Study Of Diffeomorphic Image Registration Modelling And Fast Algorithms

Image registration has a wide range of applications in target tracking,geological exploration,disease detection,angiography and other industrial and medical fields.According to the application,it can be divided into rigid registration and non-rigid registration.Rigid registration is to search for a global transformation(such as rotation,translation and scaling)registration between reference image and template image.This kind of registration is widely used in the underlying image processing,but often has some limitations in medical image,motion tracking and other aspects.Non-rigid registration can more accurately realize the local deformation between images.According to the introduced regularization term,it can be divided into elastic model,viscous fluid model,optical flow model,diffusion model and curvature model.The deformation field obtained by these models has good geometric smoothness,but no further description of the inverse transformation.Recently,with the development and wide application of registration technology,there is a higher demand for the geometric properties of deformation field between two images,such as topology preserving,area preserving or volume preserving,quasi-conformal and so on.Therefore,the study for non-rigid registration model of diffeomorphism deformation field has gradually become a hot and difficult issue in the field of image registration.In this paper,we consider the establishment of non-rigid diffeomorphic registration model,and focus on the mathematical derivation,the design of fast algorithm and numerical comparison experiment.The main contributions are as follows:1.Based on diffusion registration model and diffeomorphism theory,a new non-rigid diffeomorphic registration model is proposed in this paper,based on Augmented Lagrangian multiplier method,a fast registration algorithm(D-ALMM)is designed to solve the model.Numerical experiments show that the D-ALMM algorithm designed in this paper has better registration speed and accuracy than several common registration algorithms,the deformation field keeps diffeomorphic and other practicability.2.In view of the non-rigid diffeomorphic registration model proposed above,the equality constraint is introduced to split the optimization variables,and the mathematical derivation of the optimization methods are given respectively in combination with the alternating direction method of multipliers and proximal point algorithm to design the fast D-ADMM algorithm and D-PPA algorithm.The experimental results show that the two registration algorithms designed have good registration effect on large deformation and small deformation registration,the diffeomorphism of deformation field is also maintained,and the registration performance of the designed D-PPA algorithm is the best.