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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.