[Insight-users] Spline interpolation on irregular point set

[Nick Tustison]

Hi Julien,

Have you looked at the B-spline scattered data approximation filter I
submitted awhile ago?  It appears as though it might have some of the
functionality you need.  The documentation and source code are located
at the Insight Journal at the following link:

http://hdl.handle.net/1926/140

Nick Tustison


On 5/11/07, Julien Michel <julien.michel at c-s.cnes.fr> wrote:
> Dear itk users,
>
> In one of our current developments, we have a set of points spread in
> our image (irregularly and possibly at non-grid positions), and we did
> approximate for each of this point the value of a given function thanks
> to optimization.
>
> Now we would like to use this set of points and values to interpolate a
> map of this function superimposable to our image. That means, we want to
> interpolate the value of this function at each pixel position of our
> image, and this interpolation must be done using BSplines.
>
> The ITK component the closest to our goal is the itk::KernelTransform
> and its derived transforms. It performs exactly the interpolation we
> want, but unfortunately, it performs it only on displacements (that
> means translation in both directions) between target and source landmarks.
>
> The solution we thought of would be to derive a new class from
> itk::FunctionBase, called LankmarkInterpolateKernelFunction, which takes
> as input a list of landmarks, their associated values, and provide the
> interpolated value via the Evaluate method. This class would also
> implement the methods from itk::KernelTransform specific to kernel
> algorithms. I believe their would be almost nothing to change in these
> methods. One could then derive the LandmarkInterpolateKernelFunction to
> provide thin plate interpolation or any other Kernel based interpolation.
>
> Anyway, this would duplicate quite a lot of code between the
> KernelTransform classes tree and the LandmarkInterpolateKernelFunction
> classes tree. This classes are already performing this interpolation on
> the displacement between source and target landmarks, so they could
> probably encapsulate the new interpolation function to avoid code
> duplication.
>
> Before starting the implementation of the
> LandkMarkInterpolateKernelFunction in our project, we wanted to ask the
> mailing list for feedback on this solution, since we may have miss a
> point. Of course, if ITK is interested in these new classes we could
> provide the code.
>
> Thank you for your help and work,
>
> Best regards,
>
> Julien
>
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