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pROST: a smoothed \(\ell _p\)-norm robust online subspace tracking method for background subtraction in video

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Abstract

An increasing number of methods for background subtraction use Robust PCA to identify sparse foreground objects. While many algorithms use the \(\ell _1\)-norm as a convex relaxation of the ideal sparsifying function, we approach the problem with a smoothed \(\ell _p\)-quasi-norm and present pROST, a method for robust online subspace tracking. The algorithm is based on alternating minimization on manifolds. Implemented on a graphics processing unit, it achieves realtime performance at a resolution of \(160 \times 120\). Experimental results on a state-of-the-art benchmark for background subtraction on real-world video data indicate that the method succeeds at a broad variety of background subtraction scenarios, and it outperforms competing approaches when video quality is deteriorated by camera jitter.

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Notes

  1. http://www.changedetection.net.

  2. https://sites.google.com/site/hejunzz/grasta.

References

  1. Absil, P.A., Mahony, R., Sepulchre, R.: Optimization algorithms on matrix manifolds. Princeton University Press, Princeton (2008)

    MATH  Google Scholar 

  2. Balzano, L., Nowak, R., Recht, B.: Online identification and tracking of subspaces from highly incomplete information. In: Allerton Conference on Communication, Control, and, Computing, pp. 704–711 (2010)

  3. Boumal, N., Absil, P.A.: RTRMC: A Riemannian trust-region method for low-rank matrix completion. In: Advances in Neural Information Processing Systems, pp. 406–414 (2011)

  4. Bouwmans, T.: Subspace learning for background modeling: a survey. RPCS 2(3), 223–234 (2009)

    Article  Google Scholar 

  5. Bouwmans, T.: Recent advanced statistical background modeling for foreground detection: A systematic survey. RPCS 4(3), 147–176 (2011)

    Article  Google Scholar 

  6. Brutzer, S., Höferlin, B., Heidemann, G.: Evaluation of background subtraction techniques for video surveillance. In: Computer Vision and Pattern Recognition, pp. 1937–1944. IEEE (2011)

  7. Candès, E., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? J ACM 58(3), 1–37 (2011)

    Article  Google Scholar 

  8. Cristani, M., Farenzena, M., Bloisi, D., Murino, V.: Background subtraction for automated multisensor surveillance: a comprehensive review. EURASIP J. Adv. Signal Process 43(1–43), 24 (2010)

    Google Scholar 

  9. Edelman, A., Arias, T.A., Smith, S.T.: The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl. 20(2), 303–353 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  10. Elhabian, S.Y., El-Sayed, K.M., Ahmed, S.H.: Moving object detection in spatial domain using background removal techniques: state-of-art. RPCS 1, 32–34 (2008)

    Article  Google Scholar 

  11. Gasso, G., Rakotomamonjy, A., Canu, S.: Recovering sparse signals with a certain family of nonconvex penalties and DC programming. Trans Signal Process 57(12), 4686–4698 (2009)

    Article  MathSciNet  Google Scholar 

  12. Goyette, N., Jodoin, P., Porikli, F., Konrad, J., Ishwar, P.: Changedetection.net: a new change detection benchmark dataset. In: Computer vision and pattern recognition workshops, pp. 1–8 (2012)

  13. Guyon, C., Bouwmans, T., Zahzah, E.: Robust principal component analysis for background subtraction: systematic evaluation and comparative analysis. In: Principal component analysis, chap. 12, pp. 223–238. INTECH (2012)

  14. Hage, C., Kleinsteuber, M.: Robust PCA and subspace tracking from incomplete observations using \(\ell _0\)-surrogates. Comput Stat (2013). doi:10.1007/s00180-013-0435-4

  15. Harris, M.: Optimizing parallel reduction in CUDA. http://developer.download.nvidia.com/assets/cuda/files/reduction.pdf (2008)

  16. Hassanpour, H., Sedighi, M., Manashty, A.R.: Video frame’s background modeling: reviewing the techniques. J. Signal Inf. Process. 2(2), 72–78 (2011)

    Google Scholar 

  17. He, J., Balzano, L., Szlam, A.: Incremental gradient on the Grassmannian for online foreground and background separation in subsampled video. In: Computer vision and, pattern recognition, pp. 1568–1575 (2012)

  18. Hestenes, M.R., Stiefel, E.: Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bureau Stand. 49, 409–436 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  19. Huang, J., Huang, X., Metaxas, D.: Learning with dynamic group sparsity. In: ICCV, pp. 64–71 (2009)

  20. Keshavan, R.H., Montanari, A.: Matrix completion from noisy entries. J. Mach. Learn. Res. 11, 2057–2078 (2010)

    MATH  MathSciNet  Google Scholar 

  21. Leahy, R.M., Jeffs, B.D.: On the design of maximally sparse beamforming arrays. Antennas Propag. IEEE Trans. 39(8), 1178–1187 (1991)

    Article  Google Scholar 

  22. Li, L., Huang, W., Gu, I.Y.H., Tian, Q.: Statistical modeling of complex backgrounds for foreground object detection. Trans. Image Process. 13(11), 1459–1472 (2004)

    Article  Google Scholar 

  23. Li, Y.: On incremental and robust subspace learning. Pattern Recognit. 37, 1509–1518 (2004)

    Article  MATH  Google Scholar 

  24. Oliver, N., Rosario, B., Pentland, A.: A bayesian computer vision system for modeling human interactions. Trans. Pattern Anal. Mach. Intell. 22(8), 831–843 (2000)

    Article  Google Scholar 

  25. Pearson, K.: On lines and planes of closest fit to systems of points in space. Philos. Mag. 2(6), 559–572 (1901)

    Article  Google Scholar 

  26. Toyama, K., Krumm, J., Brumitt, B., Meyers, B.: Wallflower: principles and practice of background maintenance. Int. Conf. Comput. Vis. 1, 255–261 (1999)

    Google Scholar 

  27. Waters, A., Sankaranarayanan, A.C., Baraniuk, R.G.: SpaRCS: Recovering Low-Rank and Sparse Matrices from Compressive Measurements. In: Proceedings of Advances in Neural Information Processing Systems (2011)

  28. Xu, Z., Shi, P., Gu, I.Y.H.: An eigenbackground subtraction method using recursive error compensation. In: Zhuang, Y., Yang,S., Rui Y., He, Q (eds.) PCM, Lecture notes in computer science, vol. 4261, pp. 779–787. Springer, Heidelberg (2006)

  29. Zhou, T., Tao, D.: GoDec: Randomized low-rank & sparse matrix decomposition in noisy case. In: International Conference on Machine Learning, pp. 33–40 (2011)

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Correspondence to Clemens Hage.

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Seidel, F., Hage, C. & Kleinsteuber, M. pROST: a smoothed \(\ell _p\)-norm robust online subspace tracking method for background subtraction in video. Machine Vision and Applications 25, 1227–1240 (2014). https://doi.org/10.1007/s00138-013-0555-4

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