Studies Of Variational Models And Numerical Methods For Image Registration

Image registration which is also called image matching is one of the most useful and funda-mental tasks in imaging processing domain.The task of image registration is to find an optimal geometric transformation between corresponding data such that they could be well matched.It is often encountered in many fields such as astronomy,biology,chemistry,medical imaging and remote sensing and so on.Recently,variation-based registration model has been successfully proven to be a very value tool in many image registration applications.Usually,a variational image registration model can be described by following form:giv-en two images,one kept unchanged is called reference and another kept transformed is called template image.The purpose of registration is to look for an optimal geometric transformation such that transformed template image is similar to reference image as much as possible.Though the problem is easy to state,it is hard to solve.The main reason is that the problem is ill-posed.In the process of registration,adding a regularizer is inevitable to conveniently find an optimal geometric transformation.We know that different regularizer techniques can produce different registration model,and the choice of regularizer techniques is very crucial for the solution and its properties.How to design a suitable registration model is a main problem in the variational registration model-based fields.It is usually difficult to solve analytically the variational regis-tration model,thus numerical schemes and appropriate discretizations are necessary.We know that the number of unknowns of discretized variational model is proportional to the number of image pixels,for this reason,fast,efficient and stable numerical algorithms become another key issue in the variational registration model-based fields.In view of these two kinds of problems,the main contributions of this paper include the following aspects:1.We extend the modified total variational regularization proposed by Chumchob-Chen using the vectorization method mentioned in color image de-noising,and propose an improved discontinuity-Preserving image registration model.To solve the new model,we propose a method of’ frozen coefficients’ combine with Gauss-Newton scheme with Armijo’ s Line Search and further to combine with a multilevel method to achieve fast convergence.Numerical experiments not only confirm that our proposed method is efficient and stable,but also it can give more sat-isfying registration results according to image quality.2.To utilize interdependence between the primary components of the deformation field,we proposed a new vectorial curvature model for image registration.The proposed regularizer is related but not identical to previoxis high order regularizers that have been proved to be useful in vector-valued image denoising and in optical flow computation.To solve the new model,we pro-posed a fixed point method combined with a Gauss-Newton scheme with Armijo’s Line Search and further with a multilevel method to achieve fast convergence.Numerical experiments con?firm that the proposed method can effectively find a highly accurate solution for both synthetic and realistic images and produce more robust registration results in quality than the previously best model[1].3.In this section,a novel variational image registration model using a second-order fiunc-tional as regularizer is presented.The main motivation for the new model stems from the LLT model.In order to avoid mesh folding,inequality constraint on the determinant of the Jacobian matrix J of the transformation is also proposed.Furthermore,a fast solver is provided for numer-ical implementation of registration model with inequality constraints.Numerical experiments are illustrated to show the good performance of our new model according to the registration quality.