An improved SIMPLEC scheme for fluid registration
The image registration is always a strongly ill-posed problem, a stable numerical approach is then desired to better approximate the deformation vectors. This paper introduces an efficient numerical implementation of the Navier Stokes equation in the fluid image registration context. Although fluid registration approaches have succeeded in handling large image deformations, the numerical results are sometimes inconsistent and unexpected. This is related, in fact, to the used numerical scheme which does not take into consideration the different properties of the continuous operators. To take into account these properties, we use a robust numerical scheme based on finite volume with pressure correction. This scheme, which is called by the Semi-Implicit Method for Pressure-Linked Equation-Consistent (SIMPLEC), is known for its stability and consistency in fluid dynamics context. The experimental results demonstrate that the proposed method is more efficient and stable, visually and quantitatively, compared to some classical registration methods.
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