直线摄像机参数校正过程中系数矩阵特性的分析

Analysis of the Coefficient Matrix in Camera Calibration with Line Correspondences

探讨在利用对应直线进行摄像机外部参数校正的过程中，如何快速简便地确定齐次方程组系数矩阵秩的问题．通过对该系数矩阵的分析，得到关于此矩阵的约束条件，并在此基础上，推导了判断此矩阵秩的大小的一个充分条件．利用这一结论，避免在参数计算过程中多次对矩阵进行奇异值分解，从而使计算过程大为简化，而且也使选取对应直线的过程变得更有目的性．

In camera calibration with line correspondences, it is important to determine the rank of the coefficient matrix of the equation system in a quick and efficient way. Based on the analysis of this matrix, the constraints for the coefficient matrix were got. Setting out from this conclusion, a sufficiency condition for estimating the rank of this matrix was obtained. With the help of this condition, we no longer need to perform singular value decomposition (SVD) as each new correspondence enters, therefore, the overall computation time can be greatly reduced. Also, it enables more objective selection of the line correspondences.