中文摘要：

多视三角化是在给定测量点对应和摄像机投影矩阵的情况下，求解相应的空间点的过程．由于测量点存在测量误差，所以只能求解在某种准则下的最优空间点．文中提出一种新的优化准则：在空间平面矩阵最小奇异值为0的约束下最小化估计点到测量点的L2-范数距离．在此基础上，采用该准则约束的Sampson近似得到一种简单的迭代求解方法；通过空间平面矩阵最小奇异值单调递减的条件和共轭梯度方法得到另一种收敛性更好的迭代算法．实验结果表明，这2种迭代算法不仅迭代次数及运算时间明显少于黄金标准算法，而且能得到基本相同的计算精度．

英文摘要：

Given a set of measured point correspondences across images and the associated camera projection matrices, the multi-view triangulation refers to the process of estimating the corresponding 3D point. Due to various errors in measured points, an optimality criterion is required for the triangulation. This paper proposes a new optimality criterion which minimizes the Lz-norm distance between the estimated point and the measured point under the constraint that the least singular value of the space plane matrix must be zero. Based on Sampson approximation of the constraint, a simple iterative algorithm is obtained. In addition, by using the conjugate gradient and enforcing the decreasing condition of the least singular value of the space plane matrix in the iterative process, another iterative algorithm with better convergence rate is obtained. Experiments show that our two proposed algorithms both require less number of iterations and have less running time than the Gold Standard algorithm, while yielding comparable estimation accuracy.