一种重构直线运动轨迹的新方法

A New Method of Reconstructing Moving Track which Along Line

由于拍摄图象的摄像机可以是一个移动的摄像机 ,或是由空间中多个不同位置的摄像机组成的集合 ,因此开展由多幅图象上的测量值来重构物体在三维空间中运动轨迹的方法研究是一个热点问题 .Shashua等首先提出了一种 "轨迹三角形法 " .该方法是在关于运动轨迹的某些约束条件下 ,借助于 Grassmann- Carley代数和 Plücker坐标 ,再利用点与直线的相关性来求出 3D空间中的直线 (运动轨迹 ) ,但该方法较复杂 .为了快速简便地实现直线运动轨迹的重构 ,提出了一种基于“测量矩阵”秩的 2约束的新方法 .这种方法简单、直接 ,可在一般的射影坐标系下实现 .虽然该方法是针对直线运动轨迹提出的 ,但它可以方便地推广到高次多项式曲线运动轨迹的重构 .

This paper investigates a new method of reconstructing moving track from the measured value over several views when the object moves along line in 3D space. Here the camera can be one moving camera, or a set of camera being located at different position. This problem was put forward by A.Shashua first and was defined as 'trajectory triangulation'. Under some restriction of the track of moving, they determined the line in 3D (moving track) from the relativity of point and line and by the aids of Grassmann-Carley algebra and Plücker coordinate. This paper brings forward a new method based on the rank restriction of the 'measured matrix', that is to say if the points are on a line, the matrix formed by the coordinates of these points must have rank 3. In order to simplify the computation, the camera matrices have been transformed so that the last column of every projective matrices has only one no zero value. The algorism of the method is evaluated on both synthetic and real world images. Comparing with the method in, our method is simply and directly, and it can be realized in a general projective coordinate system. Moreover, it can be generalized to any situation as long as the shape of trajectory of moving object is polynomial, although only moving along line is investigated in this paper.