二次曲线运动轨迹恢复的新方法

The New Approach to Trajectory Triangulation over Conic Sections

研究了摄像机和景物同时运动时三维结构的重构问题,即从运动物体在多幅图像上的测量值重构物体在三维空间中的运动轨迹。这里的摄像机可以是一个移动的摄像机,也可以是由空间中多个不同位置的摄像机组成的集合。这个问题首先由AShashua等提出并定义为摴旒Ｈ切畏ā?在关于运动轨迹的某些约束条件下,他们恢复了物体在三维空间中的运动轨迹。这里提出一种基于“测量矩阵”的秩5约束的新方法,这种方法只要求解一个单变量高次方程组,没有用到优化问题,因此是简单、直接的。虽然讨论的运动轨迹是二次曲线,但它也可以方便地推广到运动轨迹为高次多项式曲线的情况。

This paper considers the problem of reconstructing the 3D coordinates of a moving point seen from a monocular moving camera, i.e., to reconstruct moving objects from line of sight measurements only. The task was originally suggested by A.Shashua and was defined as 搕rajectory triangulation? Under some constraints placed on the shape of the trajectory of the moving point, they determined the line in 3D (moving track) from the relativity of point and line and by the aids of Grassmann-Carley algebra and Pl cker coordinate. This paper proposes a novel method to deal with the problem based on the rank 5 constraints of the measurement matrix. The method is simpler and more directly than theirs. And above all, the method proposed here can deal with any curves, i.e., the trajectory of moving object is polynomial.