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Rare-Event Detection by Quasi-Wang–Landau Monte Carlo Sampling with Approximate Bayesian Computation

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Abstract

We propose a new rare-event detection method based on quasi-Wang–Landau Monte Carlo (QWLMC) sampling with approximate Bayesian computation (ABC) called QWLMC-ABC. QWLMC-ABC integrates ABC and a Halton sequence into Wang–Landau Monte Carlo (WLMC) sampling methods. The Halton sequence provides an improved proposal function and increases the accuracy of WLMC sampling, which results in QWLMC sampling. ABC approximates a likelihood function and boosts the speed of QWLMC sampling, which yields QWLMC-ABC. QWLMC-ABC is applied to estimate the rareness of events in a statistical manner. Experimental results demonstrate that our method is comparable to state-of-the-art methods. Compared with sampling-based approaches including WLMC and QWLMC sampling, QWLMC-ABC localizes rare events at a fraction of the computation time.

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References

  1. Adam, A., Rivlin, E., Shimshoni, I., Reinitz, D.: Robust real-time unusual event detection using multiple fixed-location monitors. TPAMI 30(3), 555–560 (2008)

    Article  Google Scholar 

  2. Akcay, S., Abarghouei, A.A., Breckon, T.P.: Ganomaly: Semi-supervised anomaly detection via adversarial training (2018). arXiv preprint arXiv:1805.06725

  3. Antic, B., Ommer, B.: Video parsing for abnormality detection. In: ICCV (2011)

  4. AVSS (2007). dataset: http://www.eecs.qmul.ac.uk/~andrea/avss2007_d.html

  5. Beaumont, M.A., Zhang, W., Balding, D.J.: Approximate bayesian computation in population genetics. Genetics 162, 2025–2035 (2002)

    Google Scholar 

  6. Boiman, O., Irani, M.: Detecting irregularities in images and in video. IJCV 74(1), 17–31 (2007)

    Article  Google Scholar 

  7. BOSS dataset: http://www.multitel.be/image/researchdevelopment/research-projects/boss.php

  8. Caltech256 dataset: https://authors.library.caltech.edu/7694/

  9. Cong, Y., Yuan, J., Liu, J.: Sparse reconstruction cost for abnormal event detection. In: CVPR (2011)

  10. Cuhk avenue dataset: http://www.cse.cuhk.edu.hk/leojia/projects/detectabnormal/dataset.htm

  11. Feng, Y., Yuan, Y., Lu, X.: Deep representation for abnormal event detection in crowded scenes. In: ACM MM (2016)

  12. Ghosh, S., Sudderth, E.B.: Approximate bayesian computation for distance-dependent learning. In: NIPS (2015)

  13. Giorno, A.D., Bagnell, J.A., Hebert, M.: A discriminative framework for anomaly detection in large videos. In: ECCV (2016)

  14. Gorelick, L., Blank, M., Shechtman, E., Irani, M., Basri, R.: Actions as space-time shapes. TPAMI 29(12), 2247–2253 (2007)

    Google Scholar 

  15. Haines, T., Xiang, T.: Delta-dual hierarchical dirichlet processes: A pragmatic abnormal behavior detector. In: ICCV (2011)

  16. Hamalainen, W., Nykanen, M.: Efficient discovery of statistically significant association rules. In: ICDM (2008)

  17. Hasan, M., Choi, J., Neumann, J., Roy-Chowdhury, A.K., Davis, L.S.: Learning temporal regularity in video sequences. In: CVPR (2016)

  18. Israd, M., Blake, A.: CONDENSATION–conditional density propagation for visual tracking. IJCV 29(1), 893–908 (1998)

    Google Scholar 

  19. Khan, Z., Balch, T., Dellaert, F.: Mcmc-based particle filtering for tracking a variable number of interacting targets. IEEE TPAMI 27(11), 1805–1819 (2005)

    Article  Google Scholar 

  20. Kim, J., Grauman, K.: Observe locally, infer globally: a space-time MRF for detecting abnormal activities with incremental updates. In: CVPR (2009)

  21. Kocis, L., Whiten, W.J.: Computational investigations of low-discrepancy sequences. ACM Trans. Math. Softw. 23(2), 266–294 (1997)

    Article  Google Scholar 

  22. Kokaram, A.: Practical, unified, motion and missing data treatment in degraded video. JMIV 20(1–2), 163–177 (2004)

    Article  MathSciNet  Google Scholar 

  23. Kratz, L., Nishino, K.: Anomaly detection in extremely crowded scenes using spatio-temporal motion pattern models. In: CVPR (2009)

