ISPRS Commission II, Vol.34, Part 3A „Photogrammetric Computer Vision", Graz, 2002 
  
Figure 3: Clustering results for Stuttgart data (1.5m res- 
olution). a.) the original range data, b.) The clustered 
data. Bright points — part of a smooth or planar surface, 
gray points — vegetation points or ones with high elevation 
variation. 
standard deviation. The merging part involves also testing 
the surface model. The preference is for simple description 
of the surface, so if both surface elements are planar, then 
merging into one planar surface is tested first; if this test 
fails the following test analyzes if both surface elements 
are part of one smooth surface. Smooth surfaces are mod- 
eled here as biquadratic surfaces. Notice that this way an 
extension to other surface models can be incorporated in a 
very straight-forward way. 
The size of the segments is controlled by the standard devi- 
ation thresholds that are being set. In addition to the upper 
limit s,,4, a lower bound limit, 5;,;; is also set to avoid un- 
dersegmentation. The value is set in accordance with the 
expected accuracy of the laser points themselves. When 
a segment is extended and its std. is below the minimum 
threshold, s,,;, is used instead. Using the fitting accuracy 
as the measure to evaluate clusters offers a very natural 
way to control a cluster, and the use of lower threshold 
is another way to encourage bigger clusters. The prefer- 
ence of planar surfaces in the merging phase and the es- 
tablishing of upper and lower bounds for the std. of the 
parameterized surface enables avoiding over- and under- 
segmentation of the data, as well as overparameterization 
of a surface. 
4 DISCUSSION AND RESULTS 
Results for testing the algorithm are presented for datasets 
with medium to relatively low resolutions, which are less 
detailed and considered more difficult to process. The first 
dataset is taken in the Stuttgart area. The spacing is about 
1.5 m between points. The scene contains several build- 
ings, smooth ground surface and vegetation that is close to 
the buildings. The dataset is presented in Figure 3.a and 
  
Figure 4: Clustering results for Vahingen data (2.5m reso- 
lution). a.) the original range data, b.) the clustered data. 
Bright points — part of a smooth or planar surface, gray 
points — vegetation points or ones with high elevation vari- 
ation. 
the results of applying the clustering algorithm are in Fig- 
ures 3.b. Bright points are part of a smooth surface, gray 
ones are part of a vegetation or unclassified points with 
high elevation variation. As can be seen, the algorithm 
managed to separate successfully the smooth objects, like 
roof tops or smooth parts on the ground, from the vegeta- 
tion, even in cases were both were close one to the other. 
Since the vegetation is rather sparse it is difficult to dis- 
tinguish between high and low vegetation. Therefore, they 
are classified as one structure. 
The second dataset has a lower ground spacing of about 
2.5m between points. The dataset is acquired over the 
Vahingen area in Germany. Buildings here are smaller in 
size and lower in height; therefore, finding structure like 
planar surfaces is more difficult. The results show that the 
algorithm managed to identify successfully the facets of 
the building at the center of the scene and also the one 
at the far right. Considering the complexity of the shape 
of the central building and the point spacing, the results 
indicate that the algorithm is capable of identifying fine 
structures without any preliminary knowledge of their lo- 
cation. The algorithm does not favor, however, identifying 
structure when one does not exit as the mostly correct clas- 
sification of the vegetation indicate. 
The final example is a natural terrain with heavy vegeta- 
tion taken from the Stuttgart dataset. The vegetation con- 
sists mainly of wooded area over a side of a hill. Down the 
hill by the vegetation, a roof face can be noticed and then 
a part of a road. The results of the clustering algorithm are 
given in Figure 5. The algorithm has managed to separate 
the surface from the vegetation successfully, to identify the 
roof facets and to find ground segments on the sloping ter- 
rain wherever they formed a significant segment. 
The quality of the clusters is analyzed, for the first two 
datasets, by the standard deviation of the laser points from 
the fitted surface. The minimal size of clusters was set 
A - 123