Abstract: The key problem in self-calibration based on Kruppa equations is lack of robustness.In this paper，a two-step camera self-calibration technique is proposed.Firstly，the Kruppa equations are simplified and the target function is defined.Secondly，an initial solution is obtained by three linear independent translational motion of the camera.Then the initial solution is refined by optimizing the nonlinear target function.Extensive simulations as well as experiments with real images show the new technique can substantially improve the robustness aspect and increase the calibration accuracy.

Key words: Kruppa equation, camera self-calibration, linear independent, translational motion

摘要： 针对传统的基于Kruppa方程的摄像机自标定算法鲁棒性差的情况提出了一种新的二步式标定方法。首先对Kruppa方程进行简化，确定了经简化后的目标函数，再通过摄像机的三次线性无关的任意平移运动确定初值，然后用非线性优化目标函数法精化初值。实验结果表明，该方法可以大大提高基于Kruppa方程标定算法的鲁棒性及标定精度。

关键词: Kruppa方程, 摄像机自标定, 线性无关, 平移运动