Want to learn Thin Plate Spline

Dear all:

I used a "smoothing thin plate spline(tps)" for image registration,

and it usually helps to yield good results. But I am not clear about
how on earth the close-form solution is obtained from minimizing its
bending energy E(f), which is:
E(f) = \sum | y - f(x) |^2 + \lambda \int (f_xx^2 + f_xy^2 +
f_yy^2) dxdy


And if I add additional iterms to E(f), how can I calculate f again?
I am also not wondering if there is any guide/principle for deciding
the coefficient \lambda, except for trying by experiments.


Many paper refer to Wahba's book: Spline Models for Observational Data
1990. But it is difficult for me to get one. Can anyone point out
another comprehensive reference? A tutorial is most preferred.


Thanks a lot!
Jeff

student, The Chinese University of Hong Kong

.

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