Abstract
High dimensional data sequences, such as video clips, can be modeled as trajectories in a high dimensional space and, and usually exhibit a low dimensional structure intrinsic to each distinct class of data sequence [1]. In this paper, we exploit a fibre bundle formalism to model various realizations of each trajectory, and characterize these high dimensional data sequences by an optimal operator subspace. Each operator is calculated as a matched filter corresponding to a standard Gaussian output with the data as input. The low dimensional structure intrinsic to the data is further explored, by minimizing the dimension of the operator space under data driven constraints. The dimension minimization problem is reformulated as a convex nuclear norm minimization problem, and an associated algorithm is proposed. Moreover, a fast method with superior performance for video based human activity classification is implemented by searching for an optimal operator space and adapted to the data. Illustrating examples demonstrating the performance of this approach are presented.
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References
Abdelkader, M.F., Abd-Almageed, W., Srivastava, A., Chellappa, R.: Silhouette-based gesture and action recognition via modeling trajectories on riemannian shape manifolds. Computer Vision and Image Understanding 115, 439–455 (2011)
Gorelick, L., Blank, M., Shechtman, E., Irani, M., Basri, R.: Actions as space-time shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence 29, 2247–2253 (2007)
Blackburn, J., Ribeiro, E.: Human Motion Recognition Using Isomap and Dynamic Time Warping. In: Elgammal, A., Rosenhahn, B., Klette, R. (eds.) Human Motion 2007. LNCS, vol. 4814, pp. 285–298. Springer, Heidelberg (2007)
Donoho, D.: Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. Academy of Sciences of the United, 1–15 (2003)
Belkin, M., Niyogi, P., Sindhwani, V.: Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples. Journal of Machine Learning Research 7, 2399–2434 (2006)
Yi, S., Krim, H., Norris, L.K.: Human Activity Modeling as Brownian Motion on Shape Manifold. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds.) SSVM 2011. LNCS, vol. 6667, pp. 628–639. Springer, Heidelberg (2012)
Cai, J.F., Candès, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. on Optimization 20, 1956–1982 (2010)
Bian, X., Krim, H.: Video-based human activitis analysis: an operator-based approach. In: 20th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision (2012)
Savvides, M., Kumar, B.V.K.V., Khosla, P.K.: Cancelable biometric filters for face recognition. In: ICPR 2004, vol. 3, pp. 922–925 (2004)
Lin, Z., Chen, M., Ma, Y.: The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices. UIUC Technical Report UILU-ENG-09-2214 (2011)
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Bian, X., Krim, H. (2013). Optimal Operator Space Pursuit: A Framework for Video Sequence Data Analysis. In: Lee, K.M., Matsushita, Y., Rehg, J.M., Hu, Z. (eds) Computer Vision – ACCV 2012. ACCV 2012. Lecture Notes in Computer Science, vol 7725. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37444-9_59
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DOI: https://doi.org/10.1007/978-3-642-37444-9_59
Publisher Name: Springer, Berlin, Heidelberg
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