Non rigid image registration by modeling deformations as elastic waves

In this paper we propose an inter-subject non-rigid image registration method that is derived from the concept of elastodynamics. Non-rigid warps are modeled as elastic waves which tend to recover extensive deformations. The deformable transformation model is given by Navier PDE which is solved iteratively using finite difference approximations. The dynamical displacements so computed represent the warp field which is then used to bring the subject image into spatial correspondence with the atlas. The results were validated using Jaccard coefficient (J), Dice coefficient (D), Overlap coefficient (O) and Normalized Cross Correlation (NCC) with mean ± std values of 0.81 ± .04, 0.89 ± .03, 0.99 ± .01 and 0.97 ± .01 respectively. This quantitative assessment confirmed that the proposed registration method performs very well.