基于有限内存Broyden-Fletcher-Goldfarb-Shanno优化算法的图像非刚性配准方法

Non-rigid registration based on Basic-spline free form deform and limited memory Broyden-Fletcher-Goldfarb-Shanno optimal algorithm

图像配准可以分为刚性配准和非刚性配准两类,图像非刚性配准是图像处理研究的热点和难点,其中的参数模型往往转化为无约束优化问题的求解,当参数数目较大时求解比较费时,提高此类算法效率的关键之一是减少迭代算法中矩阵的计算量和存储量.本文研究了一种非刚性配准方法,该方法应用Basic样条自由变形模型,此模型改变控制点只影响其附近局部区域的形状,可以通过计算变形场的偏移量来控制局部变形,隐含地强加了平滑约束,将此问题转化为求解无约束优化问题.同时应用有限内存Broyden-Fletcher-Goldfarb-Shanno优化方法求解代价函数的最优解,此优化方法避免了计算Hessian矩阵及其逆矩阵,而且不要求存储矩阵,降低了计算量和存储量,减少内存开销,使得优化时间大为缩短.实验证明该方法不仅效率高,而且配准效果好.

Image registration is one of the basic tasks of image processing,which is widely used in military,remote sensing,medicine,computer vision,pattern recognition and other fields.Image registration is to make an image consistent with another image on the corresponding point,surface,or pixel values to using geometric transform in the same space,which will be a variety of modes of image information fusion into a new image.Multiple images from the same object are taken by the same or different sensors,at different times or different points of view,so that in these images there are some differences,we must take image registration before using these images to do research. According to the deformation characteristics of the image classification,image registration can be divided into rigid registration and non-rigid registration categories.For the three-dimensional image,rigid registration is to find a six-degree of freedom（three rotational,three translational） of the transformation,making floating-point image is mapped to the corresponding point of the reference images.Non-rigid registration is to regulate the complex non-rigid deformation between images,such as image stretching deformation,bending deformation and tensional deformation and so on.In many cases rigid registration can not meet the needs of the actual image,because the nature of a lot of images deformations are non-rigid,which need use non-rigid registration method to registration. Non-rigid registration method is calculating the deformation field offset through parametric or non-parametric methods.Parametric method is using basis functions to express the main deformation field,which contain thin plate-spline function,Basic-spline function.Non-parametric method is to directly calculate the offset of each pixel,such as diffusion model,viscous fluid model,DEMON methods.Based on B-spline registration algorithm can control the local deformation,which affects only the local deformation of the field by changing the control points.Free deformation model which has a good ability to simulate the local deformation,also has the unrestricted freedom and the advantage of efficient computation,is the best option of simulations of the local non-rigid deformation for image registration. Image Non-rigid Registration is the hotspot and difficulty of image processing research.Its parametric models are often transformed into unconstrained optimization problem which is always the research emphasis of the theoretical research.Its time-consuming for matrix＇s calculating and storing in per iterative when solving the problem.In this paper we provide a non-rigid registration method,which is based on Basic-spline free form deform model.This model can make only partial deform,and has impliedly added the smoothness constraint.This method utilizes limited memory Broyden-Fletcher-Goldfarb-Shanno optimal method for solving the cost function,which avoid calculating the Hessian matrix and its inverse matrix.This optimal method reduces computational complexity and memory capacitance,and make the cost time shorten much..The experiments prove this non-rigid registration method is not only of high efficiency,but also of good effect in registration.