[Studies in Computational Intelligence 481] Artur Babiarz, Robert Bieda, Karol Jędrasiak, Aleksander Nawrat (auth.), Aleksander Nawrat, Zygmunt Kuś (eds.) - Vision Based Systemsfor UAV Applications (2013, Sprin

Recognition and Location of Objects in the Visual Field of a UAV Vision System 43
set to 98%. As a result, the analysis using the algorithms FLD and PCA the feature
dimension space is reduced from 22 to 2. This suggests, that the
values (features forming the feature vector) describing objects in particular
classes were strongly correlated. As a result, the representation of classes
using the feature vector was shown graphically on picture 6. The
dimension of the vectors representing, in the transformation (7), where the transformation
matrix is described by the following relation (42) (for 2).
From the picture 6 analysis it is visible that a better representation, In terms of
classifier construction, can be achieved by using the FLD algorithm. The classes
of the training set objects are more concentrated around the average values than it
is in the case of the PCA algorithm. This is also confirmed by the numerical analysis
of the result of the transformation. To estimate this, both the degree of separation
( the distance between the mean vectors) of classes and the degree of
aggregation of individual vectors in the given object classes were used.
The value of the indicator is the greater when the concentration of individual
vectors around the middle class vector is greater (small value of ),
and the greater is the distance between the middle vectors of particular object
classes (great value of ). In the analyzed case the indicator value
confirms the observations from the analysis of the Fig 6. The value of the class
indicator after the PCA transformation equals to 25.7, whereas to each
class of a training set after the transformation with FLD equals to 20260.
However, despite such impressive outcome it is easily noticeable ( pic.6b ) that in
the dimension of the feature vector it is not possible to mark the hyperplane (for
2 straight line), which would clearly divide the class from other classes.
Therefore, the Assumption that the feature vectors describing the four object
classes in the space 22-dimensional are linearly inseparable. This fact explains
the impossibility of Winding the hypeplane using the described perceptron
algorithm as a linear classifier.
7 The Minimum-Distance Classifier
As a result, to every class of the training set after the transformation with the FDL
algorithm, a Simple minimum-distance classifier can be used. In this study the
classification process is all about the finding the class , to which a given vector
of feature (according to the similarity function ) is the most similar. The
function, describing the ‘similarity’ of the feature vector to one class, for each
separate class, was defined as follows:
exp 1 2 (42)