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.