International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
  
In Figure (1), the three dimensional input data are divided into 
four clusters and the cluster centres are updated via the 
competitive learning rule. 
The input vector x=[x, x, x, and the weight vector 
T . 
W;= m Ways Wa ] ; sind 
! Pp M for an output unit are generally 
assumed to be normalized to unit length. The activation value 
* ! of output unit J is then calculated by the inner product of 
the input and weight vectors: 
s 2 T 
y; = S xw, =X W (7) 
d 2 - : 
Where: w, | = X Wi =] for j= l,..., M . Therefore 
i=l 
  
we say that neuron j is the winner of competition if: 
y «y, forall /,and J] = J. 
A simple competitive learning algorithm is composed of the 
following steps: 
Step I: Initialize all weights to random values and normalize 
them (so that |w, =i). 
Step 2: Choose pattern vector X from training set (input 
vector) 
Step 3: Compute distance between pattern and weight vectors 
  
(dx, - w| ) and find the weights of the output with the 
smallest activation. 
Step 4: Update the 
w(t +1) = w(t) - (t).(x; — w(t)) (8) 
Step 5: Go to step 2 
weight vector to: 
Here Nn) is monotonically decreasing in each iteration. 
More details about the competitive learning method and its 
properties can be found in the Hung, Chih-Cheng (1993). 
3. EXPERIMENTAL INVESTIGATIONS: 
The airborne LIDAR data used in the experimental 
investigations have been recorded with TopScan's Airborne 
Laser Terrain Mapper system ALTM 1225 (TopScan, 2004). 
The data are recorded in a district called Ickern of the city of 
Castrop-Rauxel which is located in the west of Germany. The 
pixel size of the range images is one meter per pixel. This 
reflects the average density of the irregularly recorded 3D 
points which is fairly close to one per m2. Intensity images for 
the first and last pulse data have been also recorded and the 
intention was to use them too in the experimental investigations. 
Some first tests with these intensity images have been carried 
out but the current achievements have not yet been satisfactory. 
Figure (2) shows first- and last- pulse range images from the 
Ickern area. The impact of the trees in the first- and last- pulse 
images can be easily recognized by comparing the two images 
of this figure. 
The first step in every clustering process is to extract the feature 
image bands. The features of theses feature bands should carry 
useful textural or surface related information to differentiate 
between regions related to the surface. Several features have 
40 
  
          
nm. dr dut . as 
Figure 2: The first-pulse (above) and 
range images. 
the last-pulse (below) 
been proposed for clustering of range data. Axelsson (1999) 
employs the second derivatives to find textural variations and 
Maas (1999) utilizes a feature vector including the original 
height data, the Laplace operator, maximum slope measures and 
others in order to classify the data. An investigation on LIDAR 
classification with remote sensing software packages was 
presented in Arefi et al, 2003). 
In the following experiments we restrict to two types of 
features: 
- The ratio between first and last pulse range images 
- . Top-Hat filtered last pulse range image 
The normalized difference of the first and last pulse range 
images is used as the major feature band for discrimination of 
the vegetation pixels from the others. In analogy to the NDVI 
definition in Remote Sensing which is based on Red and NIR 
Internatioi 
channels « 
defined by 
where fp 
image dat: 
  
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