B spline2

[rijobro]

Supersedes #743.

[rijobro]

@KrisThielemans Not adjoint unforunately:

ControlPointGridToDeformationConverter is not adjoint, with normalized error of 1.2098765463674779 (max: 0.0001)

I don't know if we expected it to be or what we can do if it isn't.

[KrisThielemans]

I didn't see an error really. sigh. Might be worth checking if NiftyMomo moved on.

I am confused by the hierarchy. For me, NiftiImageData3DBSpline should be a data object, and then something else (the "converter") that implements the Model (which should be derived from Transformation), but it's more important that it works of course.

[KrisThielemans]

what about the following test to visualise this a bit more: construct the forward and backward matrices by hand, e.g.

mat=zeroes(cpg.num_elems(), dvf.num_elems())
cpg.fill(0)
for i in all_indices_in_cpg:
   cpg(i)=1
   dvf=converter.forward(cpg)
   for j in all_indices_in_dvf:
      mat(i,j)=dvf(j)
   cpg(i)=0 # reset to zero

and similar for backward. Then we compare it with the transpose in numpy. Not sure how easy this is to do.

(Note: all indices have to run over "linearised" vectors (reshaped to vectors in numpy).)

Raw matrix will be tough to look at, but can take a raw and convert to dvf, an ddisplay that for instance. should be very sparse of course.