[Insight-developers] NIfTI, DiffusionTensor3D Pixels, SymmetricSecondRankTensor

[kent williams]

I've managed to get myself confused and throw myself on the mercy of the
more mathematically inclined.

Luke logged this bug http://public.kitware.com/Bug/view.php?id=7485 a while
back.  In essence the problem is that ITK and NIfTI disagree about the order
of values when storing a DiffusionTensor3D, and one presumes
SymmetricSecondRankTensor as well. ITK stores upper-triangular and NIfTI
stores lower-triangular.

In the case of DiffusionTensor3D, a symmetric 3x3 matrix, the ordering for a
matrix

A B C
B D E is A B C D E F for ITK, and A B D C E F for NIfTI.
C E F

Given how the NIfTI filter works when it's copying pixels to and from ITK
images, I handle this with an ordering array.  In other words I have an
array
    int niftiorder[9] = { 0,1,3,2,4,5,6 };
and in essence, NIfTIPixel[i] = ITKPixel[order[i]];

That's good for DiffusionTensor3D, but the general case of
SymmetricSecondRankTensor is baffling me. For a 4x4 symmetric matrix
 int niftiorder[10] = { 0, 1, 4, 2, 5, 7, 3, 6, 8, 9 };

and 5x5 is even crazier.
 int niftiorder[15] = { 0, 1, 5, 2, 6, 9, 3, 7, 10, 2, 4, 8, 11, 13, 14 };

So I'm not seeing how I would go about deriving this ordering.  I.e. I don't
know what general purpose code would handle re-ordering the scalars from an
upper triangular to a lower triangular or vice verse.

Does anyone have a suggestion on how to go about this?

And while I'm on the subject, why is the VNL Symmetric Matrix lower
triangular, yet ITK is upper triangular?

 



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