It indeed has the basic TPS (no tension, no smoothing) so
something like this may be added (based on my reading of the code and
the referenced paper):
Thin plate spline in the following form is used for interpolation:
f(x,y) = a +bx + cy + \sum_{j=1}^N \w_j r^2 \ln r^2
where r^2 = (x_i-x_j)^2 + (y_i-y_j)^2, N is number of points and
a,b,c,\w_j are coefficients
Donato and Belongie paper: www-cse.ucsd.edu/~sjb/pami_tps.pdf
If the instability becomes annoying it can certainly be improved.