Estimating 3D Trajectories of Periodic Motions from Stationary Monocular Views

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.

• Type: Conference
• Year: 2008
• Where: ECCV
• Authors: Evan Ribnick, Nikolaos Papanikolopoulos
• Keywords: Apparent Trajectory, Computer Vision, ECCV 2008, Local Optimization Methods, Periodic Trajectories, Single Stationary Camera, Strong Local Convexity