Trajectory Triangulation of Lines: Reconstruction of a 3D point Moving along a Line from a Monocular Image Sequence

We consider the problem of reconstructing the location of a moving 3D point seen from a monocular moving camera, i.e., to reconstruct moving objects from line-of-sight measurements only. Since the point is moving while the camera is moving, then even if the camera motion is known, it is impossible to reconstruct the 3D location of the point under general circumstances. However, we show that if the point is moving along a straight line, then the parameters of the line (and hence the 3D position of the point at each time instance) can be uniquely recovered, and by linear methods, from at least 5 views. Consequently, we propose a new approach for dealing with dynamic scenes (rich with moving objects) in which once the camera motion is recovered, the 3D trajectory (straight line) of the moving target can be recovered — even when the moving target consists of a single point.