[Insight-users] ImageMomentsCalculator question

[Luis Ibanez]

Hi Benjamin,


The

            "Principal moments"


                  *ARE*

the

        "variances of the sample
         along the principal axes".


This class is simply taking the Matrix of second order
moments of the points and performing Eigen Analysis on
this Matrix.



    Regards,



       Luis


---------------------
Benjamin King wrote:

> Hi Luis,
> 
> 
>>If you want to do Principal Components Analysis,
>>you can use directly the Moments Calculator.
>>[...]
>>Reading the Doxygen documentation of 
>>this class will certainly help you  :-)
>>[...]
> 
> 
> Unfortunately, after reading the documentation again, I still don't understand 
> the relationship between principal moments and the variance of a point set 
> projected onto the principal axes.
> I also grep'd the ITK source for GetPrincipalMoments, but apart from a test 
> program, no other code is using it.
> 
> I hope the attached program better illustrates my problem:
> 
> $ tar xvzf CalculateMoments.tar.gz
> $ cd moments/binary
> $ cmake ../source
> $ make
> $ cd ..
> $ ./CalculateMoments data/ellipse.hdr
> 
> This will print the image moments according to itk::ImageMomentsCalculator 
> before and after PCA. The third output block is a manual calculation of the 
> mean index and index variance after PCA. The index variance is what I'm 
> looking for.
> 
> Is it possible to derive this value directly from the moments before PCA?
> 
> 
> Thanks for your help,
> 	Benjamin
> 
>