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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
e The grid width of the resulting elevation grid is a fundamental 
parameter that is in general selected according to the 
application-specific requirements for the DTM, within certain 
limits given by the scale of the aerial images used for 
matching. Selecting a larger grid size yields a smoothing 
effect that helps to eliminate off-terrain points, but also 
smoothes terrain structures that one might want to preserve. 
The terrain type (flat, undulating, mountainous) has to be 
selected in accordance with the actual terrain type to make 
matching successful. 
The degree of smoothing (high, medium, low) is the 
parameter that is best suited for controlling whether to obtain 
a DTM or a DSM. In this work, we selected the degree of 
smoothing to be “high”, to obtain an initial elevation grid as 
close as possible to the terrain. 
The density of the original point cloud (dense, medium, 
sparse) also influences the degree of smoothing: a sparse 
point cloud results in a model closer to the terrain than a 
dense point cloud. 
MATCH-T can consider geomorphologic elements and 
additional points in the interpolation process, typically 
measured interactively by a human operator. The standard 
deviation of surface points and break lines has an influence 
on the weights of these additional observations in the 
interpolation process. 
MATCH-T delivers DSMs of good quality. If a DTM is 
required, the algorithms for smoothing work well if the grid 
width is not too small compared to the extents of groups of off- 
terrain points in the original point cloud. For instance, groups of 
trees and single buildings can be eliminated if the grid width is 
in the range of about 5-10 m. However, if the grid width is 
chosen smaller, e.g. 1.5 m, these objects remain in the matching 
results, even if a high degree of smoothing is selected. Figure 1 
shows a DSM generated by image matching with a resolution of 
1.25 m. The remaining buildings are clearly visible. 
  
Fionre 1 Shaded view of an elevation grid acquired by image 
matching (Eggenburg east; cf. section 5). 
As in general the grid width has to be chosen in dependence of 
the proposed application of a DTM, there is only a small band 
width for adapting this parameter. That is why we propose to 
improve the image matching results by hierarchical robust linear 
prediction in a post-processing step. Our good experience with 
that technique gives us reason to believe that it should be 
possible to eliminate buildings and groups of trees in high- 
density DSMs delivered by image matching techniques. 
3. HIERARCHICAL ROBUST LINEAR PREDICTION 
We use the program SCOP--* (Briese et al., 2002) for the 
interpolation of a hybrid raster DTM on the basis of irregular 
415 
point and vector data by linear prediction. This method is based 
on the assumption that the heights of terrain points, after 
removing a trend, are correlated, the correlation being a 
function of the horizontal distance between the points (Kraus, 
2000). Linear prediction will be fragile if gross errors occur, so 
that a more robust approach has to be found. In this section, we 
want to describe how this can be accomplished. 
3.1 Robust Interpolation 
Robust interpolation (Kraus and Pfeifer, 1998) was developed 
for DTM generation from ALS-data in wooded areas. In this 
process the elimination of gross errors and the interpolation of 
the terrain are carried out simultaneously. This process consists 
of three steps: 
I. Interpolation of a surface model by linear prediction 
considering individual weights for each point. At the 
beginning all weights are assumed to be equal. 
2. Calculation of the filter values, i.e., the vertical distances 
from the interpolated surface to the measured points 
Recomputation of the weights of the individual points in 
dependence of the filter values, using a weight function 
adapted to the stochastic properties of the filter values of the 
off-terrain points. 
Uu 
The steps are repeated in an iterative process until all gross 
errors are eliminated. The elimination of gross errors (off- 
terrain points) is controlled by the weight function. This weight 
function is controlled by 3 parameters (figure 2): Halfweight h 
(the size of a filter value obtaining a weight of 0.5), slant s (co- 
tangent of the slope at /=h), and the cut-off point 1. 
| A p=p(f) 
Eus h=0. 3m agi 
Ï 
Y = 
E. Om mode, / 
  
to foe 
  
  
  
  
Figure 2. Weight function (Briese et al., 2002). 
The values for 4, s, and t can be set independently for the 
positive and the negative branches of the weight function, i.e. 
for points above and below the surface interpolated in the 
previous iteration. As a consequence, the weight function can 
be asymmetric. This allows to favour points on or below the 
intermediate surface (considered to be terrain points) and to 
decrease the weights of points above the intermediate surface 
that are more likely to be off-terrain points. The function is also 
shifted by a value g. This also should compensate for the fact 
that the intermediate surface is more likely to be above the 
terrain than below it. By choosing the weight function to be 
asymmetric and excentric, we model the actual distribution of 
the errors of the off-terrain points with respect to the terrain. 
Figure 2 shows a weight function for the elimination of off- 
terrain points; note that in this case. points having a filter value 
f « g are not affected by robust estimation (Briese et al., 2002). 
3.2 Hierarchical Robust Interpolation 
Robust interpolation relies on a ‘good mixture’ of terrain and 
off-terrain points, but the algorithm is not able to eliminate 
clusters of off-terrain points as they occur, e.g., in densely 
developed urban areas. To meet this problem, robust