network 
in such a manner that the snake reaches a suitable position. 
parameter 
a 
ß 
К/ 
value 
0.1 
0.2 
5 
Table 1: Weights for the different energy terms of the snakes 
for all illustrated examples. 
RMS of 
point to line 
distances (m) 
Bridge 1 
Bridge 2 
without 
with 
without 
with 
Initialisation 
8.24 
8.24 
5.63 
5.63 
Solution 
6.00 
0.61 
3.95 
1.87 
Table 2: Evaluation of the results in examples 1 and 2. 
RMS of 
point to line 
distances (in) 
Bridge 3 
Bridge 4 
without 
with 
without 
with 
Initialisation 
4.84 
4.84 
5.11 
5.11 
Solution 
3.77 
2.13 
2.42 
2.06 
Table 3: Evaluation of the results in examples 3 and 4. 
In the first example (Fig. 3a) a straight road is adapted. For the 
simulation of inconsistencies the initialisation was shifted by 
6 m both in x and y. The results without the bridge energy could 
be improved by larger weights for the internal energy terms in 
order to increase the smoothness of the contour. However, this 
means that other road parts with strong curvature can not be 
treated without defining different weights for special segments. 
This would make the algorithm more complex and the 
transferability to other data sets would suffer. With the bridge 
information it is much easier to define weights that can be 
applied to the entire road network. The second and the fourth 
examples (Figs. 3b and 3d) show a similar behaviour. Each 
initialisation was shifted by 5 m both in ,v andy. The integration 
of the bridge energy significantly improves the quality of the 
results. Obviously, the bridge energy affects only the network 
nodes in a certain vicinity. Therefore, the quality improvement 
in the example 2 is larger (2.08 m) than in example 4 (0.36 m). 
In the third test the underpass road is not located in the centre of 
the bridge (cf. DTM in the centre of Fig. 2(a)). Therefore, the 
assigned new image energy forces this road segment to the 
bridge centre, which is in this case not the correct position. 
Thus, a larger RMS difference to the reference (2.13 m) can be 
observed than in the other examples. For this situation the 
bridge detection method has to be extended by position and 
direction information of the underpass road. 
Fig. 4 visualises the adaptation of a larger road network 
including four bridges. The initialisation was again shifted by 
5 m in each coordinate axis, resulting in a RMS of the 
perpendicular point to line distances of 4.88 m. After the 
optimisation process this value decreases to 2.91 m. 
Figure 3. Adaptation of four small road networks to ALS data 
near single bridges (blue: initialisation; red: final 
position; left/right: without / with bridge energy. 
Figure 4. Adaptation of larger road networks (2199 nodes) to 
ALS data with bridge energy (blue: initialisation; 
red: final position). 
One of the main problems causing the remaining large 
differences to the reference is that road parts with strong 
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