![](bg6.png)
can also refer to tracking errors because of their very
short lengths. The system in such a situations has not
sufficient information and then is not able to reliably
associate the two trajectories to any cluster containing
normal trajectories.
In conclusion the performance, yet acceptable for
many practical application, can be considered even
better at the light of the above considerations. How-
ever, we could think, as future work, the introduc-
tion of a mixed solution based both on clustering and
boundary-constraints so as to catch the advantages of
both these approaches, even at the cost of introduc-
ing a little more heavy a priory knowledge about the
scene to be processed.
5 CONCLUSIONS
We have proposed a system able to identify abnor-
mal trajectories without the explicit definition of the
rules by a human operator. It has been achieved by
introducing an unsupervised method able to deduce
properties of a scene from a set of trajectories. Start-
ing from a set of normal trajectories acquired by a
video analytics system, our method represents each
trajectory by a sequence of symbols associated to rel-
evant features of trajectories (crossed zones, shape
and speed in each zone). This quantization is obtained
by partitioning the scene into a fixed number of adap-
tive zones. Similarity between trajectories is evalu-
ated by means of a fast alignment global kernel. Tra-
jectories are then grouped into homogenous clusters
encoding normal trajectories. The classification into
(ab)normal trajectories is performed by taking advan-
taging on the statistical properties of the clusters. Ex-
periments have been performed on a real dataset and
the obtained results, compared with other state of the
art methods, confirm the efficiency of the proposed
approach.
ACKNOWLEDGEMENTS
This research has been partially supported by
A.I.Tech s.r.l. (a spin-off company of the University
of Salerno, www.aitech-solutions.eu).
REFERENCES
Acampora, G., Foggia, P., Saggese, A., and Vento, M.
(2012). Combining neural networks and fuzzy sys-
tems for human behavior understanding. In Proceed-
ings of the IEEE AVSS Conference, pages 88–93.
Aggarwal, J. and Ryoo, M. (2011). Human activity analy-
sis: A review. ACM Comput. Surv., 43(3):16:1–16:43.
Brun, L., Saggese, A., and Vento, M. (2012). A clustering
algorithm of trajectories for behaviour understanding
based on string kernels. In Proceedings of the 2012
SITIS Conference, pages 267–274. IEEE.
Brun, L. and Tr
´
emeau, A. (2002). Digital Color Imaging
Handbook, chapter 9 : Color quantization, pages 589–
637. Electrical and Applied Signal Processing. CRC
Press.
Chandola, V., Banerjee, A., and Kumar, V. (2009).
Anomaly detection: A survey. ACM Comput. Surv.,
41(3):15:1–15:58.
Cortes, C. and Vapnik, V. (1995). Support-vector networks.
Machine Learning, 20:273–297.
Cuturi, M. (2011). Fast global alignment kernels. In
Getoor, L. and Scheffer, T., editors, Proceedings of
the 28th International Conference on Machine Learn-
ing (ICML-11), ICML ’11, pages 929–936, New York,
NY, USA. ACM.
d’Acierno, A., Leone, M., Saggese, A., and Vento, M.
(2012a). An efficient strategy for spatio-temporal data
indexing and retrieval. In Proceedings of the KDIR
Conference, pages 227,232.
d’Acierno, A., Leone, M., Saggese, A., and Vento, M.
(2012b). A system for storing and retrieving huge
amount of trajectory data, allowing spatio-temporal
dynamic queries. In Proceedings of the IEEE ITS Con-
ference, pages 989,994.
Di Lascio, R., Foggia, P., Saggese, A., and Vento, M.
(2012). Tracking interacting objects in complex sit-
uations by using contextual reasoning. In Csurka,
G. and Braz, J., editors, VISAPP (2), pages 104–113.
SciTePress.
Foggia, P., Percannella, G., Sansone, C., and Vento, M.
(2008). A graph-based algorithm for cluster detection.
IJPRAI, 22(5):843–860.
Morris, B. and Trivedi, M. (2011). Trajectory learning
for activity understanding: Unsupervised, multilevel,
and long-term adaptive approach. Pattern Analy-
sis and Machine Intelligence, IEEE Transactions on,
33(11):2287 –2301.
Neuhaus, M. and Bunke, H. (2006). Edit distance-based
kernel functions for structural pattern classification.
Pattern Recognition, 39(10):1852 – 1863.
Saigo, H., Vert, J.-P., Ueda, N., and Akutsu, T. (2004). Pro-
tein homology detection using string alignment ker-
nels. Bioinformatics, 20(11):1682–1689.
Schaeffer, S. (2007). Graph clustering. Computer Science
Review, 1(1):27–64.
Sch
¨
olkopf, B., Smola, A., and M
¨
uller, K.-R. (1998). Non-
linear component analysis as a kernel eigenvalue prob-
lem. Neural Comput., 10(5):1299–1319.
Wang, X., Ma, K. T., Ng, G.-W., and Grimson, W. E.
(2011). Trajectory analysis and semantic region mod-
eling using nonparametric hierarchical bayesian mod-
els. Int. J. Comput. Vision, 95:287–312.
Zhou, Y., Yan, S., and Huang, T. (2007). Detecting anomaly
in videos from trajectory similarity analysis. In Multi-
media and Expo, 2007 IEEE International Conference
on, pages 1087 –1090.
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