02-05-2012, 01:51 PM
Face Recognition using Principle Component Analysis
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Introduction
The Principal Component Analysis (PCA) is one of the most successful techniques that have
been used in image recognition and compression. PCA is a statistical method under the broad
title of factor analysis. The purpose of PCA is to reduce the large dimensionality of the data
space (observed variables) to the smaller intrinsic dimensionality of feature space (independent
variables), which are needed to describe the data economically. This is the case when there is a
strong correlation between observed variables.
Face recognition
Once the eigenfaces have been computed, several types of decision can be made depending on the
application. What we call face recognition is a broad term which may be further specified to one
of following tasks:
² identification where the labels of individuals must be obtained,
² recognition of a person, where it must be decided if the individual has already been seen,
² categorization where the face must be assigned to a certain class.
PCA computes the basis of a space which is represented by its training vectors. These basis
vectors, actually eigenvectors, computed by PCA are in the direction of the largest variance of
the training vectors. As it has been said earlier, we call them eigenfaces. Each eigenface can
be viewed a feature. When a particular face is projected onto the face space, its vector into the
face space describe the importance of each of those features in the face. The face is expressed
in the face space by its eigenface coefficients (or weights). We can handle a large input vector,
facial image, only by taking its small weight vector in the face space. This means that we can
reconstruct the original face with some error, since the dimensionality of the image space is much
larger than that of face space.
Critical Reviews
In order to examine more carefully how well the idea works, I did much extensive and exhaustive
experiments with different sets of training images. These are done by some criteria not considered
by the authors. For the accuracy of the experiments, the training set should not overlapped the
test set. The size of the training set was increased, i.e., 1st configuration - 10 subjects each of
whom has 8 images (totally 80 images), 2nd configuration - 20 subject each of whom has 8 images
(totally 160 images), ... up to 40 subjects which is the maximum number of subject in the given
database. The results showed me that the system gave correct identification for the known faces
which is trained by the system. The noticeable fact is that the bigger the size of training set is,
the less the reconstruction errors are. This is because there are more basis vectors (eigenvectors)
to express the given data (faces + non-faces) in the feature space. But this makes the non-faces
have less reconstruction error - this is undesirable case.