[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

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40 R. Bieda et al. Vector is the mean vector of the elements composing a given class. The value is the average to all classes of features variation. The scattering matrix of inter-class , where is the global mean vector (32) (33) The greatness of defines the average distance between given mean vectors of given classes. This is the form of the mixture of the matrix dispersal/scattered matrix: (34) Such matrix is known as the covariance matrix of the feature vectors in relation to the global mean vector of all the analyzed classes. It can be easily shown that this matrix can be determined using the (29) and (32) values in their form: (35) The Fisher ratio describing the separation degree of the classes In the feature dimension is often defined in the following way: (36) The construction of the transformation matrix is based on the problem of maximizing the ratio (36). The problem of maximizing is a classical problem of appointing the individual value and the value of individual matrices corresponding with them (37) where matrix is a diagonal matrix of which the elements on the diagonal are the individual values of matrix: D λ1 0 0 0 λ 0 0 0 λl 2 = (38)
Recognition and Location of Objects in the Visual Field of a UAV Vision System 41 Whereas the matrix is the column matrix with the dimension, that is corresponding to its individual values of specific vectors , … . 6.2 The PCA Algorithm The second, frequently used technique of determining the reducing redundancy transformation and „increasing” separability between the classes is the principal component analysis PCA. This technique is also often named a KL (Karhunen- Loève) transformation The task of appointing the transformation matrix (28), as before, is All about determining the eigenvalues of the matrix (38) and its corresponding column matrix (39) of individual vectors. The analysis is made on the basis of the covariance matrix (24) (or (34) and (35)): (39) The individual values are often interpreter as cumulative energy content, thanks to which we can determine the amount of information carried by the individual components of the feature vectors after the transformation with the usage of the matrix . The percentage amount of the carried information can be determined using he following formula: ∑ 100% ∑ (40) where is -th quantity of the individual value. The amount of the information In the feature vector after transformation with the usage of matrix is the same as the amount of information in the given vector before its transformation. However, while determining the transformation matrix based on the matrix of the individual vectors only -vectors, to which the -biggest eigenvalues correspond to, are taken into the account. Assuming the accuracy of the mapping information , carried with the feature vector of the transformation matrix can be constructed using the -first individual vectors grouped according to the corresponding individual values , , , … (41) In the described experiment the previously presented methods of the transformation matrix construction were analyzed with the aim of construction the object classifier defined In four classes. The accuracy of mapping the information by the feature vectors obtained after the transformation of the primary vectors, is
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Studies in Computational Intelligen
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Aleksander Nawrat · Zygmunt Kuś E
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Omnidirectional Video Acquisition D
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206 Practical Applications of Class
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344 Conclusions Control algorithms
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[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

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