Zena Mohammed

Based PCA

ABSTRACT• Images play an important role in todays information

because A single image represents a thousand words.

• Google's image search, where we can easily search for images using keywords.

Getting the computer to understand the semantics inside of images isn't easy. The reason for this is simply because the computer isn't able to understand the context.

But

INTRODUCTION• Face recognition has become a popular area of research in

computer vision and one of the most successful applications of image analysis and understanding.

• A set of two task:– Face Identification: Given a face image that belongs

to a person in a database, tell whose image it is.

– Face Verification: Given a face image that might not belong to the database, verify whether it is from the person it is claimed to be in the database.

HOW FACIAL RECOGNITION WORKS ?

PCA• Principal Component Analysis (PCA) is a

dimension-reduction tool that can be used to reduce a large set of variables to a small set that still contains most of the information in the large set

• PCA was invented in 1901 by Karl Pearson.• PCA involves the calculation of the

eigenvalue decomposition of a data covariance matrix or singular value decomposition of a data matrix, usually after mean centering the data for each attribute.

Dimensionality Reduction

The set of faces is a “subspace” of the set

of images– Suppose it is K dimensional– We can find the best subspace

using PCA

– This is like fitting a “hyper-plane” to the set of faces• spanned by vectors v1, v2, ...,

vK

Any face:

In this section, the original scheme for determination of the eigenfaces using PCA will be presented.

Calculation of Eigenfaces with PCA

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Eigenfaces: representing faces

Training set of face images T1,T2,T3,……TM.-

• Average Face of Image ; M : No. of images

Ψ average face

We compute the average face

The covariance matrix has eigenvectors covariance matrix eigenvectors

eigenvalues

Eigenvectors with larger eigenvectors correspond to

directions in which the data varies more

Finding the eigenvectors and eigenvalues of the covariance matrix for a set of data is termed principle components analysis

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The covariance of two variables is:

Variations in lighting conditionso Different lighting conditions for enrolment and query. o Bright light causing image saturation.

DEMERITS

• Relatively simple• Fast• Robust• Expression

- Change in feature location and shape.

MERITS

More Problems: Outliers

Need to explicitly reject outliers before or during computing PCA.

Sample Outliers

Intra-sample outliers

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• Face Recognition has been successfully implemented using

Eigen face approach. Eigen face approach of face

recognition has been found to be a robust technique that

can be used in security systems

CONCLUSION