  24. Kuettel, D., Breitenstein, M.D., Gool, L.V., Ferrari, V.: What’s going on? discovering spatio-temporal dependencies in dynamic scenes. In: CVPR (2010)

  25. Kulkarni, T.D., Yildirim, I., Kohli, P., Freiwald, W.A., Tenenbaum, J.B.: Deep generative vision as approximate bayesian computation. In: NIPS (2014)

  26. Kwon, J., Lee, K.M.: Wang-Landau Monte Carlo-based tracking methods for abrupt motions. IEEE TPAMI 35(4), 1011–1024 (2013)

    Article  MathSciNet  Google Scholar 

  27. Kwon, J., Lee, K.M.: A unified framework for event summarization and rare event detection from multiple views. IEEE TPAMI 37(9), 1737–1750 (2014)

    Article  Google Scholar 

  28. Kwon, J., Lee, K.M.: A unified framework for event summarization and rare event detection from multiple views. TPAMI 37(9), 1737–1750 (2015)

    Article  Google Scholar 

  29. Kwon, J., Dragon, R., Gool, L.V.: Joint tracking and ground plane estimation. IEEE SPL 23(11), 1514–1517 (2016)

    Google Scholar 

  30. Li, W., Mahadevan, V., Vasconcelos, N.: Anomaly detection and localization in crowded scenes. TPAMI 36(1), 18–32 (2014)

    Article  Google Scholar 

  31. Lintusaari, J., Gutmann, M.U., Dutta, R., Kaski, S., Corander, J.: Fundamentals and recent developments in approximate Bayesian computation. Syst. Biol. 66(1), 66–82 (2017)

    Google Scholar 

  32. Liu, G., Lin, Z., Yu., Y.: Robust subspace segmentation by low-rank representation. In: ICML (2010)

  33. Lu, C., Shi, J., Jia, J.: Abnormal event detection at 150 fps in matlab. In: ICCV (2013)

  34. Luo, W., Liu, W., Gao, S.: A revisit of sparse coding based anomaly detection in stacked RNN framework. In: ICCV (2017)

  35. Mahadevan, V., Li, W., Bhalodia, V., Vasconcelos, N.: Anomaly detection in crowded scenes. In: CVPR (2010)

  36. Mansinghka, V., Kulkarni, T.D., Perov, Y.N., Tenenbaum, J.: Approximate bayesian image interpretation using generative probabilistic graphics programs. NIPS (2013)

  37. Mehran, R., Oyama, A., Shah, M.: Abnormal crowd behavior detection using social force model. In: CVPR (2009)

  38. Morokoff, W.J., Caflisch, R.E.: Quasi-random sequences and their discrepancies. SIAM J. Sci. Comput. 15(6), 1251–1279 (1994)

    Article  MathSciNet  Google Scholar 

  39. Niederreiter, H.: Random Number Generation and quasi-Monte Carlo Methods. Society for Industrial and Applied Mathematics, Philadelphia (1992)

    Book  Google Scholar 

  40. Owen, A.B., Tribble, S.D.: A quasi-Monte Carlo Metropolis algorithm. PNAS 102(25), 8844–8849 (2005)

    Article  MathSciNet  Google Scholar 

  41. Parrott, D., Li, X.: Locating and tracking multiple dynamic optima by a particle swarm model using speciation. IEEE Trans. Evol. Comput. 10(4), 440–458 (2006)

    Article  Google Scholar 

  42. PETS 2006 dataset: http://www.cvg.reading.ac.uk/PETS2006/data.html

  43. PETS 2007 dataset: http://www.cvg.reading.ac.uk/PETS2007/data.html

  44. Pritchard, J.K., Seielstad, M.T., Perez-Lezaun, A., Feldman, M.W.: Population growth of human Y chromosomes: a study of Y chromosome microsatellites. Mol. Biol. Evol. 16, 1791–1798 (1999)

    Article  Google Scholar 

  45. Rahmani, M., Atia, G.: Coherence pursuit: fast, simple, and robust principal component analysis (2016). arXiv preprint arXiv:1609.04789

  46. Ravanbakhsh, M., Sangineto, E., Nabi, M., Sebe, N.: Training adversarial discriminators for cross-channel abnormal event detection in crowds (2017). arXiv preprint arXiv:1706.07680

  47. Roshtkhari, M.J., Levine, M.D.: An on-line, real-time learning method for detecting anomalies in videos using spatio-temporal compositions. CVIU 117(10), 1436–1452 (2013)

    Google Scholar 

  48. Sabokrou, M., Fathy, M., Hoseini, M., Klette, R.: Real-time anomaly detection and localization in crowded scenes. In: CVPR Workshop (2015)

