0.32 
0.23 
0.14 
0.05 
-0.03 ! 
-0.12 
-0.21 
-0.30 
-0.39 | 
-0.48 | 
-0.57 J 
  
  
ElReihe1 
  
  
  
  
  
  
0 20 40 60 80 100 120 
Figure 6: Distribution of heights above a facade level 
After the projection we perform an image based matching 
between the participating images. The candidates in the 
neighbourhood are used to improve the initial values of the 
affine transformation of the Least Squares Matching (LSM) 
process (Klemt & Gendt 2001). If the matching succeeds, the 
3D coordinates can be calculated and the new point can be used 
again as seed point. If the matching fails, the region growing 
stops at that point. The results of these processes are shown to 
the operator in each image. This allows the operator to provide 
new seed points and select areas, where a higher density of 
matching points is required (e.g. in areas of special interest). 
  
0 2 4 6 0 2 4 6 
Figure 7: Non suitable interpolation results using algorithms 
for topographic surfaces. Nearest Neighbour (left) 
and Inverse Distance to a Power (ri ght) 
3. DSM INTERPOLATION 
3.1 Data Preparation 
Before the next step four gradient images are calculated from 
each used image, showing the horizontal, the vertical and the 
two diagonal gradients in the images (Fig. 5). Furthermore a 
histogram is calculated, showing the usually irregular 
distribution of height values of the 3D points above the 
projection plane (Fig. 6). 
Surface interpolation algorithms designed for the topographic 
usage (Schiewe 2000) are not suitable for the use with facades, 
due to their failure at discontinuities (Fig. 7). Therefore special 
algorithms have be de developed or adapted for the special 
requirements of DSM interpolation of facades. 
3.2 Interpolation Algorithm 
After the matching process a DSM is interpolated to describe 
the height of the grid points over or below the projection plane. 
The DSM is interpolated using fuzzy logic (Kahlert & Frank 
1993) and is based on the assessed heights of the neighbouring 
3D points. The fuzzification is based on several probabilities of 
the different fuzzy sets. For this purpose linguistic values as 
listed below are used to define the un-sharp fuzzy sets.. 
Inference and composition are used to combine the fuzzy sets 
and allows to make a decision based un the de-fuzzification of 
the result of this combinations. 
The following information contributes to the computation of the 
height of the grid point: 
* The probability is high, that the grid point has the 
same height as one of his neighbours. 
* The geometric quality of the 3D points, depending on 
correlation coefficients and ray intersection 
e The projected distance to the next 3D points. 
e The sums of absolute gradient values in the different 
images along the connection between image points of 
the assumed grid point and the 3D points. 
e The probability is high, that the horizontal and 
vertical curvature of the surface in the neighbourhood 
is constant. It depends on the local distribution of 
curvature values. 
e The probability is high, that the height fits to one of 
the peaks of the above mentioned height histogram. It 
is derived from the standard deviations of the peaks. 
In the preliminary version we only mention the gradient in the 
image. We do a simple interpolation based on the Nearest 
Neighbour interpolation under consideration of the gradient 
distribution in the neighbourhood. At the moment some 
interactive editing of the DSM remains necessary. 
4. USAGE OF THE DSM 
After this calculation the DSM may be used to derive digital 
orthoimages from all suitable raw images (Baratin et al., 2000) . 
These orthoimages are used to allow a good quality control for 
the DSM. Differences between the orthoimages may show the 
weak regions of the orthoimages. Therefore a tool for the 
interactive editing of the DSM is also required. 
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