Adaptive registration of magnetic resonance images based on a viscous fluid model

This paper develops a new viscous fluid registration algorithm that makes use of a closed incompressible viscous fluid model associated with mutual information. In our approach, we treat the image pixels as the fluid elements of a viscous fluid governed by the nonlinear Navier-Stokes partial differential equation (PDE) that varies in both temporal and spatial domains. We replace the pressure term with an image-based body force to guide the transformation that is weighted by the mutual information between the template and reference images. A computationally efficient algorithm with staggered grids is introduced to obtain stable solutions of this modified PDE for transformation. The registration process of updating the body force, the velocity and deformation fields is repeated until the mutual information reaches a prescribed threshold. We have evaluated this new algorithm in a number of synthetic and medical images. As consistent with the theory of the viscous fluid model, we found that our method faithfully transformed the template images into the reference images based on the intensity flow. Experimental results indicated that the proposed scheme achieved stable registrations and accurate transformations, which is of potential in large-scale medical image deformation applications.