Study On Numerical Method Of Total Variable Registration Model

Image registration is one of the basic research topics in the field of image processing.Based on variational image registration is one of the effective methods.The second-order variational model is simple and easy to popularize compared with the high-order variational model.This paper presents several effective numerical methods for the second-order model.The specific work is as follows:1.Aiming at the improved total variation registration model with hypersurface function as regular term kernel function,a nonlinear multigrid method with smoothing error of hierarchical refinement is proposed,and the lag-diffusion fixed point iteration in the form of successive over relaxation iteration(SOR)is used for pre smoothing and post smoothing,finally,an effective nonlinear multigrid(NMG1)algorithm is designed.The NMG1 algorithm is suitable for large deformation registration and achieves better registration results than the fixed-point iteration(FP)algorithm both in terms of registration accuracy and speed.2.The kernel function of the second-order adaptive variational TVp registration model is a power exponential function.It is difficult for nonlinear multigrid method to effectively preserve the exponential part to distinguish between smooth and discontinuous in restriction and interpolation.By pre setting a positive contant c,adaptively selecting the value of p function,simplifying the restriction and interpolation of the exponential part of the kernel function,using the Gauss-Seidel relaxation iteration form of lag-diffusion fixed point iterative smoothing method,we propose an effective nonlinear multigrid(NMG2)algorithm for TVp model.The experimental results show that NMG2 algorithm has faster registration speed and higher accuracy than FP algorithm,and is suitable for large deformation registration.3.For the u-subproblem of the augmented Lagrange multiplier(ALMM),the NMG1 algorithm and NMG2 algorithm proposed in the first two chapters are introduced into the ALMM method respectively.The experimental results show that the two algorithms can improve the registration quality while improving the speed of TV model solving.