Crowd Flow Characterization with Optimal Control Theory

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.

[1]  Serge J. Belongie,et al.  Counting Crowded Moving Objects , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[2]  Robert B. Fisher,et al.  Modelling Crowd Scenes for Event Detection , 2006, 18th International Conference on Pattern Recognition (ICPR'06).

[3]  Frank Dellaert,et al.  MCMC Data Association and Sparse Factorization Updating for Real Time Multitarget Tracking with Merged and Multiple Measurements , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Mubarak Shah,et al.  Floor Fields for Tracking in High Density Crowd Scenes , 2008, ECCV.

[5]  James J. Little,et al.  A Boosted Particle Filter: Multitarget Detection and Tracking , 2004, ECCV.

[6]  Quan Pan,et al.  Real-time multiple objects tracking with occlusion handling in dynamic scenes , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[7]  Nicolas Courty,et al.  Crowd motion capture , 2007, Comput. Animat. Virtual Worlds.

[8]  J. Lions.  Optimal Control of Systems Governed by Partial Differential Equations , 1971 .

[9]  Dirk Helbing,et al.  Dynamics of crowd disasters: an empirical study. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Mubarak Shah,et al.  A Lagrangian Particle Dynamics Approach for Crowd Flow Segmentation and Stability Analysis , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[11]  F. L. Dimet,et al.  Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects , 1986 .

[12]  Nicolas Papadakis,et al.  A Variational Technique for Time Consistent Tracking of Curves and Motion , 2008, Journal of Mathematical Imaging and Vision.

[13]  Jiří Matas,et al.  Computer Vision - ECCV 2004 , 2004, Lecture Notes in Computer Science.

[14]  Ramakant Nevatia,et al.  Tracking multiple humans in crowded environment , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[15]  Andrew J. Davison,et al.  Active Matching , 2008, ECCV.

[16]  Ron Kimmel,et al.  Optimal Algorithm for Shape from Shading and Path Planning , 2001, Journal of Mathematical Imaging and Vision.

[17]  R. Hughes.  The flow of human crowds , 2003 .

[18]  Dirk Helbing,et al.  Simulating dynamical features of escape panic , 2000, Nature.

[19]  John N. Tsitsiklis,et al.  Implementation of efficient algorithms for globally optimal trajectories , 1998, IEEE Trans. Autom. Control..

[20]  Nicolas Papadakis,et al.  Dynamically consistent optical flow estimation , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[21]  O. Talagrand,et al.  Variational Assimilation. Adjoint Equations , 2003 .

[22]  Roberto Cipolla,et al.  Unsupervised Bayesian Detection of Independent Motion in Crowds , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[23]  Takeo Kanade,et al.  An Iterative Image Registration Technique with an Application to Stereo Vision , 1981, IJCAI.