基于条件数的摄像机自标定方法的鲁棒性分析

对基于绝对二次曲线和基于绝对二次曲面的两类摄像机自标定方法的鲁棒性进行了分析,并从矩阵条件数出发,通过大量仿真实验对两类方法进行了定量比较．实验结果表明, 基于绝对二次曲线的摄像机自标定方法的系数矩阵的条件数一般小于基于绝对二次曲面方法的系数矩阵的条件数．另外,当常数因子有误差时,基于绝对二次曲面方法的系数矩阵条件数的变化一般比基于绝对二次曲线方法系数矩阵条件数的变化更剧烈．上述二点表明,基于绝对二次曲线的自标定方法的鲁棒性一般要优于基于绝对二次曲面的自标定方法．上述结论与文献中的一些实验观察正好相佐．

Analysis on the Robustness of Camera Self-calibration in Terms of Conditioning Number

Based on extensive simulations, the robustness aspect of the two main kinds of camera self-calibration methods, namely the absolute conic based method and the absolute quadric based one, is investigated and compared in terms of the conditioning number of the corresponding coefficient matrix. In addition, the sensitivity of the conditioning number to the unknown scales in the constraint equations is also investigated. It is shown that the conditioning number of the absolute conic based method is generally smaller than that of the absolute quadric based one, and the absolute quadric based method is generally more sensitive to the possible scaling errors. The above simulation results indicate that the absolute conic based method is more robust than the absolute quadric based one, a conclusion in direct contradiction to the previously reported observations in the literature.