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Figure 1: a) Front view of a target. b) The same target 
viewed from a different angle. In both cases, only the 
points of the target that correspond to highly reflective 
areas are presented for visualisation purposes. The maxrad, 
maxrad4 and radcent calculated positions of the centre are 
indicated in black, green and blue respectively. 
  
  
  
  
  
Figure 2: Surface model for a reflective target. 
Thorough examination of several targets has revealed that the 
parts of the data that correspond to the highly reflective areas of 
the target are quite noisy. Several points seem to deviate from 
the surface of the target introducing topographic artefacts. On 
the other hand, this phenomenon does not occur in areas of 
lower reflectance. This is visible in Figure 2, where a model of 
the surface of the target is presented. Therefore, in order to 
determine the centre of the target as precisely as possible, it is 
critical to classify the points of the point cloud according to 
their reflectance. This is considered to be the key to precise 
automatic target identification, because classifying based on 
reflectance allows for thorough examination of the properties of 
the target. Knowing the properties of the target is a very good 
basis for developing more sophisticated methods of target 
identification. 
Given the fact that reflectance varies according to the distance 
between the scanner and the target and according to the angle 
by which the target is viewed, it is very difficult to model the 
reflectance. Therefore, classification of the data using 
thresholds cannot be a solution. Other forms of classification, 
which require the user to give training data, are also considered 
inappropriate, as this would lead to a semi-automatic solution. 
A method that would classify the data into the desired 
categories without any input from the user is required. One such 
method is the fuzzy clustering technique. 
Clustering of numerical data forms the basis of many 
classification and system modelling algorithms. The purpose of 
clustering is to identify natural groupings of data from a large 
dataset so as to produce a concise representation of a system's 
behaviour. Therefore, this kind of processing is ideal for the 
case of targets. In order to create the fuzzy clusters, the Fuzzy 
Logic Toolbox of Matlab was used. 
Fuzzy c-means (FCM) is a data clustering technique wherein 
each data point belongs to a cluster that is, to some degree, 
specified by a membership grade. This technique was originally 
introduced by Bezdek (1981) as an improvement on earlier 
clustering methods. It provides a method that shows how to 
group data points that populate some multidimensional space 
into a specific number of different clusters. The Fuzzy Logic 
Toolbox command line function ‘fcm’ starts with an initial 
guess for the cluster centres, which are intended to mark the 
mean location of each cluster. The initial guess for these cluster 
centres is most likely incorrect. Additionally, fcm assigns every 
data point a membership grade for each cluster. By iteratively 
updating the cluster centres and the membership grades for each 
data point, fcm iteratively moves the cluster centres to the 
"right" location within a data set. This iteration is based on 
minimizing an objective function that represents the distance 
from any given data point to a cluster centre weighted by that 
point'S membership grade. The output of the ‘fem’ command 
line function is a list of cluster centres and several membership 
grades for each data point. Before describing the new 
algorithms that were developed, it is useful to give an example 
of the way that fuzzy clustering can substantially aid in data 
interpretation for the case of the targets. 
The ‘fem’ function is used to group the points of a target into 
three classes based on their reflectance. One class comprises the 
points of high reflectance, the second class consists of the 
points of low reflectance and the last class consists of the points 
of moderate reflectance. In Figure 3. a single target is shown 
from two different scan angles. The points that belong to the 
first class are depicted in red, the points of the second class are 
depicted in blue, and the remaining points are shown in green. 
The first image of Figure 3 presents the target scanned with the 
z-axis of the scanner system forming an angle of 90° degrees 
with the surface on which the target belongs. In the second 
image this angle is 45° degrees.