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Manifold Methods for Action Recognition

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Intelligent Information and Database Systems (ACIIDS 2017)

Abstract

Among a broad spectrum of published methods of recognition of human actions in video sequences, one approach stands out, different from the rest by not relying on detection of interest points or events, extraction of features, region segmentation or finding trajectories, which are all prone to errors. It is based on representation of a time segment of a video sequence as a point on a manifold, and uses a geodesic distance defined on manifold for comparing and classifying video segments. A manifold based representation of a video sequence is obtained starting with a 3d array of consecutive image frames or a 3rd order tensor, which is decomposed into three \(3 \times k\) arrays that are mapped to a point of a manifold. This article presents a review of manifold based methods for human activity recognition and sparse coding of images that also rely on a manifold representation. Results of a human activity classification experiment that uses an implemented action recognition method based on a manifold representation illustrate the presentation.

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References

  1. Cheng, G., Wan, Y., Saudagar, A.N., Namuduri, K., Buckles, B.P.: Advances in Human Action Recognition: A Survey. arXiv preprint arXiv:1501.05964v1 (2015)

  2. Li, M., Cai, Z., Wei, C., Yuan, Y.: A survey of video object tracking. Int. J. Control Autom. 8(9), 303–312 (2015)

    Article  Google Scholar 

  3. Wang, H., Ullah, M.M., Klaser, A., Laptev, I., Schmid, C.: Evaluation of local spatio-temporal features for action recognition. In: BMVC (2009)

    Google Scholar 

  4. Uijlings, J., Duta, I.C., Sangineto, E., Sebe, N.: Video classification with densely extracted HOG/HOF/MBH features: an evaluation of the accuracy/computational efficiency trade-off. Int. J. Multimed. Info. Retr. 4, 33–44 (2014)

    Article  Google Scholar 

  5. Wells, R.O.: Differential Analysis on Complex Manifolds. Springer, New York (2008)

    Book  MATH  Google Scholar 

  6. Sat, H.: Algebraic Topology: An Intuitive Approach. American Mathematical Society, Providence (1999)

    Google Scholar 

  7. Guillemin, V., Pollack, A.: Differential Topology. Prentice-Hall, Upper Saddle River (1974). pp. 2–5

    MATH  Google Scholar 

  8. Cichocki, A., Zdunek, R., Phan, A.H., Amari, S.: Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multiway Data Analysis and Blind Source Separation. Wiley, Hoboken (2009)

    Book  Google Scholar 

  9. Lui, Y.M., Beveridge, J., Kirby, M.: Action classification on product manifolds. In: Proceedings of the IEEE Conference on CVPR, pp. 833–839 (2010)

    Google Scholar 

  10. Hotelling, H.: Relations between two sets of variates. Biometrika 28, 321–377 (1936)

    Article  MATH  Google Scholar 

  11. Knyazev, A.V., Zhu, P.: Principal Angles Between Subspaces and Their Tangents. Technical report TR2012-058, Mitsubishi Electric Research Laboratories (2012)

    Google Scholar 

  12. Lui, Y.M.: Human gesture recognition on product manifolds. J. Mach. Learn. Res. 13(1), 3297–3321 (2012)

    MathSciNet  MATH  Google Scholar 

  13. Karcher, H.: Riemannian center of mass and mollifier smoothing. Commun. Pure Appl. Math. 30(5), 509–541 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  14. Dreisigmeyer, D.W.: Direct Search Algorithms Over Riemannian Manifolds (2007). http://ddma.lanl.gov/Documents/publications/dreisigm-2007-direct.pdf

  15. Harandi, M.T., Sanderson, C., Hartley, R., Lovell, B.C.: Sparse coding and dictionary learning for symmetric positive definite matrices: a kernel approach. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012. LNCS, vol. 7573, pp. 216–229. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  16. Lui, Y.M.: Advances in matrix manifolds for computer vision. Image Vis. Comput. 30(6), 380–388 (2012)

    Article  MathSciNet  Google Scholar 

  17. Tuzel, O., Porikli, F., Meer, P.: Region covariance: a fast descriptor for detection and classification. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3952, pp. 589–600. Springer, Heidelberg (2006). doi:10.1007/11744047_45

    Chapter  Google Scholar 

  18. Pennec, X.: Intrinsic statistics on Riemannian manifolds: basic tools for geometric measurements. J. Math. Imaging Vis. 25(1), 127–154 (2006)

    Article  MathSciNet  Google Scholar 

  19. Sra, S.: Positive definite matrices and the symmetric Stein divergence. arXiv:1110.1773 (2012)

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Acknowledgement

This work has been supported by the National Centre for Research and Development (project UOD-DEM-1-183/001 “Intelligent video analysis system for behavior and event recognition in surveillance networks”).

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Correspondence to Marek Kulbacki .

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Michalczuk, A. et al. (2017). Manifold Methods for Action Recognition. In: Nguyen, N., Tojo, S., Nguyen, L., Trawiński, B. (eds) Intelligent Information and Database Systems. ACIIDS 2017. Lecture Notes in Computer Science(), vol 10192. Springer, Cham. https://doi.org/10.1007/978-3-319-54430-4_59

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  • DOI: https://doi.org/10.1007/978-3-319-54430-4_59

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  • Online ISBN: 978-3-319-54430-4

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