[Insight-users] ImageMomentsCalculator question

[Benjamin King]

Hello,

I'm a little lost with the itk::ImageMomentsCalculator. What I want to know is 
the variance of a point set in the direction of greatest spread. I thought, I 
could use GetPrincipalMoments() for this, but apparently this is not the 
value that I'm looking for (see below).

Right now, I'm using the following method:
1) Use one ImageMomentsCalculator to perform PCA
2) Iterate over the transformed image to compute the mean index
3) Iterate over the transformed image to compute the index variance.

- OR -

2) Use another ImageMomentsCalculator to find the second central moments 
matrix m.
3) m[end][end] is close to the variance I'm looking for.

What's correct? Is there an easier way? Maybe I should have paid more 
attention during statistics class... ;)

Thanks for your help,
	Benjamin

PS:

For an example binary data set (rounded cuboid), I'm getting these values from 
the two ImageMomentCalculators:

Moments before principal axis transformation:
-----
  Zeroth Moment about origin: 2.10095e+08
  First Moment about origin: [127.062, 127.223, 127.987]
  Second Moment about origin:
		501.084 49.4927 123.275
		49.4927 417.388 57.1835
		123.275 57.1835 536.871

  Center of Gravity: [127.062, 127.223, 127.987]
  Second central moments:
		501.084 49.4927 123.275
		49.4927 417.388 57.1835
		123.275 57.1835 536.871

  Principal Moments: [8.2863e+10, 8.2868e+10, 1.40029e+11]
  Principal axes:
		0.776758 -0.313056 -0.546482
		-0.0677716 -0.904218 0.421659
		-0.626142 -0.290491 -0.723575

Moments after principal axis transformation:
-----
  Zeroth Moment about origin: 2.10081e+08
  First Moment about origin: [127.062, 127.222, 127.987]
  Second Moment about origin:
		394.452 0.0174592 -0.0375555
		0.0174592 394.533 0.00182282
		-0.0375555 0.00182282 666.542

  Center of Gravity: [127.062, 127.222, 127.987]
  Second central moments:
		394.452 0.0174592 -0.0375555
		0.0174592 394.533 0.00182282
		-0.0375555 0.00182282 666.542

  Principal Moments: [8.28659e+10, 8.28844e+10, 1.40027e+11]
  Principal axes:
		0.979273 -0.202545 0.000136521
		-0.202545 -0.979273 -2.14026e-05
		0.000138026 -6.69248e-06 -1