[Insight-users] Upsample bspline grid in deformableregistration6

[Reinhard Hameeteman]

Thanks Torsten and Nick for your reply,

Although the pointed references are certainly helpful in clarifying
some BSpline properties for me, my main question was about the
procedure followed in the example and the ITK Software guide. It seems
to me that two approaches are mixed up there. Either the coefficient
image contains the BSpline coefficients and then it does not make
sense to decompose it after upsampling Or the coefficient image
contains vector components and the documentation of the
BSplineDeformableTransform is not correct:
"The parameters for this transform is N x N-D grid of spline coefficients"

Thanks again,
Reinhard

On 07/03/07, Nick Tustison <ntustison at wustl.edu> wrote:
> To add to Torsten's comments --- I generalized Lee's original
> algorithm to N dimensions and arbitrary order within ITK (including
> the BSplineKernelFunction) and submitted it to the Insight Journal.
> You can find the submission at
>
> http://hdl.handle.net/1926/140
>
> The submission also includes a discussion of the upsampling process
> for arbitrary order b-splines.
>
> Good luck,
> Nick Tustison
>
> On 3/6/07, Torsten Rohlfing <torsten at synapse.sri.com> wrote:
> > Hi there:
> >
> > I am not an expert in ITK's implementation of the B-spline
> > transformation model, so I may be completely redundant here. And I may
> > be missing the point completely. Anyway, here are my thoughts:
> >
> > The B-spline grid should be upsampled (let's say: refined) using
> > appropriate relationships that guarantee identical transformations
> > before and after refinement.
> >
> > For third-order 2D transformations, the explicit formulas are given in
> >
> > S. Lee, G. Wolberg, and S. Y. Shin, "Scattered data interpolation with
> > multilevel B-splines," IEEE Transactions on Visualization and Computer
> > Graphics, vol. 3, no. 3, pp. 228-244, 1997.
> >
> > Their 2D expressions, however, are simple to generalize using the tensor
> > product of 1D refinement formulas. These can, for example, be found
> > (apologies for self citation) in
> >
> > T. Rohlfing, C. R. Maurer, Jr., W. G. O'Dell, and J. Zhong, "Modeling
> > liver motion and deformation during the respiratory cycle using
> > intensity-based free-form registration of gated MR images," in /Medical
> > Imaging: Visualization, Display, and Image-Guided Procedures/, S. K.
> > Mun, Ed., 2001, vol. 4319 of /Proceedings of the SPIE/, pp. 337-348.
> >
> > Again, this is for third-order splines. For different orders I am sure
> > there is a paper out there somewhere that generalizes things further.
> > Anyway, the correct upsampling depends on the spline order, which should
> > therefore be considered in the upsampling process.
> >
> > Not sure if that happens in the proposed procedure of getting the
> > parameter image, upsampling that and then transforming back into a
> > spline transformation.
> >
> > Best,
> > Torsten
> >
> > --
> > Torsten Rohlfing, PhD          SRI International, Neuroscience Program
> >  Research Scientist             333 Ravenswood Ave, Menlo Park, CA 94025
> >   Phone: ++1 (650) 859-3379      Fax: ++1 (650) 859-2743
> >    torsten at synapse.sri.com        http://www.stanford.edu/~rohlfing/
> >
> >      "Though this be madness, yet there is a method in't"
> >
> >
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> >
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