Image Processing Reference

In-Depth Information

FIGURE 1
Original and cropped image.

3 Principal component analysis

PCA is known as a very powerful method for feature extraction. The usage of extracting ei-

genvectors and their corresponding eigenvalues to project the input data onto has been very

common in image analysis, such as face recognition and image classification. PCA, actually,

extracts the features from the data and reduces the dimension of it. When the features are ex-

tracted, a classifier can be applied to classify them and the final decision can be made. Euclidi-

an distance is used in our algorithm which is very fast and sufficient to our purpose. In the

rest of this section, PCA is explained briefly:First, the mean canter of the images is computed.

m
represents the mean image.

(1)

The mean cantered image is calculated by Equation
(2)

(2)

First covariance matrix is calculated by:

(3)

where
W
is a matrix composed of the column vectors
w
i
placed side by side.

Assuming that
λ
is eigenvector and
v
is eigenvalue, by solving
λv
=
Cv
eigenvectors and ei-

genvalues could be obtained.

By multiplying both side by
W
and substitution of
C
, we can get the following equation.

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