[Insight-users] Elements in the jacobian?

[Luis Ibanez]

Hi Motes,

Your interpretation of the parameters is correct.

---

The reason by there are no cross-terms is that the parameters of the BSpline
are fully independent along each dimension.

That is, the first 16 parameters are strictly related to the X direction,
while the second set of 16 parameters are strictly related to the Y direction.

It is logical then than when computing how the Transform parameters affect
the outcome of the transformation, the first 16 parameters will NOT affect
the output Y coordinate, and the second 16 parameters will NOT affect the
output X coordinate.


     Regards


          Luis


----------------------------------------
On Tue, Nov 10, 2009 at 5:32 PM, motes motes <mort.motes at gmail.com> wrote:
> I am looking at the code for the BSplineDeformableTransform and the
> function GetJacobian for a 2D registration application using Sum of
> squared differences as metric and the regular gradient descent
> optimizer.
>
> I have defined 4*4 = 16 nodes and since  its 2D I get 32 parameters in
> the parameters array.
>
> As I understand the 16 weights computed are actually just stored in
> the jacobian like:
>
>
> x    w0, w1, w2, ..., w15,    0,   0,   0, ...,   0
> y      0,   0,   0, ...,    0,   w0, w1, w2, ..., w15
>
>
> Where each sequence of weights are just copies. So it could be
> interpretated as a "diagonal" matrix where only the diagonal consist
> of possible non-zero elements. The number of elements per row in the
> diagonal are:
>
>            totalNumberOfParameters/Dim
>
>
> Am I correct so far?
>
>
> What I don't understand is why there are only 16 weights and not 32
> weights? Should the weights not be computed for each parameter for
> each dimension? This would mean that the diagonal would not contain
> copies of the 16 weights.
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