Resetting the Affine Transformation matrix

[Avinash Raj]

Affine Transformation Matrix is said to be formed by initializing it using a learned projection matrix from a conventional algorithm like Eigenfaces or Fisherfaces; then it is reset by using the singular value decomposition T=UAV', where T is the transformation matrix.

Could somebody explain how the decomposition is obtained and what it is?

 

[Avinash Raj]

I didnt go into details of initialising the tranformation matrix as well as the "resetting". I presumed that those in the forum are learned enough to know the basics of affine transformation. Do let me know if somebody wants more data from me to be able to explain the concept to me.

 

[Avinash Raj]

It is obvious that SVD of the matrix T is shown.

An IEEE paper (Face Verification With Balanced Thresholds) that I read few days back says "the right orthogonal matrix of SVD of a transformation matrix does not affect the similarity measure if based on Euclidean distance." I drew blanks in my attempts to understand how it is so and wikipedia wasnt a help at all. Could you tell me why the measure is invariant to the right orthogonal matrix?

Note - The right unitary matrix becomes orthogonal as only real matrices are considered in the problem.