Center for Research in Comptuer Vision
Center for Research in Comptuer Vision

Chaotic Invariants of Lagrangian Particle Trajectories for Anomaly Detection in Crowded Scenes


A novel method for crowd flow modeling and anomaly detection is proposed for both coherent and incoherent scenes. The novelty is revealed in three aspects. First, it is a unique utilization of particle trajectories for modeling crowded scenes, in which we propose new and efficient representative trajectories for modeling arbitrarily complicated crowd flows. Second, chaotic dynamics are introduced into the crowd context to characterize complicated crowd motions by regulating a set of chaotic invariant features, which are reliably computed and used for detecting anomalies. Third, a probabilistic framework for anomaly detection and localization is formulated.

The overall work-flow begins with particle advection based on optical flow. Then particle trajectories are clustered to obtain representative trajectories for a crowd flow. Next, the chaotic dynamics of all representative trajectories are extracted and quantified using chaotic invariants known as maximal Lyapunov exponent and correlation dimension. Probabilistic model is learned from these chaotic feature set, and finally, a maximum likelihood estimation criterion is adopted to identify a query video of a scene as normal or abnormal. Furthermore, an effective anomaly localization algorithm is designed to locate the position and size of an anomaly. Experiments are conducted on known crowd data set, and results show that our method achieves higher accuracy in anomaly detection and can effectively localize anomalies.

Significance of Crowd Scene Analysis

Figure 1. Crowd scenarios with different levels of cherency.


The Idea

Figure 2. Framework for anomaly detection and localization.

The Novelties

Particle Advection

Figure 3. Particle trajectories overlayed on three crowd scenes. Top row shows zoom-in view of parts of each scene.

Cluster Particle Trajectories

Figure 4. Trajectories after low variance particles are removed. Top row shows zoom-in view of parts of each scene.

Figure 5. Trajectories clustered according to position information, (left) and representative trajectories for two clusters (right).

Figure 6. Representative trajectories for three scenes. Top row shows zoom-in view of parts of each scene.

Chaotic Invariants

Feature Set

F = { L, D, M }

Figure. The algorithm for computing L and D.

Advantages of the Algorithm

Figure 7. Largest Lyapunov exponents for representative trajectories using our method (left) and the method of [7] (right).

Anomaly Detection

Modeling Learning

Anomaly Localization

Experiment Results

Figure 8. Sample frames from three crowd scenes. The first two frames in each row show normal behavior, and the third frame shows abnormal escape panic

Figure 9. Representative trajectories for three clips in a sequence, the first one shows normal behavior and the last two are abnormal.

Figure 10. Marginal PDF of two chaotic features of x (left) and y (right) of learned 4-D mixture of Gaussian model.

Figure 11. Likelihood profile for testing clips and corresponding ground truth.

Figure 12. ROC curves for (a) our method, and (b) method of [9].

Due to change of chaotic dynamics (Exp. 2)

Figure 13. (a) Normal clapping behavior, and (b) introduction of abnormal dancing behavior.

Figure 14. For clip 30 correctly detected anomalies, red points below threshold correspond to abnormal representative trajectories, while blue points above threshold correspond to normal.

Figure 15. A frame from a clip with abnormal behavior, (a) representative trajectories, (b) candidates for local anomalies, (c) correct localization of anomalies.

Position-caused in consistent motions (Exp. 3)

Figure 16. Position-caused anomaly localization


Related Publication

Shandong Wu, Brian Moore, and Mubarak Shah, Chaotic Invariants of Lagrangian Particle Trajectories for Anomaly Detection in Crowded Scenes, IEEE Conference on Computer Vision and Pattern Recognition 2010, San Francisco, CA.

Back to Crowd Analysis Projects