TY - JOUR

T1 - Trajectory triangulation

T2 - 3D reconstruction of moving points from a monocular image sequence

AU - Avidan, Shai

AU - Shashua, Amnon

N1 - Funding Information:
This research was partially funded by DARPA through the U.S. Army Research Labs under grant DAAL01-97-R-9291. We would like to thank Yair Ramati for pointing our attention to the literature on orbit determination and reference [3].

PY - 2000

Y1 - 2000

N2 - 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.' We investigate the solutions for points moving along a straight-line and along conic-section trajectories. 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 instant) can be uniquely recovered, and by linear methods, from at least five views. For the case of conic-shaped trajectory, we show that generally nine views are sufficient for a unique reconstruction of the moving point and fewer views when the conic is of a known type (like a circle in 3D Euclidean space for which seven views are sufficient). 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).

AB - 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.' We investigate the solutions for points moving along a straight-line and along conic-section trajectories. 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 instant) can be uniquely recovered, and by linear methods, from at least five views. For the case of conic-shaped trajectory, we show that generally nine views are sufficient for a unique reconstruction of the moving point and fewer views when the conic is of a known type (like a circle in 3D Euclidean space for which seven views are sufficient). 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).

UR - http://www.scopus.com/inward/record.url?scp=0033690445&partnerID=8YFLogxK

U2 - 10.1109/34.845377

DO - 10.1109/34.845377

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AN - SCOPUS:0033690445

SN - 0162-8828

VL - 22

SP - 348

EP - 357

JO - IEEE Transactions on Pattern Analysis and Machine Intelligence

JF - IEEE Transactions on Pattern Analysis and Machine Intelligence

IS - 4

ER -