33. Istanbul 2004 
deviations from 
haracteristics of 
; can be obtained 
local curvature 
> of subsequent 
point. Inside the 
> values will be 
gnificant higher 
and last pulse 
Building roofs 
lent on the slope 
ces between first 
d. In contrast at 
etrable for laser 
tionally, a new 
local variance 
ments. But this 
ation as height 
. therefore, was 
1 principle high 
ifferences can be 
and vegetation. 
ent areas can be 
eters to avoid 
  
fferences 
contribute to the 
s (e.g. buildings, 
js of trees, rough 
ination of shape 
nent has to be 
f uniform (pixel) 
le edge tracking 
ntour lines. After 
Douglas-Peucker 
nd size of these 
ions have shown 
like roundness, 
rents which are 
t shapes in this 
(ers had been 
where at first the 
ected (e.g. n=4). 
parallelism and 
is 100 for perfect 
   
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
parallel or orthogonal lines and decreases proportional to 
increasing deviations from that. This shape parameter has 
proved to be suitable to distinguish artificial and natural objeets 
in most cases, if their area is large enough. Small object sizes 
lead to ambiguities. Fig. 7 and 8 show examples of filtered 
contour polygons of typical building and vegetation objects 
respectively. 
  
Figure 7. Contour polygons of typical building segments 
  
Figure 8. Contour polygons of typical vegetation segments 
For one test site (Salem) laser intensities were available which 
are recorded by the new TopoSys II sensor. This additional 
information was also included in the test program. The intensity 
of laser pulses depends highly on the characteristic of the 
reflecting material. In most cases buildings with commonly 
used rooftiles cause much higher or in the other case nearly the 
same intensity values than vegetation. An example of typical 
intensity characteristics of buildings and vegetation can be seen 
in Fig. 9. 
Some statistical values like minimum, maximum, average and 
RMS was determined for all features mentioned above. In every 
case the average value was selected for classification purposes 
as it has proved to be the most suitable one. 
Fuzzy classification 
The subsequent classification and its results depend on the 
preceding segmentation process because only segmented 
objects 
  
Figure 9. Laser pulse intensities with extracted building 
boundaries 
are classified. The fuzzy logic classification is based on the 
extracted features which have been described above. Fuzzy 
logic presents an opportunity to get answers to questions with a 
truth value in a range of 0 and 1. Fuzzy logic has been used in a 
wide range of applications, mainly in system controlling, and 
supports classification processes as well. The uncertain and 
often contradictory information can be handled and quite 
accurate results may be obtained. The fuzzy theory tries to blur 
the boundary between membership and non-membership. 
Therefore the elements can be members, non-members and 
partially members as well. The basic idea is to model this 
uncertainty of classification parameters (features) by so called 
membership functions. A user has to define such a membership 
function for every parameter and every class (fuzzification). 
They may be built up by straight line sections in order to make 
computation easier, but also functions of higher degree can be 
defined dependent on the respective application. But in practice 
it has been proved that different approach don't effect the 
results too much. Normally, membership functions are defined 
in an empirical way by means of training samples visually 
selected and interpreted by an operator. In this case about 25 
segments have been chosen for each class. Histogram analysis 
may help to determine the parameters of membership functions, 
but a control and — if necessary — an improvement of these 
functions should be done in every case. These membership 
functions have proved to be quite stable and robust independent 
on different locations (Voegtle, Steinle 2003). 
A concrete value of feature i leads — by means of the 
corresponding membership function — to the related degree of 
membership pi; for every class j, in this project F3 
(buildings/vegetation/terrain). All membership values for the 
same class j have to be combined for a final decision (inference 
process). The original Zadeh-type operators are used, such as 
minimum, maximum and product, besides this a weighted sum 
was tested also. The minimum, maximum and product operator 
for a class can be defined as: 
H (anBacy ©) 7 min (4 4 (X), As G9) . uc 9) 
H (AvBvc) (X) = max (140%), tp (x), pcx) 
Maso) (X) 7 ua) * up ®)* pc)