ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002 
  
The first idea was to use a terrain shading and contour lines to 
locate these errors and to eliminate these false points manually, 
but it took quite a long time to go through this dataset with 
more than 300,000 points. To automate this process we applied 
the robust interpolation technique presented in sec. 3.2. The use 
of the hierarchic set-up was not necessary, because of the low 
point density and the low number of gross errors. However we 
had to adapt the weight function to the error distribution of this 
dataset. Unlike to laser scanning this dataset includes gross 
errors above and below the terrain and therefore we had to use a 
symmetric weight function to eliminate points with positive and 
negative filter values f. This weight function P(f) With a sharp 
decline in the positive and negative branch is displayed in fig. 3. 
With the help of this weight function and a maximum number 
of three iterations the algorithm was able to eliminate these 
gross errors and a refined classification in terrain and off-terrain 
points with the help of tolerance values of +0.3m was possible. 
|^ P=p(f) 
  
  
  
  
  
Figure 3: Symetrical weight function for the elimination of 
points with high positive and negative residuals with a half 
width value of 0.2m 
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Figure 4: Perspective view of the DTM after robust Interpol- 
ation (automated elimination of off-terrain points, 5m grid with) 
  
   
  
Photogrammetric measured break lines were included in the 
modelling process, which improved the automatic result. These 
break lines are treated as gross error free, which means that only 
the random measurement error is filtered. For the robust 
filtering this means that they have the weight 1 for all iterations. 
A perspective view of this DTM is presented in fig. 4. A 
comparison of this automated result with the manually corrected 
DTM by a difference model showed that the automatic process 
was very successful und led to similar results. Currently the 
complete data of the digital map (13 mio. points, ~ 400km?) is 
processed in this way. 
4.2 Hierarchic Robust Interpolation of Airborne Laser 
Scanner Data 
The generation of a DTM from airborne laser scanner (ALS) 
data is the “classical” use of the robust interpolation technique. 
A lot of different algorithms for this task do exist (e.g. 
Axelsson, 2000; Elmqvist et al, 2001; Vosselmann and Maas, 
2001). As mentioned before, this algorithm was originally 
designed for the determination of a DTM in wooded areas 
(Kraus and Pfeifer, 1998). A pilot project with a dataset in the 
city of Vienna showed the limitations of this technique in build- 
up areas where large areas without terrain points do exist. 
Therefore we developed the hierarchical robust interpolation 
(sec. 3.3), which is also very useful in dense vegetated areas, 
which have similar characteristics for the DTM generation 
(large areas without ground points) like build-up areas. In the 
meantime the use of the hierarchical set-up, which strengthens 
the robustness and reduces computation time with two to three 
data pyramid levels, proved to be very useful in many test 
projects (see Pfeifer et al., 2001). 
In this section the results of the DTM generation process in the 
Vienna test suite are presented (fig. 5). The accuracy of the 
DTM was checked by 816 tacheometric measured control 
points. The root mean square error (RMS) of the DTM was 
0.11m. 
For the robust interpolation in each data pyramid level an 
asymmetric shifted weight function must be used (fig. 6) in 
order to give high weights to points on the terrain surface, 
whereas the influence of off-terrain points (e.g. on the 
vegetation, houses and cars) is iteratively reduced by low 
weights. 
  
Figure 5: Perspective views of the digital surface model (DSM) 
and the DTM computed by hierarchical robust interpolation of 
the Vienna test suite 
A p=p(f) 
A h=0.3m Sch An 
| 
g 00m t=0.3m f 
— 
  
BO fr 
  
  
  
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Figure 6: Typical weight function for the elimination of off- 
terrain points above the terrain. The value of g is determined 
automatically.