ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002 
  
computed, and the stochastic model which is responsible for 
weighting. 
The functional model: Linear prediction is used for modeling 
the surface. Using this model, it is possible to compute a 
smooth surface considering random measurement errors (Kraus, 
2000). 
The stochastic model: For the generation of a DTM, high 
weights must be assigned to terrain points below or on the 
averaging surface, and low weights have to be assigned to the 
non-terrain points which are above the averaging surface. A 
typical weight function p(r) parameterized by the discrepancies 
r for the generation of a DTM from laser scanner data is 
presented in. Figure 2. The weight function we use is not 
symmetrical, and it is shifted by a value g. It has a sharp decline 
defined by its half-width value h and slant s for discrepancies 
greater than its central point (i.e., for off-terrain points above 
the estimated surface) and no decline for the terrain points. The 
exclusion of points from the interpolation process is triggered 
by a threshold t derived from a user-specified tolerance for the 
size of the discrepancies. For a comprehensive description of 
this algorithm see (Kraus and Pfeifer, 1998). 
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Figure 2. Weight function for the generation of a DTM from 
laser scanner data. 
3.2 Hierarchic Robust Interpolation 
The method of iterative robust interpolation relies on a “good 
mixture" of terrain and off-terrain points. Therefore, this 
algorithm does not work in large areas without terrain points as 
they are likely to exist in densely built-up areas. To provide this 
“good mixture" also in densely builtup areas, robust 
interpolation has to be applied in a hierarchic way using data 
pyramids (comparable to image pyramids in image processing). 
The hierarchic robust interpolation proceeds as follows: 
1. Create the data pyramids. This can be achieved by selecting, 
for instance, the lowest points in a regular grid mesh. 
2. Perform robust interpolation to generate a DTM. 
3. Compare the DTM to the data of the next higher resolution 
and accept points within a certain tolerance band. 
Steps 2 and 3 are repeated at each resolution level of the data 
pyramid. The results of DTM interpolation in the lower 
resolution levels are used for the computation of the surface in 
the next higher resolution because only points having passed the 
thresholding step 3 are considered at that level. 
In (Briese, 2001), this strategy has been evaluated for the 
generation of a high-quality DTM of a test site located in the 
City of Vienna (2.5 km?) using three data pyramid levels 
(5 m, 2 m and 0,5 m). A few intermediate results of this DTM 
generation process are presented in the perspective views in 
Figures 3a-d. 
  
  
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Figure 3d. DSM (0.5 m) of the accepted original points (the 
points within a user-defined tolerance band). 
Figure 4 shows a perspective view of a detail of the final DTM. 
Further details about hierarchical robust interpolation, its 
implementation in the software package SCOP, and the results 
of some further examples can be found in (Pfeifer et al., 2001). 
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