Constrained thin-plate spline reconstruction of 2D deformations from tagged MRI

Efficient constrained thin-plate spline warps are proposed in this paper which can warp an area in the plane such that two embedded snake grids obtained from two SPAMM frames are brought into registration, interpolating a dense displacement vector field. The reconstructed vector-field adheres to the known displacement information at the intersections, forces corresponding snakes to be warped into one another, and for all other points in the myocardium, where no information is available, a C¹ continuous vector field is interpolated. The formalism proposed in this paper improves on the authors´ previous variational-based implementation and generalizes warp methods to include biologically relevant contiguous open curves, in addition to standard landmark points. The method has been extensively validated with a cardiac motion simulator, in addition to in-vivo tagging data sets