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People trajectory analysis and anomaly detection

People trajectory analysis is a recurrent task in many pattern recognition applications, such as surveillance, behavior analysis, video annotation, and many others. We develop a new framework for analyzing trajectory shape, invariant to spatial shifts of the people motion in the scene.

Von mises model for trajectory analysis

In order to cope with the noise and the uncertainty of the trajectory samples, we propose to describe the trajectories as a sequence of angles modeled by distributions of circular statistics, i.e., a mixture of von Mises (MovM) distributions. To deal with MovM, we define a new specific expectation-maximization (EM) algorithm for estimating the parameters and derive a closed form of the Bhattacharyya distance between single von Mises pdfs. Trajectories are then modeled with a sequence of symbols, corresponding to the most suitable distribution in the mixture, and compared each other after a global alignment procedure to cope with trajectories of different lengths.

The trajectories in the training set are clustered according to their shape similarity in an off-line phase, and testing trajectories are then classified with a specific on-line EM, based on sufficient statistics. The approach is particularly suitable for classifying people trajectories in video surveillance, searching for abnormal (i.e., infrequent) paths.


1 Calderara, Simone; Cucchiara, Rita "Understanding dyadic interactions applying proxemic theory on videosurveillance trajectories" 2012 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, Providence, RI, usa, pp. 20 -27 , 16-21 June 2012, 2012 | DOI: 10.1109/CVPRW.2012.6239351 Conference
2 Calderara, Simone; Prati, Andrea; Cucchiara, Rita "Integrate tool for online analysis and offline mining of people trajectories" IET COMPUTER VISION, vol. 6, pp. 334 -347 , 2012 | DOI: 10.1049/iet-cvi.2010.0143 Journal
3 Calderara, Simone; Prati, Andrea; Cucchiara, Rita "Mixtures of von Mises Distributions for People Trajectory Shape Analysis" IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, vol. 21, pp. 457 -471 , 2011 | DOI: 10.1109/TCSVT.2011.2125550 Journal
4 Calderara, Simone; Uri, Heinemann; Prati, Andrea; Cucchiara, Rita; Naftali, Tishby "Detecting Anomalies in People’s Trajectories using Spectral Graph Analysis" COMPUTER VISION AND IMAGE UNDERSTANDING, vol. 115, pp. 1099 -1111 , 2011 | DOI: 10.1016/j.cviu.2011.03.003 Journal
5 Calderara, Simone; Prati, Andrea; Cucchiara, Rita "Alignment-based Similarity of People Trajectories using Semi-directional Statistics" 2010 20th international conference on Pattern Recognition: ICPR 2010, Istanbul ,Turkey, pp. 4275 -4278 , 23-26 August 2010, 2010 | DOI: 10.1109/ICPR.2010.1039 Conference
6 Calderara, Simone; Cucchiara, Rita "People trajectory mining with statistical pattern recognition" Computer Vision and Pattern Recognition Workshops (CVPRW), 2010 IEEE Computer Society Conference on, San Francisco, USA, pp. 1 -8 , June 13 2010, 2010 | DOI: 10.1109/CVPRW.2010.5543158 Conference
7 Calderara, Simone; C., Alaimo; Prati, Andrea; Cucchiara, Rita "A Real-Time System for Abnormal Path Detection" Proceedings of 3rd International Conference on Imaging for Crime Detection and Prevention (ICDP-09), vol. 2009, London, gbr, pp. 1 -6 , 3 December 2009, 2009 | DOI: 10.1049/ic.2009.0251 Conference
8 Calderara, Simone; Prati, Andrea; Cucchiara, Rita "Video surveillance and multimedia forensics: an application to trajectory analysis" Proceedings of the First ACM Workshop on Multimedia in Forensics, Beijing, China, pp. 13 -18 , 19-24 October 2009, 2009 | DOI: 10.1145/1631081.1631085 Conference
9 Calderara, Simone; Cucchiara, Rita; Prati, Andrea; Vezzani, Roberto "Statistical Pattern Recognition for Multi-Camera Detection, Tracking and Trajectory Analysis" Multi-Camera Networks: Concepts and Applications, Electrical Engineering, pp. 389 -413 , 2009 | DOI: 10.1016/B978-0-12-374633-7.00018-5 Chapter in Book

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