一种对非线性配准问题的信赖域方法综述

A Trust Region Method For Nonlinear Image Registration

该文主要介绍了应用信赖域方法来得到一个向量u（x）=（u1（x）,u2（x））t,使得匹配由相同的成像设备获取的两幅很相的图像,应用u（x）使得浮动图像T的像素点x=（x1,x2）t变化后而得到的灰度值与参照图像R的灰度值近似相同或相同。主要思想是通过对函数D（u（x））=‖R（x）-T（x-u（x））‖2进行极小化,该文是对非线性函数D（u（x））在当前点线性化估计,但是二次极小化问题也许会出现病态,这样就需要一个辅助的光滑弹性项来对其最小二乘泛函进行惩罚,本文介绍了相应的算法描述。

This paper introduces a trust region method to obtain a displacement vector field u（x）=（u1（x）,u2（x））t,which matches two images recorded with the same imaging machinery.The displacement vector should transform the image location x =（x1,x2）t of an image T,such that the grey level are equal to another image R.The problem leads to minimize the nonlinear least squares functional D（u（x））=‖R（x）-T（x-u（x））‖2.To apply the Newton iteration method,we replace the nonlinear functional D（u（x）） by its linearization around a current approximation.But the quadratic minimization problem is ill-posed,.We use an auxiliary linear elasticity term,which incorporates smoothness constraints to the displacement field.