Trajectory Triangulation over Conic Sections

Abstract

We consider 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 is feasible only when some constraints are placed on the shape of the trajectory of the moving point. We coin the family of such tasks as ``trajectory triangulation''. In this paper we focus on trajectories whose shape is a conic-section and show that generally 9 views are sufficient for a unique reconstruction of the moving point and fewer views when the conic is a known type (like a circle in 3D Euclidean space for which 7 views are sufficient). Experiments demonstrate that our solutions are practical. The paradigm of Trajectory Triangulation in general pushes the envelope of processing dynamic scenes forward. Thus static scenes become a particular case of a more general task of reconstructing scenes rich with moving objects (where an object could be a single point).