Abstract
Analyzing the crowd dynamics from video sequences is an open challenge in computer vision. Under a high crowd density assumption, we characterize the dynamics of the crowd flow by two related information: velocity and a disturbance potential which accounts for several elements likely to disturb the flow (the density of pedestrians, their interactions with the flow and the environment). The aim of this paper to simultaneously estimate from a sequence of crowded images those two quantities. While the velocity of the flow can be observed directly from the images with traditional techniques, this disturbance potential is far more trickier to estimate. We propose here to couple, through optimal control theory, a dynamical crowd evolution model with observations from the image sequence in order to estimate at the same time those two quantities from a video sequence. For this purpose, we derive a new and original continuum formulation of the crowd dynamics which appears to be well adapted to dense crowd video sequences. We demonstrate the efficiency of our approach on both synthetic and real crowd videos.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Helbing, D., Johansson, A., Al-Abideen, H.: Dynamics of crowd disasters: An empirical study. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 75(4), 046109 (2007)
Courty, N., Corpetti, T.: Crowd motion capture. CAVW, proc. of CASA 2007 18(4-5), 361–370 (2007)
Lions, J.L.: Optimal Control of Systems Governed by Partial Differential Equations. Springer, Heidelberg (1971)
Le-Dimet, F., Talagrand, O.: Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus, 97–110 (1986)
Yang, T., Li, S., Pan, Q., JingLi: Real-time multiple object tracking with occlusion handling in dynamic scenes. In: CVPR, San Diego, USA, June 2005, pp. 406–413 (2005)
Zhao, T., Nevatia, R.: Tracking multiple humans in crowded environment. In: CVPR, Washington, DC, USA, pp. 406–413 (2004)
Rabaud, V., Belongie, S.: Counting crowded moving objects. In: CVPR, New York, June 2006), pp. 705–711 (2006)
Brostow, G.J., Cipolla, R.: Unsupervised bayesian detection of independent motion in crowds. In: CVPR, NYC, June 2006, pp. 594–601 (2006)
Okuma, K., Taleghani, A., de Freitas, N., Little, J., Lowe, D.: A boosted particle filter: Multitarget detection and tracking. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3021, pp. 28–39. Springer, Heidelberg (2004)
Khan, Z., Balch, T., Dellaert, F.: MCMC data association and sparse factorization updating for real time multitarget tracking with merged and multiple measurements. IEEE PAMI 28(12), 1960–1972 (2006)
Ali, S., Shah, M.: A lagrangian particle dynamics approach for crowd flow segmentation and stability analysis. In: CVPR, Minneapolis, Minnesota, June 2007, pp. 1–6 (2007)
Andrade, E., Blunsden, S., Fisher, R.: Modelling crowd scenes for event detection. In: ICPR, Hong Kong, China, August 2006, pp. 175–178 (2006)
Hughes, R.L.: The flow of human crowds. Annual revue of Fluid. Mech. 20(10), 169–182 (2003)
Ali, S., Shah, M.: Floor fields for tracking in high density crowd scenes. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part II. LNCS, vol. 5303, pp. 1–14. Springer, Heidelberg (2008)
Papadakis, N., Corpetti, T., Mémin, E.: Dynamically consistent optical flow estimation. In: Proc. Int. Conf. Comp. Vis. (ICCV 2007), Rio de Janeiro, Brazil (October 2007)
Papadakis, N., Mémin, E.: A variational technique for time consistent tracking of curves and motion. Journal of Mathematical Imaging and Vision (2008) (available online first)
Polymenakos, L., Bertsekas, D., Tsitsiklis, J.: Implementation of efficient algorithms for globally optimal trajectories. IEEE Trans. on Automatic Control 43, 278–282 (1998)
Kimmel, R., Sethian, J.: Optimal algorithm for shape from shading and path planning. J. of Math. Ima. and Vis. 14(3), 237–244 (2001)
Talagrand, O.: Variational assimilation. Adjoint equations. Kluwer Academic Publishers, Dordrecht (2002)
Lucas, B., Kanade, T.: An iterative image registration technique with an application to stereo vision. In: IJCAI, Vancouver, Canada, pp. 674–679 (1981)
Helbing, D., Farkas, I., Vicsek, T.: Simulating dynamical features of escape panic. Nature 407(1), 487–490 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Allain, P., Courty, N., Corpetti, T. (2010). Crowd Flow Characterization with Optimal Control Theory. In: Zha, H., Taniguchi, Ri., Maybank, S. (eds) Computer Vision – ACCV 2009. ACCV 2009. Lecture Notes in Computer Science, vol 5995. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12304-7_27
Download citation
DOI: https://doi.org/10.1007/978-3-642-12304-7_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12303-0
Online ISBN: 978-3-642-12304-7
eBook Packages: Computer ScienceComputer Science (R0)