Fluid image registration using a finite volume scheme of the incompressible Navier Stokes equation
The authors focus on a stable and fast numerical method for resolving the fluid image registration problem by using the Navier-Stokes equations for an incompressible fluid. At the beginning, the authors introduce a mathematical model of fluid registration and, based on the properties of the regularization, they propose a dynamic equation for the incompressible Newtonian fluids, which are governed by the Navier-Stokes equations. Next, the authors present a discretization scheme for the proposed Navier-Stokes equation. In the scheme, a finite volume discretization based on a staggered control volume is used. Using the proposed discretization scheme and the semi-implicit method for pressure linked equations (SIMPLE) algorithm, the authors solve the equations. To correct the pressure in each step of the method, the authors propose a correction equation. To evaluate the proposed method, the authors test it on a benchmark of approximately of \(100\) MRI images and present the results of only five of them. To measure the robustness of the algorithm, the authors compare it with the classical implementation of the fluid registration model presented in [\textit{G. E. Christensen} et al., ``Deformable templates using large deformation kinematics'', IEEE Trans. Image Process. 5, No. 10, 1435--1447 (1996)], in which a finite difference scheme is used.
scientific article; zbMATH DE number 6945041
scientific article