[Insight-users] Elements in the jacobian?

[motes motes]

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.