Hi Christian,
This sounds interesting... Though I take it that the answer to
Michael's original question about whether anything had been published
on this (even if just a mention in-passing) is a no then?
I'm a little curious about what's going on here... The Jacobian images
are of course very smooth due to the nature of the DCT basis
functions, but it's not immediately obvious to me that multiplying
something rough with something smooth increases the smoothness. For
example, a completely uniform Jacobian of 1 over the entire image
(corresponding to no warping at all) would be as smooth as possible,
and yet would not change the smoothness of the modulated data at all.
Also, by smoothness of the data, what is really meant is the
smoothness of the residuals of the GLM, right? So it might be the case
that modulated data is simply modelled better. Or for example is more
uniform over scans, and so has reduced variability and hence possibly
reduced roughness (as I believe SPM's smoothness computation is
actually a measure of the roughness of the residuals in terms of the
variance of their derivatives).
This perhaps deserves to be looked into in more detail, especially if
nothing has been published so far...
Best,
Ged
Christian Gaser wrote:
> On Tue, 29 May 2007 15:43:25 +0200, Marko Wilke <[log in to unmask]>
> wrote:
>
> Hi Michael,
>
> I have never tried to estimate the smoothness of the deformations directly. However, you can
> approximate the smoothness if you have analyzed modulated and unmodulated images by using
> the estimated smoothness (which can be found at the bottom right on the results page):
> FWHM_deformation = sqrt(FWHM_modulated^2 - FWHM_unmodulated^2)
>
> The FWHM of the deformations is mostly influenced by the cut-off value (and also by the
> regularization). If these parameters are not changed you only need to approximate the FWHM
> once. The you can reorder the formula to:
> FWHM_modulated = sqrt(FWM_deformation^2+FWHM_unmodulated^2)
>
> You see that smoothness is added by the deformations and this usually leads to an increase of the
> smoothness by 20-40%. However, this calculation was thought to make modulated and
> unmodulated data comparable.
>
> Best,
>
> Christian
>
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