Human Activity Modeling as Brownian Motion on Shape Manifold

  • Sheng Yi
  • Hamid Krim
  • Larry K. Norris
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6667)


In this paper we propose a stochastic modeling of human activity on a shape manifold. From a video sequence, human activity is extracted as a sequence of shape. Such a sequence is considered as one realization of a random process on shape manifold. Then Different activities are modeled by manifold valued random processes with different distributions. To solve the problem of stochastic modeling on a manifold, we first regress a manifold values process to a Euclidean process. The resulted process then could be modeled by linear models such as a stationary incremental process and a piecewise stationary incremental process. The mapping from manifold to Euclidean space is known as a stochastic development. The idea is to parallelly transport the tangent along curve on manifold to a single tangent space. The advantage of such technique is the one to one correspondence between the process in Euclidean space and the one on manifold. The proposed algorithm is tested on database [5] and compared with the related work in [5]. The result demonstrate the high accuracy of our modeling in characterizing different activities.


Brownian Motion Random Process Video Sequence Tangent Space Curve Development 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Klassen, E., Srivastava, A., Mio, W., Joshi, S.H.: Analysis of planar shapes using geodesic paths on shape spaces. IEEE Trans. Pattern Analysis and Machine Intelligence (2004)Google Scholar
  2. 2.
    Hsu, E.P.: Stochastic analysis on manifold. Graduate Studies in Mathematics, 38Google Scholar
  3. 3.
    Bishop, R.L., Crittenden, R.J.: Geometry of Manifold. Academic Press, New York (1964)zbMATHGoogle Scholar
  4. 4.
    Kobayashi, S., Nomizu, k.: Foundations of differential geometry, vol. 1. John Wiley & Sons, West Sussex (1996)zbMATHGoogle Scholar
  5. 5.
    Blank, M., Gorelick, L., Shechtman, E., Basri, M.I.R.: Action as Space-Time Shapes. In: IEEE ICCV (2005)Google Scholar
  6. 6.
    Priestley, M.B., Subba Rao, T.: A Test for Non stationarity of Time-Series. Journal of the Royal Statistical Society. Series B 31(1), 140–149 (1969)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Keogh, E., Chu, S., Hart, D., Pazzani, M.: Segmenting time series: A survey and novel approach, Data Mining in Time Series Databases. World Scientific, Singapore (2004)Google Scholar
  8. 8.
    Aggarwal, J.K., Cai, Q.: Human Motion Analysis: A Reivew. Computer Vision and Image Understanding 73, 428–440 (1999)CrossRefGoogle Scholar
  9. 9.
    Turaga, P., Chellappa, R., Subrahmanian, V., Udrea, O.: Machine recognition of human activities: A survey. IEEE Transactions on Circuits and Systems for Video Technology 18, 1473–1488 (2008)CrossRefGoogle Scholar
  10. 10.
    Elgammal, A.M., Lee, C.-S.: Inferring 3D body pose from silhouettes using activity manifold learning. In: Proceedings of the Conference on Computer Vision and Pattern Recognition (CVPR 2004), Washington, DC, vol. 2, pp. 681–688 (June 2004)Google Scholar
  11. 11.
    Veeraraghavan, A., Roy-Chowdhury, A.K., Chellappa, R.: Matching Shape Sequences in Video with Applications in Human Movement Analysis. IEEE Trans. Pattern Analysis and Machine Intelligence 27(12) (December 2005)Google Scholar
  12. 12.
    Veeraraghavan, A., Chowdhury, A.R., Chellappa, R.: Role of shape and kinematics in human movement analysis. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2004)Google Scholar
  13. 13.
    Kendall, D.: Shape Manifolds, Procrustean Metrics and Complex Projective Spaces. Bull. London Math. Soc. 16, 81–121 (1984)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Chen, P., Steen, R., Yezzi, A., Krim, H.: Joint brain parametric T1-Map segmentation and RF inhomogeneity calibration. International Journal of Biomedical Imaging (269525), 14 p. (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sheng Yi
    • 1
  • Hamid Krim
    • 1
  • Larry K. Norris
    • 1
  1. 1.North Carolina Sate UniversityUSA

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