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

Jonathan Campbell wrote:
PeterOut wrote:
On Jan 6, 5:37 am, Jonathan Campbell <jg.campbell...@xxxxxxxxx> wrote:
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
[...]
Thank you very much for your reply. You are right. I checked and it
would appear that it is indeed the covariance matrix that I should
use. However, it would appear that I would have the same problem
since covariance is reflective and, consequently, the covariance
matrix between the two data sets would be

M=1 a
a 1


Not unless the variance of both channels is 1? As I say, I have never applied PCA/K-L to 2-d. data, so I'm a little hesitant.


You probably 'standardized' the data before computing the variance-cov. matrix. xij = xij/si, where i indexes the channel; j indexes the data and si = std. dev. of channel.

Jon C.
.

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