Image registration (non-rigid \ non-linear)

I am looking for some algorithm (preferably if source code is available) for registering images. The deformation of the image cannot be described by a homography matrix (because I believe that the distortion is not symmetrical, but not homogeneous), more specifically, the deformations are reminiscent of barrel deformation / distortion and trapezoid, possibly some rotation of the image. I want to get pairs of pixels from two images, and so I can get a representation of the "warp field".

I google a lot and find out that there are some base algorithms for some ideas of physics, but it seems that they can converge to local maxima, but not global ones. I can limit the program to semi-automatic, this means some simple user interaction.

maybe some algorithms like SIFT? but I think that it cannot provide a “deformation field” with a regular sufficient density.

If it is important that the scale changes do not change.

complex field example http://www.math.ucla.edu/~yanovsky/Research/ImageRegistration/2DMRI/2DMRI_lambda400_grid_only1.png