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Subject:

Re: Jacobian logtransform for TBM analysis

From:

John Ashburner <[log in to unmask]>

Reply-To:

John Ashburner <[log in to unmask]>

Date:

Fri, 23 Jan 2009 12:57:25 +0100

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> 1. Are there any DARTEL specific constraints on TBM-approaches? I searched
> the whole DARTEL mailing-list archives and couldnīt find a single note on
> DARTEL and cross-sectional TBM-approaches.

DARTEL isn't really geared for longitudinal studies for two main reasons:
1) It is very memory intensive, so working with imported images at very high 
resolution could be a problem for most desktop computers.  Longitudinal 
studies based purely on Jacobians usually involve high res image alignment.
2) It is based on simultaneously matching GM with GM and WM with WM, so 
requires very precise segmentation in order to achieve very accurate 
alignment.  Because longitudinal scans may be better matched using something 
like a least-squares objective function (as there is more chance of there 
being a more accurate one-to-one mapping), it may be easier at the moment to 
try the HDW code.

>
> 2. The resulting Flow-Fields (u_rc1*) (and the associated Jacobians) are
> composed of the warpings of grey matter and white matter (despite the
> name). Am I seeing that right?

Pretty much.  The rc1 part of the name is just taking the name of the first 
set of scans selected.  If rc2 images were selected first, then you would 
obtain u_rc2* files.  Whether you have u_rc1 or u_rc2 should not matter as 
their contents should be almost identical.

>
> 3. Does anyone has a SPM5/Nifti compatible script to log-tansform the
> Jacobians and is willing to provide it to me? That would spare me a lot of
> (silly) work with the imCalc.

I haven't tested it, but this may work...

P=spm_select(Inf,'^j.*\.nii');
for i=1:size(P,1),
    p = deblank(P(i,:));
    N = nifti(p);

    [pth,nam,ext] = fileparts(p);
    NL = N;
    NL.dat.fname = fullfile(pth,['l', nam ext]);
    NL.descrip = 'Log Jacobians';
    create(NL);

    NL.dat(:,:,:) = log(N.dat(:,:,:));

end


>
> 4. Applying the u_rc1* DARTEL Flow-Fields to the rc1* or rc2*-Images
> ,respectively, in the Deformations-Utility leads to strikingly different
> warping results than using the "create warped"-tool (no modulation) in the
> DARTEL Toolbox. Does anyone has a explanation for that?

There are some fudges involved in terms of the two different matrices in the 
NIfTI headers of the "imported" images.  Only the code within the DARTEL 
toolbox knows how it should deal with these headers.  The Deformations 
utility does not make use of this information.

If you do a check reg between an imported and an original GM image (ie rc1 and 
c1), you will see that they do not appear to be in alignment with each other. 
There is a second matrix in the NIfTI headers that actually encodes the 
relative orientations of the images, but this one is not used by anything 
other than the DARTEL toolbox.  When the Deformations-Utility is used to 
create a deformation field from a u_rc1 file, it creates a deformation that 
should work on the c1, but not the rc1.  Try comparing the behaviour of the 
Deformations utility and the Create Warped tool when you use eg c1* files 
instead.


> 6. In order to avoid all that problems I thought of applying the sn.mat
> File of the affine transform from DARTEL-Template to MNI to the DARTEL
> Jacobians using normalise-write with preserve amount (total). This would
> still allow me to present the results in MNI-Space but I am not sure about
> the approach and the error I am introducing by doing so.

This sounds reasonable.  I'm not actually sure how large the error would be.  
To be honest, I'm not even sure what the most appropriate interpolation 
approach is for such Jacobian determinant fields.  If you use different 
methods to compute weighted averages, you get very different answers.  Here 
are four different ways of doing it (although two of them - the log-Euclidean 
approaches - give the same answers)...

J1=expm(randn(3));
J2=expm(randn(3));
w=0.5;
[w*det(J1)+(1-w)*det(J2)...
 det(w*J1+(1-w)*J2)...
 exp(w*log(det(J1))+(1-w)*log(det(J2)))...
 exp(trace(w*logm(J1)+(1-w)*logm(J2)))]


And then there are the iterative Karcher mean type approaches.  If anyone is 
still reading this, and interested, then the literature on "parallel 
transport" will give clues about the most rigorous approaches.  This is far 
beyond my level of expertise though.

Best regards,
-John

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