[Insight-users] RE: increasing bspline control point density

[Luis Ibanez]

Jim,

The control points are not quite on the trace of the spline,
(at least not for splines with order larger than one) since
BSplines are approximating splines after that order.

The consequence is that if we put specific deformations
on the grid nodes of the BSplineDeformableTransform, and
then we sample the transform at a grid point, we will not
recover the same value of deformation set in that node.
Instead we will find the value resulting from the weighted
interpolation of values in the neighboring grid nodes.


   Luis



----------------------------------------
Miller, James V (Research) wrote:

> Luis, 
> 
> For ITK's B-spline representation, are the control points "on" the trace
> of the spline? Normally, only some of the control points are on the spline
> and the remainder are off the trace of the spline (but nearby).  Sometimes,
> splines are implemented by specifying only the control points that are on
> the trace (with the other implicitly calculated).
> 
> Jim
> 
> 
> 
> -----Original Message-----
> From: Luis Ibanez [mailto:luis.ibanez at kitware.com]
> Sent: Friday, July 23, 2004 11:26 AM
> To: Karl Baum
> Cc: insight-users at itk.org
> Subject: Re: [Insight-users] RE: increasing bspline control point
> density
> 
> 
> 
> Hi Karl,
> 
> For your convenience we just added an example to ITK
> illustrating how you can increase the resolution of
> the BSpline transform grid in order to refine a
> deformable registration.
> 
> 
> You will find this new example under:
> 
>    Insight/Examples/Registration/
>              DeformableRegistration6.cxx
> 
> http://www.itk.org/cgi-bin/viewcvs.cgi/Examples/Registration/DeformableRegis
> tration6.cxx?root=Insight
> 
> You will have to update your CVS checkout in order
> to get this new file.
> 
> 
> The example is mostly based on DeformableRegistration4.cxx,
> and a second stage was added in which another BSpline
> transform with higher resolution grid is configured.
> 
> Please let us know if you find any problems or
> have further questions.
> 
> 
>     Thanks
> 
> 
>       Luis
> 
> 
> ----------------
> Karl Baum wrote:
> 
>>Jim,
>>You are correct in stating that I would like to "upsample" the B-Spline
> 
> and
> 
>>not the image.
>>Thanks,
>>Karl
>>
>>
>>Date: Fri, 23 Jul 2004 10:25:43 -0400
>>From: "Miller, James V (Research)" <millerjv at crd.ge.com>
>>Subject: RE: [Insight-users] increasing bspline control point density
>>To: "'Stefan Klein'" <stefan at isi.uu.nl>, insight-users at itk.org
>>
>>I think the BSplineUpsampleImageFilter upsamples an image via B-spline
>>interpolation. I think Karl wants to "upsample" his B-spline not an image.
>> 
>>Jim
>>
>>-----Original Message-----
>>From: Stefan Klein [mailto:stefan at isi.uu.nl]
>>Sent: Friday, July 23, 2004 9:21 AM
>>To: insight-users at itk.org
>>Subject: RE: [Insight-users] increasing bspline control point density
>>
>>
>>Hi Karl,
>>
>>You may use the itk::BSplineUpsampleImageFilter.
>>Look at the help of itk::BSplineUpsampleImageFilterBase. There it's
>>explained how it works.
>>
>>Regards,
>>Stefan.
>>
>>
>>
>>
>>At 08:46 23/07/04, Miller, James V (Research) wrote:
>>
>>
>>I do not think ITK provides a mechanism for increasing the number of 
>>control points in a B-spline grid.  However, the mathematics of B-splines
>>do support this operation.  There are formulas for adding a control point
>>to a B-spline that maintain the trace of the B-spline (shape of the
>>B-spline).
>>
>>Any good book on B-splines will provide the formulas. 
>>
>>Jim
>>
>>
>>
>>-----Original Message-----
>>From: Karl Baum [ mailto:kgbaum at syr.edu <mailto:kgbaum at syr.edu> ]
>>Sent: Thursday, July 22, 2004 5:22 PM
>>To: insight-users at itk.org
>>Subject: [Insight-users] increasing bspline control point density
>>
>>
>>Hi,
>>I am using BSplines to provide the transformations necessary for my
>>registration.  I would like to take an iterative approach where I first do
>>registration with a low control point density, and then use the results as
>>input to a registration with a higher control point density.  The issue I
> 
> am
> 
>>facing at this point in time is how to initialize the parameters of the
>>second iteration with the results of the first iteration.  In other words
> 
> I
> 
>>need to take the grid defined by the deformation coefficients of the first
>>iteration, and use it as input into the second.  To do this I need to
>>calculate the starting deformation coefficients on the higher density
> 
> grid. 
> 
>>Does itk provide anything to do this?  I was unable to find any
>>documentation addressing this.
>>
>>Thanks,
>>Karl
>>
>>
>>_______________________________________________
>>Insight-users mailing list
>>Insight-users at itk.org
>>http://www.itk.org/mailman/listinfo/insight-users
>>
> 
> 
> 
> 
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