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

Luis Ibanez luis.ibanez at kitware.com
Sat Jul 24 10:15:10 EDT 2004 

Hi Karl,

1) In theory you are right.

    The formal way to do this would be to compute the
    control points of the high resolution grid directly
    from the control points of the low resolution grid.
    That's certainly an interesting exercise for an exam
    in a numerical methods course, or for a friendly
    homework.


2) A semi-pragmatic way to get the control points for
    the high resolution spline could be to sample the
    deformation field produced by the first stage of
    the registration process, then estimate the control
    points in the high resolution BSpline that would
    generate a good approximation to those sampled
    deformations. A classical option is to do a
    least-squares minimization in order to find the
    control point values.


3) In practice, However...
    You just need to initialize the high resolution
    BSpline with reasonable values. Once you initialize
    the BSpline transform, the *next* thing you do is
    to run an iterative optimization method that is
    going to refine the BSpline.  In that context it
    doesn't seem to be too critical to adhere to the
    formality of computing the perfect control points
    at initialization.


The full formal estimation of the high resolution
control points will be critical if you were going
to use it directly without further refinement...
but then,... given that this high resolution BSpline
will be fully equivalent to the low resolution one,
.... there will be no point in the whole computation
because you could have used the low resolution grid
from the beginning.     :-)


If your goal is to publish a paper, you probably want
to do the nice formal theoretical approach in (1).
That will populate your paper with beautiful equations
that will certainly help to impress the reviewers and
the readers with your intelligence and math skills.

If want you want is to get these two images registered,
then, you better invest your energy and time in fine
tunning the parameters of the optimizer and in evaluating
the quality of the registration, since after all, the whole
purpose of the second stage of registration is to change
the deformation field represented by the BSpline in order
to better register the two images.


  "Flexibility increases your chances for survival"



Regards,



    Luis



------------------
Karl Baum wrote:

> Luis,
> Thanks for your help.
> 
> Could you please clarify something for me though.  In the sample when
> initializing the parameters for the second registration, you are finding the
> displacement(deformation) from the first iteration at the coordinates of the
> new control points.  You are then using this as the start for the new
> control points.  However doesn't this change the deformation.  Because the
> control points are not actually on the spline, don't you need to find a
> control point that causes this same displacement, not use this as the
> displacement of our new control point.
> 
> Sorry this was hard to explain and sounds confusing.
> 
> Thanks,
> Karl
> 
> -----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
>>
>>
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>>
> 
> 
> 
> 
> 
> 
> 
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