[Insight-users] Bspline Grid Elements

[Lars Hegenbart]

Hi ITK-community,

I am new to ITK so please forgive me, if I missed something important to
read (I checked the manual (PDF), the Doxygen-pages and had a look at the
Insight Journal).

I am having difficulties understanding the Bspline parameters. Therefore I
tried to set the parameters in a simple 5x5x5 grid (3rd order splines, 3
dimensions) manually.

1) bspline-parameter-array:
I assume the array is built like that:
array[0] to array[2] = Grid coordinate (x,y,z) = (0,0,0): x-,y- and z-part
of deformation vector
array[3] to array[5] = Grid coordinate (x,y,z) = (1,0,0): x-,y- and z-part
of deformation vector
array[6] to array[8] = Grid coordinate (x,y,z) = (2,0,0): x-,y- and z-part
of deformation vector
...
array[372] to array[374] = Grid coordinate (x,y,z) = (4,4,4): x-,y- and
z-part of deformation vector

Is this correct?

2) If I apply a deformation vector (x-vector part, y- vector part, z- vector
part) of (0,0,0) nothing happens of the points around the grid. Correct?

3) If I choose (1,0,0) as my deformtion vector does this mean, the point of
my image coinciding with the grid node of the bspline grid will be
transformed to positive x-direction? If yes, how far, 1 mm?
Is there a formula somewhere about this? I mean, I could analyze the source
code, but is it not documented/illustrated somewhere for easy understanding?