Life of Inches

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http://anthonychan.blogbus.com/logs/31672500.html

The process of PCA can be roughly divided into the following ? steps: 

1)      The construction of eigenfaces

    *  Given M faces, each containing N*N pixels, we construct M vectors, each being a N*N-tuple;

    *  Then we calculate the average vector Ψ of the M ones we’ve obtained and then ‘sharpen’ each vector by subtracting Ψ from it;

    *  Now each vector serves as an eigenface, we use these new M vectors to form a matrix A with M*(N*N) elements 

2)      Further construction of Face Space

    *  We construct a covariance matrix A^TA and furthermore obtain its eigenvectors v;

    *  The Face Space will be constructed by calculating each u_i = Av_i and form them. (Note that U is an M*M matrix)

 3)      Projection of coming images

    *  The test image, Γ, is projected into the face space to obtain a vector, Ω (recalling that Ψ is the ‘average’):

                                 Ω = U^T(Γ – Ψ)* 

    And we can further define distance using the norms of Ω.