The Visual Computer

, Volume 35, Issue 3, pp 415–427 | Cite as

A novel point-line duality feature for trajectory classification

  • Rajkumar SainiEmail author
  • Partha Pratim Roy
  • Debi Prosad Dogra
Original Article


Trajectory classification is important for understanding object movements within the surveillance area. Raw trajectories are represented by object location in form of (xy) coordinates. The length of trajectories varies in terms of number of points; thus, it is difficult to classify them into correct classes. The raw features extracted from trajectory do not yield satisfactory results in classification. Thus, robust features are needed that can efficiently represent trajectory sequences and help to improve the classification performance. In this paper, we present a new feature vector that is based on the concept of point-line duality (PLD) transformation, i.e., transformation of a trajectory point from its primal plane into a straight line in dual plane. Classification has been done using hidden Markov model (HMM) framework. We also propose a fusion approach combining classification results obtained from raw feature and PLD feature to improve the performance. Experiments have been carried out on raw trajectories with reduced lengths as well as adding Gaussian noise. Proposed approach has been tested on three publicly available datasets, namely T15, MIT, and CROSS. It has been found that the PLD feature outperforms existing features as well as raw feature when used in HHM-based classification. We have obtained encouraging results by feature combination at the decision level with 97, 96.75 and 99.80% accuracy, respectively, on T15, MIT, and CROSS datasets.


Trajectory classification Hidden Markov model (HMM) Point-line duality (PLD) Fusion 


