颅脑手术可视化中手术场空间与图像空间之间的四点配准算法

A Four\|Point Registration Algorithm of Image\|Space With Surgery\|Space in Brain Surgery Visualization System

手术场空间与图像空间之间的配准是影响颅脑手术可视化系统精度的一个主要因素， 给定两个三维空间之间的对应两组点 ｛ｐｉ｝ 和 ｛ｐ′ｉ｝； ｉ＝ １， ２， …， Ｎ。两个空间中点之间的关系可由ｐ′ｉ＝ Ｒｐｉ＋ Ｔ表示， 其中Ｒ是旋转矩阵，Ｔ是平移矢量。本文提供一种基于矩阵单值分解（ＳＶＤ） 求解Ｒ和Ｔ的最小二乘解的四点算法， 并对算法进行了推导， 该算法与迭代法相比， 具有速度快、用点少的优点， 尤其适用于实际应用的颅脑手术可视化系统。

Registration between Surgery\|Space and Image\|Space is one of the key factors that affect the accuracy of the brain surgery visualization system.Given two sets of 3\|D corresponding points｛ p i ｝ and ｛p′ i｝,i=1,2,…,N .Relationship between 3\|D point sets of two spaces fits p′ i=Rp\-i+T, where R is a rotation matrix, T is a translation vector.A four\|point algorithm is presented in this paper for finding the least\|squares solution of R and T ,which is based on the singular value decomposition (SVD) of matrix,and the derivation of the algorithm is provided too.The algorithm has advantages of less computing time,and requires the least number of registration points,compared with conventional iterative algorithm.Especially,it is applicable in practical brain surgery visualization system.\;