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Issue No.05 - May (2009 vol.31)
pp: 938-944
Evan Ribnick , University of Minnesota, Minneapolis
Stefan Atev , University of Minnesota, Minneapolis
Nikolaos P. Papanikolopoulos , University of Minnesota, Minneapolis
In this paper, we consider the problem of localizing a projectile in 3D based on its apparent motion in a stationary monocular view. A thorough theoretical analysis is developed, from which we establish the minimum conditions for the existence of a unique solution. The theoretical results obtained have important implications for applications involving projectile motion. A robust, nonlinear optimization-based formulation is proposed, and the use of a local optimization method is justified by detailed examination of the local convexity structure of the cost function. The potential of this approach is validated by experimental results.
3D localization, optimization, projectile motion.
Evan Ribnick, Stefan Atev, Nikolaos P. Papanikolopoulos, "Estimating 3D Positions and Velocities of Projectiles from Monocular Views", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.31, no. 5, pp. 938-944, May 2009, doi:10.1109/TPAMI.2008.247
[1] E. Ribnick, S. Atev, O. Masoud, N.P. Papanikolopoulos, and R. Voyles, “Detection of Thrown Objects in Indoor and Outdoor Scenes,” Proc. IEEE/RSJ Int'l Conf. Intelligent Robots Systems, Oct. 2007.
[2] K. Nishiwaki, A. Konno, K. Nagashima, M. Inaba, and H. Inoue, “The Humanoid Saika that Catches a Thrown Ball,” Proc. IEEE Int'l Workshop Robot Human Comm.n, pp. 94-99, Oct. 1997.
[3] M. Riley and C.G. Atkeson, “Robot Catching: Towards Engaging Human-Humanoid Interaction,” Autonomous Robots, vol. 12, no. 1, pp. 119-128, Jan. 2002.
[4] J. Ren, J. Orwell, G.A. Jones, and M. Xu, “A General Framework for 3D Soccer Ball Estimation and Tracking,” Proc. IEEE Int'l Conf. Image Processing, pp. 1935-1938, Oct. 2004.
[5] T. Kim, Y. Seo, and K.-S. Hong, “Physics-Based 3D Position Analysis of a Soccer Ball from Monocular Image Sequences,” Proc. IEEE Int'l Conf. Computer Vision, pp. 721-726, Jan. 1998.
[6] Y. Liu, D. Liang, Q. Huang, and W. Gao, “Extracting 3D Information from Broadcast Soccer Video,” Image and Vision Computing, vol. 24, no. 10, pp.1146-1162, Oct. 2006.
[7] Y. Ohno, J. Miura, and Y. Shirai, “Tracking Players and Estimation of the 3D Position of a Ball in Soccer Games,” Proc. Int'l Conf. Pattern Recognition, vol. 1, pp. 1145-1148, Sept. 2000.
[8] I.D. Reid and A. North, “3D Trajectories from a Single Viewpoint Using Shadows,” Proc. British Machine Vision Conf., pp. 721-726, Sept. 1998.
[9] J. Assfalg, C.C. Marco Bertini, A.D. Bimbo, and W. Nunziati, “Semantic Annotation of Soccer Videos: Automatic Highlights Identification,” Computer Vision and Image Understanding, vol. 92, nos. 2-3, pp. 285-305, Nov./Dec. 2003.
[10] B.K. Ghosh and E. Loucks, “An Introduction to Perspective Observability and Recursive Identification Problems in Machine Vision,” Proc. 33rd Conf. Decision and Control, vol. 13, pp. 3229-3234, 1994.
[11] S. Avidan and A. Shashua, “Trajectory Triangulation: 3D Reconstruction of Movinb Points from a Monocular Image Sequence,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 4, pp. 348-357, Apr. 2000.
[12] J. Kaminski and M. Teicher, “A General Framework for Trajectory Triangulation,” J. Math. Imaging and Vision, vol. 21, pp. 27-41, 2004.
[13] J. Kaminski, M. Fryers, and M. Teicher, “Recovering an Algebraic Curve Using its Projections from Different Points,” J. European Math. Soc., vol. 7, pp. 145-172, 2005.
[14] R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, second ed. Cambridge Univ. Press, 2003.
[15] F. Kahl and D. Henrion, “Globally Optimal Estimates for Geometric Reconstruction Problems,” Int'l J. Computer Vision, vol. 74, no. 1, pp. 3-15, Aug. 2007.
[16] S. Schaible and J. Shi, “Fractional Programming: The Sum-of-Ratios Case,” Optimization Methods and Software, vol. 18, pp. 219-229, Apr. 2003.
[17] S.P. Boyd and L. Vandenberghe, Convex Optimization. Cambridge Univ. Press, 2004.
[18] K.C. Kiwiel and K. Murty, “Convergence of the Steepest Descent Method for Minimizing Quasiconvex Functions,” J. Optimization Theory and Applications, vol. 89, pp. 221-226, 1996.
[19] J. Nocedal and S.J. Wright, Numerical Optimization. Springer, 1999.
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