根据抛物线运动特有的射影几何性质, 提出了一种应用抛物线运动估计摄像机姿态的新方法。首先, 计算不同位置自由落体运动轨迹在摄像机图像平面上投影直线的交点, 并证明该交点即为地球重力方向的灭点。其次, 使用Sampson近似计算抛物线运动轨迹在摄像机平面上的投影二次曲线方程。最后, 在摄像机内参数已知的条件下, 利用抛物线投影二次曲线中隐含的关于灭点和灭线的射影几何性质, 完成摄像机姿态的估计。 通过数值模拟和实际实验验证了提出算法的正确性和可行性。结果表明: 与传统的棋盘估计方法比较, 本文算法估计旋转矢量的轴平均误差为0.017 rad, 角平均误差为0.007 rad, 平移矢量方向的平均误差为0.071 rad。得到的结果显示该方法可以应用于计算机视觉中摄像机的姿态估计。

A new method was proposed for the camera pose estimation based on specific geometric properties of parabolic motion. The intersection of lines which was the projections of trajectories of a free falling subject from different locations was first calculated. According to the nature of the vanishing point, the intersection was proved to be the vanishing point of the Earth's gravity direction. Then, the equation of conic obtained by projecting parabolic trajectory on the image plane was solved using Sampson approximation. Finally, under the condition of known intrinsic parameters, the camera pose was evaluated by using the geometric properties of vanishing point and vanishing line hidden in the projective conic. The experiments with numerical simulation as well as with real images indicate that the method is correct and feasible. By the proposed method, experimental results show that the mean error of evaluated rotation axis is 0.017 rad, and the rotation angle is 0.007 rad, and the mean error of translation direction is 0.071 rad as compared to the traditional checkerboard method. Results indicate that the proposed method can be used for camera pose estimation in computer vision.