一维单应矩阵的进一步研究与应用

Further Study and Application for One-Dimensional Homography Matrix

一维(1D)标定具有抗遮挡和制作成本低等优点,是摄像机标定中的重要方法之一。首先,以1D单应矩阵为基础,给出了绕固定点运动1D标定方法的几何解释;其次,在小孔成像模型下,证明了摄影几何中的交比不变性与1D单应矩阵的等价性。相比于共线4点的交比不变性,1D单应矩阵约束更具有一般性。最后,针对基于平面运动的1D标定,由1D单应矩阵计算运动前后1D标定物延长线的交点,提出了一种简便的方法,将平面运动转化为绕固定点运动,并通过仿真和真实实验验证了算法的正确性。实验结果表明:与已有方法相比,本文算法的标定精度得到了显著提高。

One-dimensional（1 D）calibration is one of the most important methods in camera calibration because of its advantages of anti-occlusion and low cost.Firstly,we propose the geometric interpretation of 1 D calibration rotating around a fixed point based on the 1 D homography matrix.Secondly,it is proved that the cross ratio invariance in projective geometry is equivalent to the 1 D homography matrix in the pinhole imaging model.Compared to the cross ratio invarianceof four collinear points,the constraint of 1 D homography matrix is more general.Finally,aiming at the 1 D calibration under planar motion,the intersection point of two extension lines is calculated by 1 D homography matrix.A new convenient method is given to convert planar motion into rotating around a fixed point.The correctness of the proposed algorithm is verified by simulation experiments and real experiments.The experimental results show that the calibration accuracy of the proposed algorithm is improved greatly compared with that of the existing methods.