  49. Sabokrou, M., Fathy, M., Hoseini, M.: Video anomaly detection and localisation based on the sparsity and reconstruction error of auto-encoder. IET Comput. Vis. 52(13), 1122–1124 (2016)

    Google Scholar 

  50. Sabokrou, M., Fayyaz, M., Fathy, M., Klette, R.: Fully convolutional neural network for fast anomaly detection in crowded scenes (2016). arXiv preprint arXiv:1609.00866

  51. Sabokrou, M., Fayyaz, M., Fathy, M., Klette, R.: Deep-cascade: Cascading 3d deep neural networks for fast anomaly detection and localization in crowded scenes. IEEE TIP 26(4), 1992–2004 (2017)

    MathSciNet  MATH  Google Scholar 

  52. Sabokrou, M., Fayyaz, M., Fathy, M., Klette, R.: Deep-cascade: Cascading 3d deep neural networks for fast anomaly detection and localization in crowded scenes. IEEE Trans. Image Process. 26(4), 1992–2004 (2017)

    Article  MathSciNet  Google Scholar 

  53. Sabokrou, M., Khalooei, M., Fathy, M., Adeli, E.: Adversarially learned one-class classifier for novelty detection. In: CVPR (2018)

  54. Sabokrou, M., Pourreza, M., Fayyaz, M., Entezari, R., Fathy, M., Gall, J., Adeli, E.: AVID: Adversarial visual irregularity detection (2018). arXiv preprint arXiv:1805.09521

  55. Saligrama, V., Chen, Z.: Video anomaly detection based on local statistical aggregates. In: CVPR (2012)

  56. Schlegl, T., Seeböck, P., Waldstein, S.M., Schmidt-Erfurth, U., Langs, G.: Unsupervised anomaly detection with generative adversarial networks to guide marker discovery (2017). arXiv preprint arXiv:1703.05921

  57. Sultani, W., Chen, C., Shah, M.: Real-world anomaly detection in surveillance videos (2018). arXiv:1801.04264

  58. Tu, Z., Zhu, S.C.: Image segmentation by data-driven markov chain monte carlo. IEEE TPAMI 24(5), 657–673 (2002)

    Article  Google Scholar 

  59. UCSD dataset: http://www.svcl.ucsd.edu/projects/anomaly/dataset.html

  60. UMN dataset: http://mha.cs.umn.edu/Movies/Crowd-Activity-All.avi

  61. Wang, F., Landau, D.: Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett 86(10), 2050–2053 (2001)

    Article  Google Scholar 

  62. Weinland, D., Boyer, E., Ronfard, R.: Action recognition from arbitrary views using 3d exemplars. In: ICCV (2007)

  63. Wu, S., Moore, B.E., Shah, M.: Chaotic invariants of lagrangian particle trajectories for anomaly detection in crowded scenes. In: CVPR (2010)

  64. Wu, S., Oreifej, O., Shah, M.: Action recognition in videos acquired by a moving camera using motion decomposition of lagrangian particle trajectories. In: ICCV (2011)

  65. Xiang, T., Gong, S.: Video behavior profiling for anomaly detection. IEEE TPAMI 30(5), 893–908 (2008)

    Article  Google Scholar 

  66. Xu, D., Yan, Y., Ricci, E., Sebe, N.: Detecting anomalous events in videos by learning deep representations of appearance and motion. CVIU 156, 117–127 (2017)

    Google Scholar 

  67. You, C., Robinson, D.P., Vidal, R.: Provable self representation based outlier detection in a union of subspaces. In: CVPR (2017)

  68. Zelnik-Manor, L., Irani, M.: Statistical analysis of dynamic actions. IEEE TPAMI 28(9), 1530–1530 (2006)

    Article  Google Scholar 

  69. Zhang, X., Hu, W., Maybank, S., Li, X., Zhu, M.: Sequential particle swarm optimization for visual tracking. In: CVPR (2008)

  70. Zhao, B., Fei-Fei, L., Xing, E.P.: Online detection of unusual events in videos via dynamic sparse coding. In: CVPR (2011)

  71. Zhou, X., Lu, Y., Lu, J., Zhou, J.: Abrupt motion tracking via intensively adaptive Markov-chain Monte Carlo sampling. IEEE TPAMI 21(2), 789–801 (2012)

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (No. 2017R1C1B1003354).

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    Junseok Kwon

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Kwon, J. Rare-Event Detection by Quasi-Wang–Landau Monte Carlo Sampling with Approximate Bayesian Computation. J Math Imaging Vis 61, 1258–1275 (2019). https://doi.org/10.1007/s10851-019-00906-y

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