Image Processing Reference
In-Depth Information
is the mean matrix of input images and finally we have
First, the n × n matrix of G t is calculated from all of the training images. Then, the unitary
vectors X are obtained by geting the eigenvector matrix of G t . This stage decides how many
eigenvectors are to be used in the projection of data. To achieve this, the eigenvalues of the cor-
responding eigenvectors are arranged in a descending order, and a subset of the higher values
is selected. Assuming d eigenvectors (with optimal projection axes X 1 , X 2 , …, X d ) are selected,
then how to achieve feature extraction and classification stages are explained in the next sec-
4 Kernel mapping along row and column direction
4.1 Two-Dimensional KPCA
The main idea of using kernel function in PCA is that the data are first mapped into another
space using a mapping function and then PCA is performed on the nonlinearly mapped data.
2DPCA is beter than 1D PCA in terms of speed and accuracy. The idea of using kernel func-
tion in 2DPCA is to improve the accuracy of the system. With N input images, let A i be the
i th image, where i = 1, 2, …, N , and A i j be the j th row of the matrix A i , where j = 1, 2, …, n . The
nonlinear mapping is defined as follows:
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