[Insight-users] spline as a combination of b-splines

[Amy C]

Hi Luis,

Thanks a lot for that, I had a look at the class and it does seem do what
I'd like it to (and then some), so I might modify it to just do the
evaluating & calculating of derivatives (I need the bspline object, but
don't need it to approximate any data). After perusal of the code, I think
my problem is to do with my understanding of B-splines. I thought I
understood them, but I've become more and more confused as to exactly how
many knots/control points are needed and where they should be placed. I'm
going to do a bit more reading and then come back this question later.

thanks for all the help,
Amy

On Mon, Jan 4, 2010 at 6:26 AM, Luis Ibanez <luis.ibanez at kitware.com> wrote:

> Hi Amy,
>
> There are several forms of BSplines in ITK.
>
> From your detailed description, it seems that the class:
>
>   Insight/Code/Review/
>      itkBSplineScatteredDataPointSetToImageFilter.h
>
> provides the functionalities that you are looking for.
>
> This class is described in the following Insight Journal paper:
> http://www.insight-journal.org/browse/publication/57
>
>
> Please take a look and let us know what you think,
>
> Otherwise we could point you to other of the
> BSpline implementations in ITK.
>
>
>       Regards,
>
>
>                 Luis
>
>
> -------------------------------------------------------------
> On Sun, Jan 3, 2010 at 2:41 AM, Amy C <mathematical.coffee at gmail.com>
> wrote:
> > Hello,
> >
> > I'm after some sort of B-spline class, but I'm not sure what to use.
> > I have a spline that is a linear combination of cubic (uniform, centered)
> > b-splines, it maps from R^(image dimension) -> R.  ( spline[px] = sum(
> > coefficient[px]*b-spline[px] ).
> > In this case, instead of interpolating a set of numbers, I -know- the
> > coefficients(/control points) and knots of the spline. More or less, each
> > pixel in the image contains a coefficient/control point (or every n
> pixels,
> > where n is an integer) and I'd like to evaluate the spline.
> > I guess I just need some object with the following properties
> > - set coefficients(/control points)
> > - set knots ( or spacing? )
> > - evaluate the spline at every pixel
> > - calculate the derivative
> > - will be used in a loop - will recalculate coefficients each loop
> > - need to convolve the coefficient 'image' and possibly downsample every
> now
> > and then
> >
> > At first I thought of just using a normal array to hold the coefficients
> > etc, but the last two points suggest I should use something within ITK. I
> > was thinking of making an object that is more or less an itk::Image (for
> the
> > coefficients) with an Evaluate/EvaluateDerivative method.
> >
> > Does anyone know of a class that does this already? (Set knots, set
> > coefficients, evaluate both spline and derivatives, where the spline is
> made
> > up of bsplines?) BSplineInterpolateImageFunction seems closest, but it
> > calculates coefficients to fit the input image, while I know the
> > coefficients and just want to calculate the derivative/values.
> >
> > Thanks,
> > Amy
> >
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