[Insight-users] question about b-spline field to a dense deformation field: BSplineDeformableTransform

[Nicholas Tustison]

Hi Anja,

> My question is that say we want to extract a dense deformation field
> from this parameterised deformation field. Then each voxel is affected
> by a few control points. Do we basically add contributions from each
> of the control points to obtain the final deformation at each voxel?

Yes, the B-spline interpolated deformation value at a point within the
transform domain is calculated by summing the weighted contributions
of the 16 neighboring control points and corresponding B-spline basis-
functions evaluated at that point (for spline order = 3).

> Is that what ITK does when we resample an image using this transformation?

The resampling operation is agnostic with respect to the mechanisms of
the transformation itself.  The resampling filter simply queries the transform
as to how the point under consideration is mapped.

Nick