Elastic Registration Of Medical Image Using The B-spline

Medical image registration refers to the same anatomical structure of the two medical images,the goal is to obtained a space transformation for one of the medical images,so that the points in one image can be related to their corresponding points in the other.In the medical field,image registration is mainly used for medical image fusion,image and map matching,surgical navigation,stereotactic radiotherapy and so on.In computer-assisted surgery and image guided surgery, medical image registration is an important aspect,although preoperative three-dimensional images lack real-time data,the two-dimensional image registration can compensate for some spatial information,and be able to reduce the exposure of patients and doctors in the radiation environment,therefore there is an important clinical value,and more and more attention.However currently a lot of medical image registration algorithms only concentrate on rigid transformation, elastic registration algorithm has been made a number of methods,but rigid registration is more sophisticated.In addition,the elastic registration algorithm can not meet the real-time clinical needs,In addition,because of diversity and complexity,even though a lot of elastic registration algorithm has been proposed, no registration method can be reached at all aspects of clinical needs.This means that the method has certain limitations,including lack of effective real-time restrict and less than automatic nature,those disadvantages extent the restrict of medical image registration algorithm in the actual clinical application,therefore elastic registration of medical image have a wide range of clinical applications,and is also a hot spots in the field of medical processing research.In this paper,the single-mode automatic medical image registration is effectively implemented,this algorithm is based on the B-spline deformation model,and Leven berg-Marquardt optimization algorithm and SSD method are used.Because of B-spline with three consecutive second-order differential characteristics,we choose thethree B-spline as the variable model.Three B-spline deformation model has characteristics of a good local control,each control points changes,only the deformation caused by neighborhood,control surfaces grid spacing can be used to control the degree of deformation,when the control surfaces have more dense grid, the deformation models tend to describe the local deformation;control surface have reduced grid,the deformation of tend to describe the local deformation.Because the optimization algorithm iterative methods is used to look for the best image registration,the general calculation of each iteration requires the calculation B-spline basis function value of the integer points,extract 16 control points,and then calculate the product of B-spline function and the corresponding control points,and then calculate the sum.A high computational complexity,speed slow and so on these disadvantages seriously affect the real-time image registration of clinical needs. Because the B-spline deformation model has good approximation property and characteristics of rapid calculation,w e applied convolution calculaltion algorithm which B-spline function is used as the convolution nuclear.The B-spline basis function is calculated separately,using it to convolute with the two-dimensional control point matrix,the calculation save time in order to improve computing speed. To a certain extent to meet the clinical real-time demand.At the same time,the general optimization algorithm such as the gradient descent method easily calculate.but too many iterations are often restricted the speed of image registration.we choose the Levenberg_Marquart optimization algorithm, Levenberg Marquart optimization algorithm apply Hessian matrix of control coefficient,because of the three B-splines with continuous second-order differential properties, although the Levenberg-Marquardt optimization algorithm introduced the Hessian matrix which can be seen from the fourth chapter,in the fourth chapter the process of solving math are showed. It does not increase the computation time and iterations is greatly reduced to accelerate the matching speed,at the same time improve the matching accuracy.From the math point of view,the cost function which is used in the current popular single-mode image registration algorithm are reviewed in this article.namely, to a certain extent,elastic registration problem means find solutions of the minimum cost function.After determining the single-mode image registration cost function, from the perspective of differential the focus of study describes the minimum cost function for numerical calculation.We apply AOS method(additive operator splitting scheme) to transform the Euler-Lagrange equations of the similarity matching function.We transform the sum of the inverse matrix to the inverse matrix of the sum matrixThen we apply Thoms method to solve the Euler-Lagrange equation,computing time is reduced,and the computing speed is improved.because the theoretical solution of gradient-based offset is likely to result in non-continuous,Gaussian filter is applied to a smooth offset.the existing medical image registration algorithm is not sophisticated enough that the algorithm is not very robust.