Variational Problems And Numerical Algorithm In Medical Image Registration

As a branch of image processing,image registration plays an important role in remote sens-ing,bio-anthropophic,medical science and so on.Especially in medical science,image regis-tration is widely used in assistant diagnoses,computer-assisted surgery and so on.This thesis is mainly concerned with some variational problems arising in medical image registration.We prove the existence of global minimizer for the variational problems arising in diffusion tensor image(DTI)registration,which can provide a theoretical guidance on numerical simulation of DTI registration.At the same time,we also put forward a fractional order DTI registration model and prove the existence of global minimizer to this variational model.This is an extension of variational model for DTI with integer order regularity term.Moreover,we also study the multi-modal image registration based on trust region and mutual information and provide an numerical algorithm.Some numerical experiments show that our model has an advantage on registration between images with different modalities.In Chapter 1,some background and references on image registration are summarized.The main results of this paper are listed.In Chapter 2,we firstly introduce DTI registration model and related results.Then,we prove the existence of global minimizer to the variational problem arising in DTI registration.In Chapter 3,based on the nonlocal properties of fractional order derivative,we establish a new DTI registration model with fractional order regularity term to improve the regularity of transformation and prove the existence of global minimizer to this variational model.This result is a extension of that of Chapter 2.In Chapter 4,we give a multi-modal image registration model based on trust region and mu-tual information and design a numerical algorithm.Numerical experiments show that our model has an advantage on registration between images with different modalities.In Chapter 5,some prospects of the problems we will study in future are listed.