Hi Stamatis - I may get this wrong so I've copied Danny in. It's been a
while since I read the paper.
I believe the easiest way to implement the PDD preserving algorithm is
this:
Take a flirt Matrix A,
Take the first 3 rows and columns, F
At each voxel, compute the eigenspectrum of your tensor: vectors V1,V2,V3,
values L1,L2,L3
Compute the new PDD
V1tmp=F*V1
normalise this direction
V1new=V1tmp/|V1tmp|
Do exactly the same for V2
V2tmp=F*V2
V2new=V2tmp/|V2tmp|
Then compute V3new= cross(V1new,V2new)
You can then form the New tensor out of this new eigenspectrum.
Vnew=[V1new V2new V3new];
L=[L1 0 0;0 L2 0;0 0 L3];
Dnew=Vnew*L*Vnew'
I think Danny suggests that you can compute an equivalent rotation
matrix,R, at each voxel, such that Dnew=R*D*R', but I think that working
with the eigenspectrum will work just as well.
Is this right Danny?
Cheers
T
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Tim Behrens
Centre for Functional MRI of the Brain
The John Radcliffe Hospital
Headley Way Oxford OX3 9DU
Oxford University
Work 01865 222782
Mobile 07980 884537
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On Thu, 7 Oct 2004, Stamatis Sotiropoulos wrote:
> Hi all,
> I am trying to use the PDD algorithm described by D. C. Alexander et
> al, IEEE Trans on medical Imaging, 2001 . It is an algorithm that is used
> to preserve orientational information that DTI images contain, when they
> are registered to another space than the original one of the scanner. It
> actually rotates the eigenvectors of the Diffusion tensor in the new
> coordinate system.
> I am a bit confused by the description of the algorithm in the above
> paper. Has anybody used this algorithm? I am assuming that for each voxel
> of a DT image, the original eigenvectors e1,e2,e3 are transformed to
> v1,v2,v3 eigenvectors through a Rotation Matrix R. What is the
> relationship between ei and vi? vi=Rei?
> It is not very clear in the paper and it gets even more confusing in a
> more recent paper (Coulon, Alexander, Arridge, Medical Image Analysis,
> 2004), where there is a short description of the algorithm.
>
> Thank you in advance,
> Stamatis
>
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