Abstract

We present a method for estimating the 3D trajectory of an object undergoing periodic motion in world coordinates by observing its apparent tra- jectory 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 signi ficant insight regard- ing 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 effec- tiveness of the proposed method for reconstructing periodic trajectories in 3D.