Hi Jesper,
I gather that FNIRT
http://www.fmrib.ox.ac.uk/fsl/fnirt/#fnirt_diffeomorphic
and invwarp
https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0810&L=FSL&P=R31927
can project "non-diffeomorphic fields ... onto the closest diffeomorphic field."
How is this done? I'm guessing this kind of closeness is not related
to Miller et al's LDDMM diffeomorphic metric distance between
transformations (since I think that would place non-diffeo
transformations infinitely far from diffeo ones...). Is it just an RMS
distance between displacement fields? Even if so, it's not obvious to
me how the projection would occur... E.g. I could see how to project
an arbitrary displacement field onto an arbitrary (e.g. spline) basis,
but not in a way that would guarantee diffeomorphism...
I think Vercauteren et al's diffeo demons
http://www.insight-journal.org/browse/publication/154
would deal with folding by smoothing (globally) the velocity field
until achieving positive Jacobians, but I don't think this could
really be claimed to give the nearest diffeo in any sense...
Kind of similarly, in Postelnicu's CVS registration method
http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4601460
They "remove the tangles in the deformed mesh [...] while modifying the
nodal displacements as little as possible [...] based on *local* smoothing
[with the linear elastic differential operator]"
I guess that could be interpreted as approximating the closest diffeo,
within the assumptions of elasticity, and within the tolerance of how
much smoothing they do between checking for folding. Does FNIRT do
something similar?
Yours eagerly awaiting the FNIRT journal paper ;-)
Ged
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