Re: Principal Components (Hotelling of KL Transform) of 2 Band (Red and Green) Real Color Image

PeterOut wrote:
Say you have a 2 channel image (red and green channels for example)
and you want to get the principal components in order to do a
Hotelling (Karhunen-Loève) transform on the image so as to minimize
the correlation between the red and green channel. You would get the
correlation matrix but, since correlation is reflective, the
correlation matrix M would be given by.
M=1 a
a 1

where a is the correlation coefficient between the two bands. It
seems that, whatever the value of a is, the eigenvectors would be
(0.7071,0.7071) and (-0.7071,0.7071). So the transformation would be
the same regardless of what is in the input images. This does not
seem very useful since I thought the idea of the Hotelling transform
was to rotate the axes to minimize the correlation between the bands.
Is there something I'm misunderstanding?


I use K-L / PCA a lot, but never on 2-d. data; and I always use the covariance matrix. What happens if you use the covariance instead of correlation?

Otherwise, sci.stat.math may be able to help.

Best regards,

Jon C.
.

Relevant Pages