The Deformations toolbox of SPM2 gives you the option touse a Procrustes
method to (if I remember correctly) factor out any rotations and translations
(and an optional isotropic zoom) from the deformation field. The following
reference explains a bit more about the procrustes method
% F. L. Bookstein (1997). "Landmark Methods for Forms Without
% Landmarks: Morphometrics of Group Differences in Outline Shape"
% Medical Image Analysis 1(3):225-243
See also http://www.paleo.geol.vt.edu/geos5384/Gloss.htm , which defines:
Procrustes methods - A term for least-squares methods for estimating nuisance
parameters of the Euclidean similarity transformations. The adjective
"Procrustes" refers to the Greek giant who would stretch or shorten victims
to fit a bed and was first used in the context of superimposition methods by
Hurley and Cattell, 1962, The Procrustes program: producing a direct rotation
to test an hypothesized factor structure, Behav. Sci. 7:258-262. Modern
workers have often cited Mosier (1939), a psychometrician, as the earliest
known developer of these methods. However, Cole (1996) reports that Franz
Boas in 1905 suggested the "method of least differences" (ordinary Procrustes
analysis) as a means of comparing homologous points to address obvious
problems with the standard point-line registrations (Boas, 1905). Cole
further points out that one of Boas' students extended the method to the
construction of mean configurations from the superimposition of multiple
specimens using either the standard registrations of Boas' method (Phelps,
1932). The latter being essentially a Generalized Procrustes Analysis.
References:
Cole, T. M. 1996. Historical note: early anthropological contributions to
"geometric morphometrics." Amer. J. Phys. Anthropol. 101:291-296.
Boas, F. 1905. The horizontal plane of the skull and the general problem of
the comparision of variable forms. Science, 21:862-863.
Phelps, E. M. 1932. A critique of the principle of the horizontal plane of the
skull. Amer. J. Phys. Anthropol., 17:71-98.
Mosier, 1939, Determining a simple structure when loadings for certain tests
are known, Psychometrika 4:149-162.
Alternatively, if you use SPM5b, then the _seg_sn.mat has the parameters saved
in a form that has been decomposed into a rigid-body transform and nonlinear
deformations.
Note that factoring out the rotations and translations is based on weighting
the deformation field by some image - rather than by using discrete
landmarks.
All the best,
-John
> I wondered if it is possible to run a non-linear deformation *without*
> performing the affine-registration first? I know I can do it the other way
> around, i.e. to run just an affine deformation (by setting the basis
> functions to zero in the defaults). Alternatively, is there a way that I
> can isolate the affine and nonlinear components of the deformation?
>
> I wanted to use the 'Invert Deformations' part of the Deformations toolbox
> - and to invert just the nonlinear part of the deformation.
>
> I guess I could do a two-step process - so that I just do an affine
> transformation first, and use these normalized images to create a new
> *sn3d.mat file, from which to compute the nonlinear deformation field (and
> its inverse) - but thought there might be a quicker way?
>
> Many thanks in advance
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