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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 C 1 continuous vector field is interpolated. The formalism proposed in this paper improves on our 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.

Dense 2D displacement reconstruction from SPAMM-MRI with constrained elastic splines: Implementation and validation