  1. 1.
    Appiah, K., Hunter, A., Lotfi, A., Waltham, C., Dickinson, P.: Human behavioural analysis with self-organizing map for ambient assisted living. In: IEEE International Conference on Fuzzy Systems, pp. 2430–2437 (2014)Google Scholar
  2. 2.
    Brun, L., Saggese, A., Vento, M.: Dynamic scene understanding for behavior analysis based on string kernels. IEEE Trans. CSVT 24(10), 1669–1681 (2014)Google Scholar
  3. 3.
    Cai, Y., Wang, H., Chen, X., Jiang, H.: Trajectory-based anomalous behaviour detection for intelligent traffic surveillance. IET Intell. Transp. Syst. 9(8), 810–816 (2015)CrossRefGoogle Scholar
  4. 4.
    Dahmane, M. ,Meunier, J.:. Real-time video surveillance with self-organizing maps. In: Canadian Conference on Computer and Robot Vision, vol. 2, pp. 136–143 (2005)Google Scholar
  5. 5.
    David, D., Thomas, P.: Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Cartographica IJGIG 10, 112–122 (1973)Google Scholar
  6. 6.
    Dinh, T., Vo, N., Medioni, G.: Context tracker: exploring supporters and distracters in unconstrained environments. In: CVPR, pp. 1177–1184 (2011)Google Scholar
  7. 7.
    Dogra, D., Reddy, R., Subramanyam, K., Ahmed, A., Bhaskar, H.: Scene representation and anomalous activity detection using weighted region association graph. In: Proceedings of the of ICCVTA, pp. 104–112 (2015)Google Scholar
  8. 8.
    Domínguez, R., Onieva, E., Alonso, J., Villagra, J., González, C: Lidar based perception solution for autonomous vehicles. In: 2011 11th International Conference on Intelligent Systems Design and Applications (ISDA), pp. 790–795 (2011)Google Scholar
  9. 9.
    Fuse, T., Kamiya, K.: Statistical anomaly detection in human dynamics monitoring using a hierarchical dirichlet process hidden Markov model. IEEE Trans. Intell. Transp. Syst. PP(99), 1–10 (2017)Google Scholar
  10. 10.
    Hu, W., Li, X., Tian, G., Maybank, S., Zhang, Z.: An incremental DPMM-based method for trajectory clustering, modeling, and retrieval. IEEE Trans. Pattern Anal. Mach. Intell. 35(5), 1051–1065.
  11. 11.
    Jan, T.: Neural network based threat assessment for automated visual surveillance. In: IEEE International Joint Conference on Neural Networks, vol. 2, pp. 1309–1312(2004)Google Scholar
  12. 12.
    Kihwan, K., Dongryeol, L., Irfan, E.: Gaussian process regression flow for analysis of motion trajectories. In: International Conference on Computer Vision, pp. 1164–1171 (2011)Google Scholar
  13. 13.
    Kim, E., Helal, S., Cook, D.: Human activity recognition and pattern discovery. Pervasive Comput. 9(1), 48–53 (2010)CrossRefGoogle Scholar
  14. 14.
    Kumar, P., Gauba, H., Roy, P.P., Dogra, D.P.: A multimodal framework for sensor based sign language recognition. Neurocomputing 259, 21–38 (2017)CrossRefGoogle Scholar
  15. 15.
    Kwon, Yongjin, Kang, Kyuchang, Jin, Junho, Moon, Jinyoung, Park, Jongyoul: Hierarchically linked infinite hidden Markov model based trajectory analysis and semantic region retrieval in a trajectory dataset. Expert Syst. Appl. 78, 386–395 (2017)CrossRefGoogle Scholar
  16. 16.
    Lee, Anthony J.T., Chen, Yi-An, Ip, Weng-Chong: Mining frequent trajectory patterns in spatial-temporal databases. Inf. Sci. 179(13), 2218–2231 (2009)CrossRefzbMATHGoogle Scholar
  17. 17.
    Lee, J.G., Han, J., Li, X., Gonzalez, H.: Traclass: trajectory classification using hierarchical region-based and trajectory-based clustering. Proc VLDE 1(1), 1081–1094 (2008)Google Scholar
  18. 18.
    Mehta, P., Shah, H., Kori, V., Vikani, V., Shukla, S., Shenoy, M.: Survey of unsupervised machine learning algorithms on precision agricultural data. In ICIIECS, pp. 1–8 (2015)Google Scholar
  19. 19.
    Melo, J., Naftel, A., Bernardino, A., Santos-Victor, J.: Detection and classification of highway lanes using vehicle motion trajectories. IEEE Trans. ITS 7(2), 188–200 (2006)Google Scholar
  20. 20.
    Mozerov, M., Amato, A., Roca, F., Gonzlez, J.: Trajectory occlusion handling with multiple view distance minimization clustering. J Opt Eng 47, 2021–2029 (2008)CrossRefGoogle Scholar
  21. 21.
    Nascimento, J., Figueiredo, M.A.T., Marques, J.S.: Trajectory classification using switched dynamical hidden markov models. IEEE Trans. Image Process. 19(5), 1338–1348 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    O’Rourke, J.: Computational geometry in C, 2nd edn. Cambridge University Press, New York (1998)CrossRefzbMATHGoogle Scholar
  23. 23.
    Pan, X., Wang, H., He, Y., Xiong, W., Jian, T.: Online classification of frequent behaviours based on multidimensional trajectories. In: Sonar and Navigation, IET Radar (2017)Google Scholar
  24. 24.
    Pei, W., Dibeklioglu, H., Tax, D.M.J., van der Maaten, L.: Multivariate time-series classification using the hidden-unit logistic model. IEEE Trans. Neural Netw. Learn. Syst. PP(99), 1–12 (2017)Google Scholar
  25. 25.
    Pereira, E., Ciobanu, L., Cardoso, J.S.: Social signaling descriptor for group behavior analysis. In: Proceedings of Iberian Conference on Pattern Recognition and Image Analysis (IbPRIA), vol. 9117, pp. 13–22 (2015)Google Scholar
  26. 26.
    Piciarelli, C., Micheloni, C., Foresti, G.: Trajectory-based anomalous event detection. IEEE Trans. CSVT 18(11), 1544–1554 (2008)Google Scholar
  27. 27.
    Rabiner, L.R.: A tutorial on hidden markov models and selected applications in speech recognition. Proc. IEEE 77(2), 257–286 (1989)CrossRefGoogle Scholar
  28. 28.
    Saini, R., Kumar, P., Dutta, S., Roy, P.P. Pal, U.: Local behavior analysis for trajectory classification using graph embedding. In: Asian Conference on Pattern Recognition (2017). (Accepted)Google Scholar
  29. 29.
    Saini, R., Roy, P.P., Dogra, D.P.: A segmental HMM based trajectory classification using genetic algorithm. Expert Syst. Appl. 93, 169–181 (2018)CrossRefGoogle Scholar
  30. 30.
    Siang, K.L.Y., Khor, S.W.: Path clustering using dynamic time warping technique. ICCTIM 1, 449–452 (2012)Google Scholar
  31. 31.
    Sim, G., Chung, J., Sung, Y.: 3D UAV flying path optimization method based on the Douglas-Peucker algorithm. In: Park, J., Chen, S.C., Raymond Choo, K.K. (eds.) Advanced Multimedia and Ubiquitous Engineering. MUE 2017, FutureTech 2017. Lecture Notes in Electrical Engineering, vol. 448. Springer, Singapore (2017)Google Scholar
  32. 32.
    Suzuki, N., Hirasawa, K., Tanaka, K.,  Kobayashi, Y., Sato, Y.,  Fujino, Y.: Learning motion patterns and anomaly detection by human trajectory analysis. In: ICSMC, pp. 498–503 (2007)Google Scholar
  33. 33.
    Tang, K., Zhu, S., Xu, Y., Wang, F.: Modeling drivers’ dynamic decision-making behavior during the phase transition period: an analytical approach based on hidden markov model theory. IEEE Trans. Intell.Transp. Syst. 17(1), 206–214 (2016)CrossRefGoogle Scholar
  34. 34.
    Tran, M.B., Trivedi, M.M.: Trajectory learning for activity understanding: unsupervised, multilevel, and long-term adaptive approach. IEEE Trans. PAMI 33(11), 2287–2301 (2011)CrossRefGoogle Scholar
  35. 35.
    Xiaogang, W., Keng, T.,  Gee-Wah, N., Grimson, W.. Trajectory analysis and semantic region modeling using a nonparametric Bayesian model. In CVPR, pp. 1–8 (2008)Google Scholar
  36. 36.
    Xu, D., Wu, X., Song, D.,  Li, N., Chen, Y.L.: Hierarchical activity discovery within spatio-temporal context for video anomaly detection. In: ICIP, pp.  3597–3601 (2013)Google Scholar
  37. 37.
    Xu, H., Zhou, Y., Lin, W., Zha, H.: Unsupervised trajectory clustering via adaptive multi-kernel-based shrinkage. In: ICCV, pp. 4328–4336 (2015)Google Scholar
  38. 38.
    Zhong, J. Wentong, C.,  Luo, L., Yin, H.: Learning behavior patterns from video: A data-driven framework for agent-based crowd modeling. In Proceedings of the of ICAAMS, pp.  801–809 (2015)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringIIT RoorkeeRoorkeeIndia
  2. 2.School of Electrical SciencesIIT BhubaneswarBhubaneswarIndia

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