Elsevier

Pattern Recognition Letters

Volume 27, Issue 15, November 2006, Pages 1835-1842
Pattern Recognition Letters

On-line trajectory clustering for anomalous events detection

https://doi.org/10.1016/j.patrec.2006.02.004Get rights and content

Abstract

In this paper, we propose a trajectory clustering algorithm suited for video surveillance systems. Trajectories are clustered on-line, as the data are collected, and clusters are organized in a tree-like structure that, augmented with probability information, can be used to perform behaviour analysis, since it allows the identification of anomalous events.

Introduction

Video surveillance systems generally have a very complex structure, since they must span different levels of abstraction, from the low-level detection of moving objects in video streams to the high-level behaviour analysis; it is not surprising that very few complete systems have been proposed so far (Collins et al., 2000, Haritaoglu et al., 2000). In particular, while there are countless works on the low-level image analysis part (such as change detection and object tracking), few have addressed the high-level semantic interpretation of the scene (Ivanov and Bobick, 2000, Minnen et al., 2003). One of the possible reasons could be the lack of a proper link between the two processing levels, in which the raw data are collected and organized in a more abstract representation, useful for activity analysis. Even if some works show that it is possible to infer high-level analysis directly from the low-level data (Ivanov and Bobick, 2000) we still believe that a “middle level” could give some benefits. In this paper, we propose one of the possible approaches in moving towards high-level analysis, based on trajectory clustering.

Trajectory clustering has been addressed in several works, for a survey see Liao (2005). Johnson and Hogg (1996) proposed an algorithm that statistically models the spatial distribution of trajectories using vector quantization. New trajectories are represented as sequences of vectors and are clustered using two competitive learning neural networks, one that finds the sequence of vectors that best represent a trajectory and the second to cluster those sequences. Stauffer and Grimson (2000) use again vector quantization, but the clusters are identified by a hierarchical analysis of the vector co-occurrences in the trajectories. Sclaroff, Kollios et al. proposed two different algorithms for track clustering, one based on a similarity measure called longest common subsequence (LCSS) (Buzan et al., 2004) and one using a probabilistic approach based on Hidden Markov Models (Alon et al., 2003). HMM were used also by Porikli (2004), which find clusters using eigenvector analysis on the HMM parameter space. Lin et al. (2004) propose a hierarchical version of the k-means algorithm well suited for time series based on wavelet analysis. Makris and Ellis (2005) propose a method for modelling paths similar to the one proposed in this article, but their approach requires an initial off-line learning step, and only the classification step is performed on-line.

In this paper, we extend our preliminary work (Piciarelli and Foresti, 2005) on on-line trajectory clustering. On-line clustering is about clustering computed as the incoming data are acquired, in opposition to off-line approaches like many of the works previously cited. Our main aim is to avoid the classical two-step clustering (data collection and off-line processing) since we want to use clustering information for on-line behaviour analysis. We also propose a tree-like structure to represent clusters that can be used for many purposes, for example detection of anomalies in the trajectories of moving objects.

Section snippets

Cluster representation, updating and matching

The proposed method groups trajectories in clusters in order to detect common patterns of activity. The trajectories are acquired by a multi-camera system, described in (Micheloni et al., 2003). The multi-camera approach allows a robust detection of trajectories, being less sensitive to occlusions and ambiguities than single-camera systems.

As previously stated, we require that the clustering algorithm performs on-line, as the data are acquired, without the need of two-step processing, in which

Building trees of clusters

Since our final goal is to analyse behaviours from the trajectory data, we have structured the clustering information in such a way that can be useful for probabilistic reasoning about trajectories. In particular we want to detect and explicitly represent the shared prefixes of clusters, where a prefix is just the starting piece of a cluster. This model of shared prefixes allows to make predictions on the possible future movements of an object (and this is why we are not interested, for

Behaviour analysis

The proposed algorithm was developed as a starting point for a behaviour identification system based on trajectory analysis. While we are currently working on explicit modelling of anomalous behaviours, we have already used the trajectory clustering algorithm to perform statistical anomaly detection. In this approach an anomaly is simply defined as an event which happens rarely. Of course an anomalous event is not necessarily a dangerous one, but we can assume that dangerous events are

Experimental results

In this section, we present two different tests to measure the clustering algorithm performances and an example of the system applied to real-world data. All the experiments were done using the values α = 0.05, δ = 0.5 (see Eqs. (4), (5)). The initial variance is set to σ2 = 1225 and a point is considered to match a cluster if it falls in the 2σ range from the nearest point of the cluster inside the temporal window.

The first test was aimed to measure the quality of the core clustering procedures,

Conclusions

In this work, we have presented an on-line trajectory clustering method. Avoiding the typical two-step approach based on off-line data collection and analysis and on-line classification, the proposed method builds the clusters as the data are acquired by the tracking system. The clusters are organized in a tree-like structure which models the relations between clusters. The probabilistic data associated to the tree branches can be used to make predictions on the possible future developments of

References (18)

  • N. Johnson et al.

    Learning the distribution of object trajectories for event recognition

    Image Vision Comput.

    (1996)
  • Alon, J., Sclaroff, S., Kollios, G., Pavlovic, V., 2003. Discovering cluster in motion time-series data. In: Proc....
  • Biliotti, D., Antonini, G., Thiran, J., 2005. Multi-layer hierarchical clustering of pedestrian trajectories for...
  • Bille, P., 2003. Tree edit distance, alignment distance and inclusion. Tech. Rep. TR-2003-23, The IT University of...
  • Buzan, D., Sclaroff, S., Kollios, G., 2004. Extraction and clustering of motion trajectories in video. In: Proc....
  • Collins, R., Lipton, A., Kanade, T., Fujiyoshi, H., Duggins, D., Tsin, Y., Tolliver, D., Enomoto, N., Hasegawa, O.,...
  • I. Haritaoglu et al.

    w4: Real-time surveillance of people and their activities

    IEEE Trans. Pattern Anal. Machine Intell.

    (2000)
  • Hayashi, A., Nakasima, R., Kanbara, T., Suematsu, N., 2002. Multi-object motion pattern classification for visual...
  • Y. Ivanov et al.

    Recognition of visual activities and interactions by stochastic parsing

    IEEE Trans. Pattern Anal. Machine Intell.

    (2000)
There are more references available in the full text version of this article.

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