For my research, I had to create a set of smooth deformation fields where I knew which points were moved and by which amount.
I tried to find a script, but I couldn’t find an appropriate one, not even talking about one in Python. So here I propose my own version, allowing to interpolate a 1D, 2D or 3D deformation field based on some points.
How does it work ? It is based on Bookstein’s algorithm. The first step is the computation of the coefficients of the smooth deformation field and then they are used to compute the values on the deformation field on a grid and this grid is returned.
The function to use is denseDeformationFieldFromSparse(), the arguments being size, the size of the desired grid, points, the locations where the deformation field is known, and displacements, the amount of displacement for each previously given point.
This code is given as is, but feel free to comment do that bugs can be ironed out (if there are bugs). It was tested with 1D, 2D and 3D test cases which can be found here.
Thanks to Bill Baxter for the distance function that was proposed on the numpy discussion list.