The various steps to calculate Eigen faces are

i) Prepare the data:

A 2-D facial image can be represented as 1-D vector by concatenating each row (or column) into a long thin vector.

Let’s suppose we have M vectors of size N (= rows x columns of image) representing a set of sampled images .Then the training set becomes:

ii) Subtract the mean:

The average matrix has to be calculated, then subtracted from the original faces (i ) and the result stored in the variable

Ψ=1/M∑Mn=1Ѓn [Φ]Xi=fi

iii) Calculate the co-variance matrix

In the next step the covariance matrix A is calculated according to:

A=ΦTΦ

iv) Calculate the Eigenvectors and Eigen values of the covariance matrix. In this step, the Eigen vectors (Eigen vectors) Xi. Calculate Eigen faces

[Φ]Xi=fi

Where, Xi are eigenvectors and fi are Eigen faces.

v) Classifying the faces:

The new image is transformed into its Eigen face components. The resulting weights form the weight vector T : k

Ωk= ΩkT(Гk-ψ)

Where,

k = 1,2,3,4

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i) Prepare the data:

A 2-D facial image can be represented as 1-D vector by concatenating each row (or column) into a long thin vector.

Let’s suppose we have M vectors of size N (= rows x columns of image) representing a set of sampled images .Then the training set becomes:

ii) Subtract the mean:

The average matrix has to be calculated, then subtracted from the original faces (i ) and the result stored in the variable

Ψ=1/M∑Mn=1Ѓn [Φ]Xi=fi

iii) Calculate the co-variance matrix

In the next step the covariance matrix A is calculated according to:

A=ΦTΦ

iv) Calculate the Eigenvectors and Eigen values of the covariance matrix. In this step, the Eigen vectors (Eigen vectors) Xi. Calculate Eigen faces

[Φ]Xi=fi

Where, Xi are eigenvectors and fi are Eigen faces.

v) Classifying the faces:

The new image is transformed into its Eigen face components. The resulting weights form the weight vector T : k

Ωk= ΩkT(Гk-ψ)

Where,

k = 1,2,3,4

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