[Insight-users] BSplineDeformableTransform parameters?

[motes motes]

I am trying to understand the parameters to the BSplineDeformableTransform
in the BSplineWarping1.cxx example.

1) As I understand the parameters are actually just a set of deformation
vectors. The location of theses vectors are distributed uniformly over the
image but the orientation and magnitude of the vectors might vary during the
registration.

2) When defining the grid extra "vectors" outside the image must be defined
following the below rule from the example:


//  Since we are using a B-spline of order 3, the coverage of the BSpling
grid
//  should exceed by one the spatial extent of the image on the lower region
of
//  image indices, and by two grid points on the upper region of image
indices.
//  We choose here to use a $8 \times 8$ B-spline grid, from which only a $5
//  \times 5$ sub-grid will be covering the input image.

But why?

If p=3 is the degree a Cubic B-spline has support over p+1=4 knots. Assuming
that clamped knot-vectors are used the first and second basis function will
only have support over 1 and 2 knots respectively.
The third basis function has full support over the 4 knots.

Is this why extra control points / deformation vectors are added?


Another thing. In the above comments is not meant to say order 4? Normally
the order = degree+1 and as I understand ITK uses cubic B-splines which is
3-degree.
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