Sorry, I missed a step - you need to ensure that V2new is orthogonal to
V1new
So, after computing V2new, you want to orthogonalise V2new wrt V1new
Something like
V2newtmp = V2new - V1new* dot(V1new,V2new)
V2new_new= (V2newtmp)/|V2newtmp|
then
V3new=cross(V1new,V2new_new)
Sorry again..
Tim
-------------------------------------------------------------------------------
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
-------------------------------------------------------------------------------
On Thu, 7 Oct 2004, Tim Behrens wrote:
> 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
>
> -------------------------------------------------------------------------------
> 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
> -------------------------------------------------------------------------------
>
> 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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