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.
KeywordsPeriodic Motion Image Sample Periodic Trajectory Local Optimization Method Ground Truth Trajectory
- 1.Belongie, S., Wills, J.: Structure from Periodic Motion. In: Proc. Int’l. Worksh. Spatial Coherence for Visual Motion Anal., pp. 16–24 (May 2004)Google Scholar
- 3.Cohen, C.J., et al.: Dynamical System Representation, Generation, and Recognition of Basic Oscillatory Motion Gestures. In: Proc. Int’l. Conf. Automatic Face and Gesture Recognition, pp. 60–65 (October 1996)Google Scholar
- 5.Dixon, M., et al.: Finding Minimal Parameterizations of Cylindrical Image Manifolds. In: Proc. Comp. Vis. and Pattern Recog. Worksh., p. 192 (June 2006)Google Scholar
- 8.Laptev, I., et al.: Periodic Motion Detection and Segmentation via Approximate Sequence Alignment. In: Proc. IEEE Int’l. Conf. Comp. Vis., vol. 1, pp. 816–823 (October 2005)Google Scholar
- 9.Liu, F., Picard, R.: Finding Periodicity in Space and Time. In: Proc. IEEE Int’l. Conf. Comp. Vis., pp. 376–383 (January 1998)Google Scholar