[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 39
correlated. In consequence, the description is redundant, and repeatedly the large
dimension of features makes the analysis more difficult. One of the stages of designing
the classified is the extraction stage or features selection. This process is
used to minimize the number of features in the vector that is described in the given
object. Many times the information contained in the selected is in excess, and the
values describing different objects are greatly corralled with each other. In consequence,
the description is redundant and a big features’ dimension makes the
analysis more difficult.
In the experiment that was carried out, some algorithms enabling to determine
the transition to the other -dimensional space were analyzed, in the space, which
features describing will not be redundant and at the same time, where there space
of this dimension can be reduced.
In general, the transformation of the state vector from the space -dimensional
to space -dimensional can be described as
, (28)
where is the matrix of a dimension.
6.1 The FLD Algorithm
One of the methods allowing to distinguish the matrix of transformation is the
method that is based on the analysis of so-called scatter matrices. The genesis of
this method taken from the description of the construction of the Fisher’s linear
discriminant also known as the FLD. The size of the constructed index of discrimination
enables to describe both the degree of the separation of given classes
and the degree of scattering vectors from each class.
In order to determine the transformation matrix it is necessary to define and determine
the few values describing the classes in our features’ dimension.
The scattering matrix of the intra-class
∑
,
(29)
where is the covariance matrix of class elements:
(30)
is the given a’priori probability of the appearance of the -th class. Such greatness
is of the appointed as a ratio of the abundance of the -th class to the abundance
of all the elements in analyzed classes
(31)