[Insight-users] Deformation field to Bspline coefficients

[Karthik Krishnan]

There are a couple of approaches to constructing your higher
order spline coeffs from the lower order ones.

-----

The example you are looking at approximates the spline coeffs
at the lower order by :

- Upsampling your BSpline coefficient image using some
  interpolation function to a higher order.
- Decomposing the resulting image, so as to construct Bspline coeffs

----

I think you could also just upsample the coefficient image directly as
an approximation, using say linear interpolation. There would be a
finite error in the envelope of the resulting spline, as compared to
the envelope at the coarser resolution spline but it would not be
too much.

---

Alternatively, you could also try the contribution from Nick Tustison.
This is an implementation of Lee's paper in N Dimensions and for
N order splines. It can take the image of Bspline control points at
the lower resolution and upsample it by a factor of 2. The resulting
spline will (I think, not sure) have the same envelope as the spline at
the lower resolution.

This can be found at :
  http://www.insight-journal.org/browse/publication/57

The classes are in ITK's review directory.


--
karthik


On Mon, Jan 12, 2009 at 12:22 PM, Benhacene Boudan Mustafa <
m.benhacene.boudan at umontreal.ca> wrote:

>
>
> Hi all,
> i am using a 3 levels multi resolution Bspline algorithm. I would like to
> smooth the deformation field obtained from the bspline coefficients and then
> to transform it back to bspline coefficients for the next resolution.
>
> I am able to transform the bspline coefficients to a dense deformation
> field and then to smooth the field, but i have a problem obtaining the
> bspline coefficients from the deformation field. I thought i could use the
> example "DeformableRegistration6.cxx" (lines 325 to 362) but i couldn't make
> it works.
>
> Anyone can point me to the right direction?
>
> thank you
>
> karim
>
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>
>


-- 
Karthik Krishnan
R&D Engineer,
Kitware Inc.
Ph: 518 371 3971 x119
Fax: 518 371 3971
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