[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 33
3 The Algorithm of the Objects Classification
For the purpose of the realization of the recognition of the objects, a perceptron
algorithm, a simple algorithm of a linear classifier was used. This method allows
for the solution of the hyperplane designation problem that exists in the l – dimensional
features’ space of the objects dividing the given space into two dimensions.
The determined hyperplane, at the same time, divides features vectors belonging
to two different objects classes. In the perceptron algorithm it is assumed that two
classes and linearly separated exist. Therefore it is possible to determine
such a hyperplane 0 where:
*
w T x > 0 ∀x
∈ω
(16.1)
*
1
w T x < 0 ∀x
∈ω
(16.2)
The case described by the definition is the one where the hyperplane passes by the
beginning of the coordinates system connected with the space features. In more
general case the hyperplane equation is 0. Taking into account how
to write the equation for the definition (16) the features space should be extended
with an extra dimension. As a result, in 1 - of the dimensional space the
features vector is defined as follows: ,1 , where the vector of the hyperplane
coefficients: , . Then . The problem of
discovering the coefficients vector w described in the hyperplane is brought down
to the classical optimization problem. In the perceptrone algorithm a following
cost function is minimized:
,
where is a subset of the training feature vectors of the two classes , that were
incorrectly classified by the weight vector . Parameter takes the value -
1if and 1 where . With the above assumptions and definitions
it can be easily shown that the rate of (17) shall always take the positive or zero
values when the set is empty (all training vectors are correctly classified).
It can be shown that this optimization problem is resolvable using the following
iterative rule:
1
with a proper selection of the parameter values the training algorithm (18)
converges the minimizing quality index solution (17).
2
(17)
(18)