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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
deviations for buildings. Hence, the value range extends 
from the minimum variance (u=0) to the maximum (u=1). 
Finally a combination of the single fuzzy values takes place 
through an unweighted averaging. Those segments, that have 
been classified as potential buildings in the first step and 
which also show here a combined membership value larger 
than 0.33, are now classified as buildings. 
4.4.4 Post-Processing: At this point of the algorithm the 
vectorisation of the selected building outlines only is 
performed. 
The problem with these c/assified edges is that they are based 
on the LE-low reflections of the laser scanning system which 
represent the outstanding objects in reduced size compared to 
the real outlines (sec figure 2). Hence, a dilation has to be 
performed. In principle, multi-spectral imagery is able to locate 
these edges which more precisely (Schenk & Csatho, 2000). It 
has to be noted that these images edges would not have been a 
suitable input into the previous segmentation step because 
numerous edges of all objects would have been detected and 
several effects like gaps or over-sampling would have 
disturbed the object delineation. At this stage of our study we 
derive the image edges simply by using the above applied 
segmentation algorithm (figure 5, top left). 
Because the image edges are rather imperfect, in the following 
the edge matching process is equivalent to a buffering of the 
classified edges into the direction of the outside image edges. 
In order to estimate the buffer distance we compute for every 
vertex of the classified edge the nearest distance to the 
surrounding image edge and build the average of those 
distances that are smaller than 1.5 pixels. This threshold is 
necessary in order to neglect incorrect or further image edges 
that are too far away from the real building outline. The value 
corresponds to the maximum positional error of the classified 
edges as derived from the LE-low reflections. The buffer 
operation yields, after dissolving barriers between the buffer 
boundaries, the dilated classified edges (figure 5, top right). 
  
Figure 5. Post-Processing: top left: selected building (yellow) 
with classified edge (red, “1”) and image edge 
(blue, “2”), top right: additionally dilated classified 
edge (black, “3”), bottom: smoothed dilated 
classified edge (orange, “4”). 
609 
Finally a smoothing of these edges takes place using the 
Douglas-Peucker algorithm (figure 5, bottom). 
4.5 First empirical results 
With respect to the segmentation process the visual inspection 
yielded satisfying results with the selected grade of 
generalisation. The geometrical accuracy of the selected 
heterogeneity feature LE-low leads to a good separation of 
buildings from their surrounding objects. 
Obviously, the key problem of the segmentation procedure is 
the proper and automatic choice of the grade of generalisation. 
It is possible to use multiple generalisation levels, for instance 
by applying the methodology of “Classification ‘on multiple 
segment levels” (Schiewe, 2003). However, due to complexity 
reasons we have chosen only one scale level for this study. 
The classification accuracy is determined through a visual 
interpretation of the obtained segments and expressed in terms 
of the error coefficient C as follows: 
omission errors * commission | errors 
C=1- 
  
total _number _of _ pixels _in_ class 
Thus, the higher the coefficient C (with a maximum of +1.0) 
the better the overall classification accuracy is. After the first 
classification stage (elimination procedure, refer to section 
4.4.3) C amounts to 0.88 where 95.3% of all buildings have 
been detected. The second stage (fuzzy logic classification) 
significantly reduces the number of commission errors so that 
the coefficient C becomes 0.92. While the remaining omission 
errors (4.7% of all buildings are not detected) are due to 
segmentation problems (see above), nearly all commission 
errors occur along the scene border. If additional knowledge 
would have been introduced here, the number of commission 
errors could have been reduced even more and the coefficient 
C would have been increased to 0.97. 
It has to be stated that in principle the detection of buildings in 
FALCON data sets can be performed with an even increased 
accuracy if the imagery would have been taken during summer 
time. For our data set, which was captured in early March, the 
NDVI was not as effective as in other studies (e.g. Schiewe, 
2003) for the distinction between buildings and vegetation (in 
particular deciduous trees). 
   
Figure 6. Result of post-processing step (orange line) 
; compared to manually digitised edge (red rectangle) 
as well as numerous image edges (blue), overlaid 
onto LE-low elevation data.