Estimating 3D Trajectories of Periodic Motions from Stationary Monocular Views

  • Evan Ribnick
  • Nikolaos Papanikolopoulos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5304)


We present a method for estimating the 3D trajectory of an object undergoing periodic motion in world coordinates by observing its apparent trajectory in a video taken from a single stationary camera. Periodicity in 3D is used here as a physical constraint, from which accurate solutions can be obtained. A detailed analysis is performed, from which we gain significant insight regarding the nature of the problem and the information that is required to arrive at a unique solution. Subsequently, a robust, numerical approach is proposed, and it is demonstrated that the cost function exhibits strong local convexity which is amenable to local optimization methods. Experimental results indicate the effectiveness of the proposed method for reconstructing periodic trajectories in 3D.


Periodic Motion Image Sample Periodic Trajectory Local Optimization Method Ground Truth Trajectory 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Evan Ribnick
    • 1
  • Nikolaos Papanikolopoulos
    • 1
  1. 1.University of MinnesotaUSA

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