[Insight-users] Spline interpolation on irregular point set

[Julien Michel]

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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